statistica - teste grila

141
TESTUL 1 *) 1) 1XFRQVWLWXLHRFRPSRQHQW DDYX LHLQD LRQDOH a) fondul funciar; b) mijloacele fixe; c) 9HQLWXO1D LRQDO3URGXVXO,QWHUQ%UXW d) resursele minerale atrase în circuitul economic; e) stocurile de materiale. 2) 0XO LPHDYDORULORUFRHILFLHQWXOXLGHFRUHOD LHFDOFXODWvQFD]XOGHSHQGHQ HORUOLQLDUHGLUHFWHHVWH a) [-1, 1] ; b) [-1, 0) ; c) PXO LPHDQXPHUHORUUHDOH d) (0, 1] ; e) [-3, 3] . 3) Într-R SRSXOD LH VWDWLVWLF VWUXFWXUDW SH JUXSH FODVH UHODWLY RPRJHQH VH FDOFXOHD] GLVSHUVLD general ( σ 2 ); media dispersiilor ( σ 2 œL GLVSHUVLD GLQWUH JUXSH δ 2 (VWH DGHY UDW vQ RULFH VLWXD LHUHOD LD a) δ σ 2 2 > ; b) δ σ 2 2 ; c) δ σ σ 2 2 2 = + ; d) δ 2 0 < ; e) comparabilitatea dintre δ 2 œL σ 2 nu are sens. 4) În cazul tabelelor Input - Output, ramurile se delimiteaz dup : a) FULWHULXODFWLYLW LLSUHSRQGHUHQWH b) FULWHULXOIXQF LRQDO c) XQLWDWHDLQVWLWX LRQDO d) VHFWRUXOLQVWLWX LRQDO e) GXS IOXxurile monetare din economie. 5) 5DWD œRPDMXOXL vQ VHQVXO %LURXOXL ,QWHUQD LRQDO DO 0XQFLL VH FDOFXOHD] SURFHQWXDO UDSRUWkQG 1XP UXOGHœRPHUL la: a) 3RSXOD LDFXUHQWDFWLY b) 3RSXOD LDRFXSDW c) 5HVXUVHOHGHPXQF d) 5H]HUYHOHGHPXQF e) 3RSXOD LDvQYkUVW GHPXQF *) 6XELHFWOD H[DPHQXO GHOLFHQ )DFXOWDWHD&LEHUQHWLF 6WDWLVWLF œL,QIRUPDWLF (FRQRPLF VHVLXQHDLXOLH 1997

Upload: andreeaolteanu

Post on 17-Nov-2014

746 views

Category:

Documents


3 download

TRANSCRIPT

Page 1: STATISTICA - TESTE GRILA

TESTUL 1 *)

1) 1X�FRQVWLWXLH�R�FRPSRQHQW �D�DYX LHL�QD LRQDOH�

a) fondul funciar; b) mijloacele fixe; c) 9HQLWXO�1D LRQDO��3URGXVXO�,QWHUQ�%UXW�� d) resursele minerale atrase în circuitul economic; e) stocurile de materiale.

2) 0XO LPHD�YDORULORU�FRHILFLHQWXOXL�GH�FRUHOD LH�FDOFXODW�vQ�FD]XO�GHSHQGHQ HORU�OLQLDUH�GLUHFWH�HVWH�

a) [-1, 1] ; b) [-1, 0) ; c) PXO LPHD�QXPHUHORU�UHDOH� d) (0, 1] ; e) [-3, 3] .

3) Într-R�SRSXOD LH� VWDWLVWLF � VWUXFWXUDW �SH�JUXSH� �FODVH�� UHODWLY�RPRJHQH�� VH�FDOFXOHD] ��GLVSHUVLD�

general (σ 2 ); media dispersiilor (σ 2 ��úL�GLVSHUVLD�GLQWUH�JUXSH��δ 2 ���(VWH�DGHY UDW � vQ�RULFH�VLWXD LH�UHOD LD�

a) δ σ2 2> ;

b) δ σ2 2≤ ;

c) δ σ σ2 2 2= + ;

d) δ 2 0< ;

e) comparabilitatea dintre δ 2 úL�σ 2 nu are sens. 4) În cazul tabelelor Input - Output, ramurile se delimiteaz dup :

a) FULWHULXO�DFWLYLW LL�SUHSRQGHUHQWH� b) FULWHULXO�IXQF LRQDO� c) XQLWDWHD�LQVWLWX LRQDO � d) VHFWRUXO�LQVWLWX LRQDO� e) GXS �IOXxurile monetare din economie.

5) 5DWD� úRPDMXOXL� vQ� VHQVXO� %LURXOXL� ,QWHUQD LRQDO� DO�0XQFLL� VH� FDOFXOHD] � SURFHQWXDO�� UDSRUWkQG�

1XP UXO�GH�úRPHUL la:

a) 3RSXOD LD�FXUHQW�DFWLY � b) 3RSXOD LD�RFXSDW � c) 5HVXUVHOH�GH�PXQF � d) 5H]HUYHOH�GH�PXQF � e) 3RSXOD LD�vQ�YkUVW �GH�PXQF �

*)�6XELHFW�OD�H[DPHQXO�GH�OLFHQ ��)DFXOWDWHD�&LEHUQHWLF ��6WDWLVWLF �úL�,QIRUPDWLF �(FRQRPLF ��VHVLXQHD�LXOLH�

1997

Page 2: STATISTICA - TESTE GRILA

6) Fenomenele social-HFRQRPLFH�GH�PDV �VWXGLDWH�GH�VWDWLVWLF �QX�VH�FDUDFWHUL]HD] �

a) SULQ�YDULDELOLWDWH�vQ�WLPS�úL�vQ�VSD LX� b) printr-R� OHJH� GH� DSDUL LH� FDUH� VH� PDQLIHVW � FD� WHQGLQ � FH� QX� SRDWH� IL� FXQRVFXW � úL�

YHULILFDW �GHFkW�OD�QLYHOXO�DQVDPEOXOXL�úi nu în fiecare caz în parte; c) printr-R�OHJH�GH�DSDUL LH�FDUH�VH�PDQLIHVW �FD�WHQGLQ �FH�SRDWH�IL�FXQRVFXW �úL�YHULILFDW �vQ�

fiecare caz în parte; d) SULQ�IRUPH�LQGLYLGXDOH�GH�DSDUL LH�DVHP Q WRDUH� e) SULQ� IDSWXO� F � HOH� VXQW� VSHFLILFH� OHJLORU� VWDWLVWLFH� - legi FDUH� VH�PDQLIHVW � VXE� IRUP �GH�

WHQGLQ � ID � GH� FDUH� DEDWHULOH� vQWkPSO WRDUH� vQWU-XQ� VHQV� VDX� DOWXO� VH� FRPSHQVHD] �reciproc.

7) 5HSUH]HQWDWLYLWDWHD�HVWH�XUP ULW �vQ�PRG�GHRVHELW�vQ�FD]XO�FXOHJHULL�GDWHORU�SULQ�

a) UHFHQV PkQW� b) sondaje statistice; c) anchete statistice; d) rapoarte statistice; e) monografii statistice;

8) Deflatorul Produsului Intern Brut este:

a) LQGLFHOH�GH�SUH XUL�GH�WLS�/DVSH\UHV� b) indicele volumului fizic de tip Paasche; c) LQGLFHOH�GH�SUH XUL�GH�WLS�)LVKHU� d) LQGLFHOH�GH�SUH XUL�GH�WLS�3DDVFKH� e) indice al valorii.

9) ([SUHVLD�VLQWHWL] ULL�YDORULORU�LQGLYLGXDOH�DOH�XQHL�YDULDELOH�VWDWLVWLFH�D�WRW�FHHD�FH�H�HVHQ LDO��WLSLF�

úL�RELHFWLY�vQWU-XQ�VLQJXU�QLYHO�UHSUH]HQWDWLY�HVWH�GDW �GH��

a) medie; b) PHGLDQ � c) YDORDUH�PRGDO � d) FRHILFLHQWXO�GH�FRUHOD LH� e) coeficientul de varia LH�

10) &DUH�LQGLFDWRU�VWDWLVWLF�QX�DUH�VHQV�V �VH�FDOFXOH]H�SHQWUX�DQDOL]D�VHULLORU�GH�UHSDUWL LH�IRUPDWH�

GXS �R�YDULDELO �DOWHUQDWLY " a) IUHFYHQ HOH�UHODWLYH� b) media; c) dispersia; d) coeficientul de asimetrie.

11) Într-R� SRSXOD LH� VWDWLVWLF � V-au cules date despre doX � YDULDELOH� QXPHULFH� GLVWLQFWH�� 6HULLOH�

IRUPDWH�vQ�XUPD�VLVWHPDWL] ULL�VXQW��

{ } { }xi i= =1 7

2 2 2 10181818,

; ; ; ; ; ; �úL�{ } { }yi i = =1 7

9 9 9 10 111111,

; ; ; ; ; ; .

2EVHUYkQG�YDULDQWHOH�FHORU�GRX �VHULL�VH�FRQVWDW �F �

a) VHULD�IRUPDW �GXS �<�HVWH�PDL�RPRJHQ �GHFkW�FHD�IRUPDW �GXS �;�

Page 3: STATISTICA - TESTE GRILA

b) serLD�IRUPDW �GXS �;�HVWH�PDL�RPRJHQ �GHFkW�FHD�IRUPDW �GXS �<� c) FHOH�GRX �VHULL�SUH]LQW �DFHHDúL�RPRJHQLWDWH��GHRDUHFH�DX�DFHHDúL�PHGLH�úL�PHGLDQ �HJDOH�

cu 10; d) QX�DUH�VHQV�FRPSDUDELOLWDWHD�RPRJHQLW LL�GLQ�FHOH�GRX �VHULL��GHRDUHFH�VXQW�IRUPDWH�GXS �

variabile distincte; e) VHULD� IRUPDW �GXS �;�HVWH�PDL�RPRJHQ �GHRDUHFH�DEDWHULOH� LQGLYLGXDOH�ID �GH�YDORDUHD�

PHGLDQ �VXQW�PDL�PDUL�

12) Un circuit economic este considerat circuit închis pentru sectorul A când:

a) QX�H[LVW �LQWU UL�vQ�$� b) QX�H[LVW �LHúLUL�GLQ�$� c) QX�H[LVW �QLFL�LQWU UL�úL�QLFL�LHúLUL�SHQWUX�VHFWRUXO�$� d) VXPD�IOX[XULORU�GH�LQWUDUH�HVWH�HJDO �FX�VXPD�IOX[XULORU�GH�LHúLUH� e) fluxurile monetare sunt identice cu fluxurile de bunuri.

13) ÌQ�XUPD�REVHUY ULL�XQHL�YDULDELOH�QXPHULFH�;��vQWU-R�SRSXOD LH�VWDWLVWLF �V-au înregistrat variantele: x1,

x2, …, xn��0HGLD�DULWPHWLF �D�DFHVWRUD� x HVWH�FDOFXODW �vQWU-R�SULP �HWDS �GXS �UHOD LD�1

1nxi

i

n

=∑ (1). În

SURFHVXO�SUHOXFU ULL�YDULDQWHOH�FXOHVH�VXQW�JUXSDWH�vQ�³U´�LQWHUYDOH��RE LQkQGX-se o serie�GH�UHSDUWL LH�GH�

IUHFYHQ H��3H�ED]D�VHULHL�IRUPDWH�V-D�UHFDOFXODW�QLYHOXO�PHGLX��XWLOL]kQG�UHOD LD�1

1

1nx n

ii

r i ii

r

=

=∑∑

�����������5H]XOWDWXO�XWLOL] ULL�FHORU�GRX �UHOD LL�HVWH�LGHQWLF�

a) vQ�RULFH�VLWXD LH� b) QLFLRGDW � c) DWXQFL�FkQG�SHQWUX�DSOLFDUHD�UHOD iei (2) s-au luat în considerare mijloacele intervalelor; d) DWXQFL�FkQG�LQWHUYDOHOH�GH�JUXSDUH�SUH]LQW �IUHFYHQ H�HJDOH� e) DWXQFL� FkQG� IUHFYHQ HOH� VXQW� QRUPDO� UHSDUWL]DWH� vQ� ILHFDUH� LQWHUYDO�� FkQG� IUHFYHQ HOH�

LQWHUYDOHORU� VXQW� HJDOH� vQWUH� HOH� úL� FkQG� vQ� UHOD La (2) se iau în considerare centrele intervalelor.

14) 6ROGXO�FRQWXOXL���³0RGLILFDUHD�SDWULPRQLXOXL´�UHSUH]LQW �

a) economiile nete; b) VROGXO�ILQDQ ULL� c) amortizarea; d) LQYHVWL LLOH�EUXWH� e) venitul disponibil

15) $PSOLWXGLQHD�LQWHUFXDUWLOLF �vQWU-R�UHSDUWL LH�QRUPDO �FRQ LQH�

a) ����GLQ�QXP UXO�REVHUYD LLORU� b) ����GLQ�QXP UXO�REVHUYD LLORU� c) ����GLQ�QXP UXO�REVHUYD LLORU� d) WRDWH�REVHUYD LLOH� e) QXPDL�YDULDQWHOH�H[WUHPH��DO�F URU�QXP U�HVWH�PDL�PDUH�GHFkW�����GLQ�PDVD�REVHUYD LLORU�

16) În cadrul conturilor macroeconomice, trecereD�GH�OD�FRQFHSWXO�³LQWHUQ´�OD�FRQFHSWXO�³QD LRQDO´�

se realizeaz în cadrul contului:

Page 4: STATISTICA - TESTE GRILA

a) contul 2 - “Crearea veniturilor”; b) contul 1 -�³3URGXF LH´� c) contul 3 -�³5HSDUWL LD�YHQLWXULORU´� d) contul 4 - “Redistribuirea veniturilor”; e) vQ�QLFL�XQXO�GLQ�FRQWXULOH�PHQ LRQate.

17) Într-R� SRSXOD LH� VWDWLVWLF � VH� XUP UHVF� YDULDELOHOH� ;�� <� úL� =�� vQWUH� FDUH� H[LVW � UHOD LD� < ;=��

0HGLD�DULWPHWLF �D�YDULDELOHL�<�HVWH�HJDO �FX�SURGXVXO�PHGLLORU�YDULDELOHORU�;�úL�=��

a) vQ�RULFH�VLWXD LH� b) FkQG�vQWUH�;�úL�=�H[LVW �R�GHSHQGHQ �OLQLDU �GH�forma Z X= +α β ;

c) FkQG�vQWUH�;�úL�=�H[LVW �R�GHSHQGHQ �OLQLDU �GH�IRUPD� X Z= +α β ;

d) FkQG�FRYDULDQ D�GLQWUH�;�úL�=�HVWH�QXO � e) FkQG�VHULLOH�IRUPDWH�GXS �;��<��=�VXQW�GLVWULEX LL�GH�IUHFYHQ H�UHODWLYH�

18) ,QGLFDWRUXO�³3RSXOD LD�FXUHQW�DFWLY ´�QX�FXSULQGH�

a) VDODULD LL�SUH]HQ L�OD�OXFUX� b) VDODULD LL�DEVHQ L�WHPSRUDU�GH�OD�OXFUX� c) úRPHULL� d) patronii; e) HOHYLL�úL�VWXGHQ LL�GH�OD�FXUVXULOH�GH�]L�

19) ÌQ�XWLOL]DUHD�PHWRGHL�UHVWXOXL�QHGHVFRPSXV�SHQWUX�P VXUDUHD� LQIOXHQ HORU� L]RODWH�DOH�IDFWRULORU�

unui fenomen complex sunt luate în considerare:

a) ponderile perioadei curente ale factorului calitativ; b) SRQGHULOH�GLQ�SHULRDGD�GH�ED] �DOH�IDFWRUXOXL�FDQWLWDWLY� c) SRQGHULOH�GLQ�SHULRDGD�GH�ED] �DOH�IDFWRUXOXL�FDOLWDWLY� d) SRQGHULOH�GLQ�SHULRDGD�FXUHQW �DOH�IDFWRUului calitativ; e) SRQGHULOH�GLQ�SHULRDGD�GH�ED] ��LQGLIHUHQW�GH�QDWXUD�FDQWLWDWLY �VDX�FDOLWDWLY �D�IDFWRUXOXL�

izolat. 20) Într-R� VHULH� GH� YDORUL� LQGLYLGXDOH� DOH� XQHL� YDULDELOH� QXPHULFH�� REVHUYDW � vQWU-R� SRSXOD LH�

VWDWLVWLF ��YDORDUHD�PRGDO �HVWH�

a) varianta pozLWLY �FHD�PDL�PDUH� b) YDULDQWD�QHJDWLY �GDU�PD[LP �vQ�YDORDUH�DEVROXW � c) YDULDQWD��SR]LWLY �VDX�QHJDWLY ��FX�FHD�PDL�PDUH�IUHFYHQ �GH�DSDUL LH� d) YDULDQWD�FDUH�PLQLPL]HD] �GLVSHUVLD� e) YDULDQWD�FDUH�vQUHJLVWUHD] �FHD�PDL�PDUH�DEDWHUH�DEVROXW �ID �GH�PHGLH�

Page 5: STATISTICA - TESTE GRILA

21) Se cunosc datele:

INDICATORII 3HU��ED] ���� 3HU��FXUHQW ���� - Salariul nominal (mii lei)

600 900

- Structura cheltuielilor familiilor (%):

-�P UIXUL�DOLPHQWDUH 60 62 -�P UIXUL�nealimentare

25 20

- servicii 15 18 - Modificarea SUH XULORU�vQ���������

ÌQ�SHULRDGD�FXUHQW �ID �GH� SHULRDGD� GH� ED] �� VDODULXO�real: �����D��FUHúWH�FX���������� b) scade cu 18,6 %; �����F��FUHúWH�FX�������� �����G��FUHúWH de 18,6 ori; �����H�� FUHúWH� FX� ������ PLL�

lei.

-�P UIXUL�DOLPHQWDUH 0 +25 -�P UIXUL�nealimentare

0 +40

- servicii 0 +10

22) &DUH�GLQ�XUP WRDUHOH�UHOD LL�H[SULP �³)RUPDUHD�EUXW �D�FDSLWDOXOXL´�

a) ,QYHVWL LL�QHWH�GH�FDSLWDO�IL[�SOXV�DPRUWL]DUHD� b) ,QYHVWL LL�EUXWH�GH�FDSLWDO�IL[�SOXV�SURILW�SOXV�PRGLILFDUHD�VWRFXULORU� c) )RUPDUHD�QHW �D�FDSLWDOXOXi fix plus modificarea stocurilor; d) )RUPDUHD�EUXW �D�FDSLWDOXOXL�IL[�SOXV�PRGLILFDUHD�VWRFXULORU� e) )RUPDUHD�EUXW �D�FDSLWDOXOXL�IL[��SOXV�DPRUWL]DUHD��SOXV�PRGLILFDUHD�VWRFXULORU�

23) /D� RSW� PXQFLWRUL� FDUH� HIHFWXHD] � DFHOHDúL� RSHUD LL� vQ� FDGUXO� XQXL� VFKLPE� V-au observat variabilele timp nelucrat�úL�QXP UXO�GH�RSHUD LL��'DWHOH�VXQW�XUP WRDUHOH�

Nr. curent 1 2 3 4 5 6 7 8 Timp nelucrat (u.m.) 7 1 2 5 8 6 3 4 1U��RSHUD LL 4 10 9 6 4 5 9 8

7HQGLQ D�OHJ WXULL�GLQWUH�YDULDELOH�HVWH�H[SULPDW �SULQ�IXQF LD�

a) ix xYi

96,02,11 −= ;

b) ix xYi

96,02,11 += ;

c) ix xYi

96,0−= ;

d) 204,096,02,11 iix xxYi

++= ;

e) ix xYi

96,0= .

24) ÌQ�6�&�1��FKHOWXLHOLOH�SHQWUX�vQO WXUDUHD�GDXQHORU�DGXVH�PHGLXOXL�VXQW�FRQVLGHUDWH�

a) &RVW�GH�SURGXF LH� b) ,QYHVWL LL�QHWH� c) ,QYHVWL Li brute; d) Venituri ale consumatorilor; e) Venituri ale statului.

25) 6H�FXQRVF�GDWHOH��FUHúWHUHD�SURGXFWLYLW LL�PHGLL�������LQGLFHOH�SURGXFWLYLW LL�PHGLL�SH�VHDPD�

SURGXFWLYLW LL�LQGLYLGXDOH�������,QGLFHOH�LQIOXHQ HL�VWUXFWXULL�DVXSUD�SURGXFWLYLW LL�PHGLL�HVWH:

Page 6: STATISTICA - TESTE GRILA

a) 100%; b) 91,7%; c) 132%; d) 110%; e) 85%;

26) ÌQ�DFWLYLWDWHD�GH�VWDWLVWLF �DQDOL]D�GLVSHUVLRQDO �QX�VH�XWLOL]HD] �SHQWUX��

a) YHULILFDUHD�QRUPDOLW LL�UHSDUWL LLORU� b) HYLGHQ LHUHD� P VXULL� vQ� FDUH� XQXO� VDX� PDL� PXO L� IDFWRUL� �VDX� R� FRPELQD LH� D� DFHVWRUD��

LQIOXHQ HD] �vQ�PRG�HVHQ LDO�YDULD LD�XQHL�YDULDELOH�UH]XOWDWLYH� c) DQDOL]D�P VXULL�vQ�FDUH�YDORULOH�UHDOH�DOH�XQHL�FDUDFWHULVWLFL�VH�DEDW�GH�OD�YDORULOH�WHRUHWLFH��

FDOFXODWH�GH�UHJXO �VXE�IRUP �GH�P ULPL�PHGLL�VDX�HFXD LL�GH�UHJUHVLH� d) DQDOL]D�P VXULL�vQ�FDUH�YDULD LLOH�XQHL�variabile rezultative sunt sau nu sunt dependente de

factorul de grupare; e) YHULILFDUHD�YDOLGLW LL�PRGHOHORU�GH�UHJUHVLH�VLPSO �úL�PXOWLSO �

27) 'LVWULEX LD�D�����GH�IDPLOLL�GXS �QXP UXO�GH�FRSLL�VH�SUH]LQW �DVWIHO��GDWH�FRQYHQ LRQDOH��

Nr. copii 0 1 2 3 4 5 Total Nr. familii 20 65 70 30 10 5 200

9DORDUHD�PHGLDQ �vQ�VHULD�SUH]HQWDW �HVWH�

a) 1 copil; b) 2 copii; c) 70 familii; d) 3 copii; e) 5 copii;

28) 'DF � VWUXFWXUD� SH� UDPXUL� D� 3URGXVXOXL� ,QWHUQ� %UXW� VH� PRGLILF � vQ� IDYRDUHD� UDPXULORU� FX�“necesarul de mijloace fixe pentru� RE LQHUHD� XQHL� XQLW L� GH� SURGXF LH´�PDL�PLF� GHFkW� QLYHOXO�mediu al acestui indicator, atunci, ca urmare a modific ULL�IDFWRUXOXL�VWUXFWXUDO��HILFLHQ D�XWLOL] rii PLMORDFHORU�IL[H�OD�QLYHOXO�HFRQRPLHL�QD LRQDOH�

a) FUHúWH� b) scade; c) U PkQH�QHPRGLILFDW � d) nu se SRDWH�SUHFL]D�VHQVXO�PRGLILF ULL� e) SRDWH�V �VFDG �

29) 2� VRFLHWDWH� FRPHUFLDO � D� vQUHJLVWUDW� OD� FLIUD� GH� DIDFHUL� vQ� SHULRDGD� 6HSW�� µ� ��� - Dec. ‘ 96 o

FUHúWHUH�PHGLH�OXQDU �FX������ÌQ�SHULRDGD�'HF��µ����-�0DL�µ����DFHODúL�LQGLFDWRU�V-a modificat în PHGLH�SH�OXQ de 1,17 ori. În perioada Sept. ‘ 96 - Mai ‘ 97 cifra medie de afaceri a crescut în PHGLH�GH�OD�R�OXQ �OD�DOWD�FX�

a) 13,5% ; b) 2,98% ; c) 3,2% ; d) 113,4% ; e) 27%.

30) 7UHL�DQJDMD L�GH�DFHHDúL�SURIHVLH�úL�FDOLILFDUH�SHQWUX�HIHFWXDUHD�XQHL�RSHUD LL� LGHQWLFH�FRQVXP �

timpiL��vQ�PLQXWH��XUP WRUL��������������7LPSXO�PHGLX�FRQVXPDW�HVWH�

a) 21,7 min./pers. ;

Page 7: STATISTICA - TESTE GRILA

b) 20 min./pers. ; c) 22,5 min./pers. ; d) 18,5 min./pers. ; e) 19 min./pers.

31) &XQRDúWHP� GDWHOH�� 3URGXVXO� JOREDO� EUXW� �������� X�P�� SRQGHUHD� FRQVXPXOXL� LQWHUPHGLDU� vQ�produsul global bruW������FRQVXPXO�SULYDW� ���FRQVXPXO�SXEOLF���IRUPDUHD�EUXW �D�FDSLWDOXOXL� �½ consumul privat=10.000 u.m. În aceste condi LL�

a) Exportul = Importul; b) Exportul > Importul; c) PIB > 100.000 u.m.; d) PIN > 80.000 u.m.; e) Exportul < Importul.

32) În perioada T0 - T1 Produsul Intern Brut a crescut cu 20%, mijloacele fixe cu 30%, iar ponderea PLMORDFHORU� IL[H� DFWLYH� vQ�PLMORDFHOH� IL[H� VFDGH� GH� OD� ���� OD� ����� (ILFLHQ D�PLMORDFHORU� IL[H�active:

a) scade cu 105,4% ; b) scade cu 92,3% ; c) FUHúWH�FX������� d) FUHúWH�FX�������� e) scade cu 7,7%.

33) Într-R�SRSXOD LH�VWDWLVWLF �GH�����XQLW L�FRPHUFLDOH�V-DX�REVHUYDW�YDULDELOHOH��YDORDUHD�DG XJDW �úL�YROXPXO�PLMORDFHORU�IL[H�SHQWUX�FDUH�V-DX�GHWHUPLQDW�GLVSHUVLLOH�������úL�UHVSHFWLY���������6H�FXQRDúWH��GH�DVHPHQHD��F �WHQGLQ D�OHJ WXULL�HVWH�H[SULPDWD�SULQ�IXQF LD� ix xY

i44,042,119 += .

0 ULPHD�FRHILFLHQWXOXL�GH�FRUHOD LD�OLQLDU �HVWH�

a) 0,72 ; b) -0,75 ; c) 0,27 ; d) 0,95 ; e) 0,44 ;

34) 'HVSUH�HYROX LD�FLIUHL�GH�DIDFHUL�D�XQHL�VRFLHW L�FRPHUFLDOH�VH�FXQRVF�GDWHOH�

ANI 1993 1994 1995 1996 ��PRGLILF ULL�UHODWLve a cifrei GH� DIDFHUL� ID � GH� DQXO�precedent

+3 +4 +2 +4

ùWLLQG� F � FLIUD� GH� DIDFHUL� GLQ� ����� D� IRVW� GH� ��� POG�� OHL�� PRGLILFDUHD� PHGLH� DQXDO � DEVROXW � vQ�perioada 1992 - 1996 a fost de:

a) 1,2 mld. lei/an; b) 1,2 %/an; c) 2,5 mld. lei/an; d) 210 %/an; e) 3 mld. lei/an;

35) 7HQGLQ D�OHJ WXULL�GLQWUH�GRX �YDULDELOH�VH�H[SULP �SULQ�IXQF LD�Y a bx cxx = + + 2 . Intensitatea

OHJ WXULL�GLQWUH�FHOH�GRX �YDULDELOH�VH�FDUDFWHUL]HD] �SULQ�

a) FRHILFLHQWXO�GH�FRUHOD LH�OLQLDU � b) coeficientul lui Spearman;

Page 8: STATISTICA - TESTE GRILA

c) coeficientul lui Kendall; d) coeficientul lui Bowley; e) UDSRUWXO�GH�FRUHOD LH�

36) 5H]XOWDWHOH� H[DPLQ ULL� XQHL� VHPLJUXSH� OD� SUREHOH� WHRUHWLFH� úL� SUDFWLFH� DOH� XQHL� GLVFLSOLQH� GH�VSHFLDOLWDWH�VXQW�XUP WRDUHOH�

Studentul A B C D E F G H I J TEORIE 8 3 9 2 7 10 4 6 1 5

35$&7,& 9 5 10 1 8 7 3 4 2 6 'HSHQGHQ D� GLQWUH� YDORULOH� FHORU� GRX � YDULDELOH� VH� P VRDU � FX� DMXWRUXO� FRHILFLHQWXOXL� GH�FRUHOD LH�D�UDQJXULORU��DO�OXL�6SHDUPDQ��D�F UXL�P ULPH�HVWH�

a) 0,855; b) -0,855; c) 1,00; d) -1,00; e) 0,225;

37) 6H�FXQRVF�GDWHOH��3URGXVXO�1D LRQDO�%UXW�OD�SUH XULOH�SLH HL�����X�P���DORFD LD�SHQWUX�FRQVXPXO�GH�FDSLWDO�IL[�����X�P��úL�YHQLWXO�QD LRQDO�����X�P��0 ULPHD�,PSR]LWHORU�,QGLUHFWH�1HWH�HVWH�

a) 300 u.m.; b) 400 u.m.; c) 200 u.m.; d) 700u.m.; e) 500 u.m.

38) 3HQWUX�RE LQHUHD�9HQLWXOXL�SHUVRQDO�DO�PHQDMHORU�GLQ�3URGXVXO�1D LRQDO�1HW�OD�SUH XULOH�SLH HL�QX�se scad:

a) &RQWULEX LLOH�OD�$VLJXU ULOH�6RFLDOH� b) Impozitele Indirecte Nete; c) $MXWRDUHOH�GH�úRPDM� d) 3URILWXO�QHGLVWULEXLW�DO�VRFLHW LORU� e) ,PSR]LWXO�SH�YHQLWXO��SURILWXO��VRFLHW LORU��ILUPHORU��

39) 6H�FXQRVF�XUP WRDUHOH�GDWH� Departamente Structura cifrei de afaceri (%)

Procentul

programat (al sarcinii de plan) al

cifrei de afaceri (%)

Procentul îndeplinirii

programului la cifra de afaceri

(%)

Perioada de ED]

Perioada FXUHQW

A 105 110 40 35 B 115 118 60 65

&DUH�LQIRUPD LH�VLQWHWLF �GLQ�FHOH�SUH]HQWDWH�PDL�MRV�HVWH�IDOV " a) Procentul mediu al îndeplinirii programului la cifra de afaceri a fost de 115,1%; b) Procentul mediu programat (al sarcinii de plan) al cifrei de afaceri a fost de 111%; c) Pe ansamblu cifra de afaceri a crescut în� SHULRDGD�FXUHQW � ID �GH�SHULRDGD�GH�ED] �FX�

27,8%; d) 3H� DQVDPEOX� FLIUD� GH� DIDFHUL� UHDOL]DW � vQ� SHULRDGD� FXUHQW � D� IRVW� PDL� PDUH� GHFkW� FHD�

SURJUDPDW �FX������� e) ,QGLFHOH�GH�GLQDPLF �SH�DQVDPEOXO�GHSDUWDPHQWHORU�D�IRVW�GH������

Page 9: STATISTICA - TESTE GRILA

40) /D�R�VRFLHWDWH�FRPHUFLDO ��GLQ vânzarea unui produs s-a realizat în luna mai 1997 o încasare de ��PLOLRDQH� OHL��&D�XUPDUH� D�PDMRU ULL� SUH XOXL� ID � GH�PDL� ������ vQFDV ULOH� OXQLL�PDL� ����� DX�FUHVFXW�FX���������OHL��&DUH�DU�IL�IRVW�vQFDV ULOH�OXQLL�PDL������GDF �SUH XO�QX�V-ar fi modificat?

a) 4,5 mil. lei; b) 3,5 mil. lei; c) 4 mil. lei; d) 8 mil. lei; e) 5 mil. lei.

Page 10: STATISTICA - TESTE GRILA

TESTUL 2 *)

1) Pe baza unei serii cronologice din perioada 1987-������ IRUPDW � GLQ� WHUPHQL� FRQVHFXWLYL�� V-a

DMXQV� OD� FRQFOX]LD� F � WHQGLQ D� GH� HYROX LH� D� XQHL� YDULDELOH� HVWH� H[SULPDW � SULQ� IXQF LD�

Y tt = +400 60 �vQ�FRQGL LLOH� vQ�FDUH� t =∑ 0 ). Valorile estimate ale variabilei analizate pentru

�����������úL�������vQ�DFHDVW �RUGLQH��VXQW�

a) 1300; 1480; 1600; b) 1120; 1180; 1240; c) 340; 280; 220; d) 460; 520; 580; e) 760; 820; 880.

2) 3HQWUX� GHVFRPSXQHUHD� XQXL� IHQRPHQ� FRPSOH[� SH� IDFWRUL� GH� LQIOXHQ � FX� DMXWRUXO� LQGLFLORU�� VH�

SRDWH�DSHOD� OD�PHWRGD�VXEVWLWX LHL� vQ� ODQ �VDX� OD�PHWRGD� UHVWXOXL�QHGHVFRPSXV��0HWRGD� UHVWXOXL�QHGHVFRPSXV��VSUH�GHRVHELUH�GH�PHWRGD�VXEVWLWX LHL�vQ�ODQ �

a) exagerHD] �LQIOXHQ D�IDFWRUXOXL�FDOLWDWLY� b) H[DJHUHD] �LQIOXHQ D�IDFWRUXOXL�FDQWLWDWLY� c) HVWH�PDL�FRUHFW �GHRDUHFH�QX� LQH�VHDPD�GH�QDWXUD�FDOLWDWLY �VDX�FDQWLWDWLY �D�IDFWRUXOXL�

izolat; d) HVWH�PDL�FRUHFW �GHRDUHFH�L]ROHD] �QXPDL�IDFWRUXO�FDOLWDWLY�OD�QLYHOXO�SHULRDGHL�GH�ED] � e) HVWH�PDL� FRUHFW � GHRDUHFH� HD� RSHUHD] � DWkW� FX�PRGLILF UL� DEVROXWH� FkW� úL� FX�PRGLILF UL�

relative.

3) 5HSUH]HQWDWLYLWDWHD�PHGLHL��FDOFXODW �SHQWUX�XQ�úLU�GH�YDORUL�LQGLYLGXDOH�HVWH�DVLJXUDW �

a) GDF � vQ� GHWHUPLQDUHD�PHGLHL� VH� LDX� vQ� FRQVLGHUDUH� IUHFYHQ HOH� DEVROXWH� GH� DSDUL LH� DOH�valorilor individuale;

b) GDF �YDORULOH�LQGLYLGXDOH�GLQ�FDUH�VH�FDOFXOHD] �PHGLD�VXQW�RPRJHQH� c) GDF �VH�XWLOL]HD] �PHGLD�DULWPHWLF � d) GDF �úLUXO�GH�YDORUL�LQGLYLGXDOH�HVWH�VWUXFWXUDW�SH�LQWHUYDOH�HJDOH� e) GDF �VXPD�DOJHEULF �D�DEDWHULORU�LQGLYLGXDOH�GH�OD�PHGLH�HVWH�QXO �

4) 6H�FXQRVF�GDWHOH��31%� OD�SUH XO�SLH HL������X�P��� DORFD LD�SHQWUX�FRQVXPXO�GH�FDSLWDO� IL[�����

X�P���LPSR]LWHOH�LQGLUHFWH�����X�P��úL�VXEYHQ LL�GH�H[SORDWDUH����X�P� 9HQLWXO�QD LRQDO�HVWH�

a) 700 u.m.; b) 600 u.m.; c) 660 u.m.; d) 960 u.m.; e) 1340 u.m.

*)� 6XELHFW� OD� H[DPHQXO� GH� OLFHQ �� )DFXOWDWHD� &LEHUQHWLF �� 6WDWLVWLF � úL� ,QIRUPDWLF � (FRQRPLF �� VHVLXQHD�

februarie 1998.

Page 11: STATISTICA - TESTE GRILA

5) ÌQ�VWXGLXO�GHSHQGHQ HORU�VWDWLVWLFH�GLQWUH�YDULDELOH�VH�FXQRDúWH�IDSWXO�F �VXQW�DQDOL]DWH��DEDWHULOH�

GLQWUH�YDORULOH�HPSLULFH�úL�FXUED��GUHDSWD��GH�UHJUHVLH�� y yi x− ) evaluate sintetic prin dispersia

σ y r/2 �� DEDWHULOH� GLQWUH� YDORULOH� DMXVWDWH� úL� PHGLD� FDUDFWHULVWLFLL� GHSHQGHQWH� � y yx − �� HYDOXDW �

sintetic prin dispersia σ y x/2 ��GLVSHUVLD� WRWDO �D�YDULDELOHL� � UH]XOWDWLYH�HVWH�σ y

2 . În orice sitXD LH�

HVWH�DGHY UDW �UHOD LD�

a) σ σy x y/2 2> ;

b) σ σy x y/2 2< ;

c) σ σy r y/2 2> ;

d) σ σ σy y r y x2 2 2= −/ / ;

e) σ

σy x

y

/.

2

21>

6) )HQRPHQHOH�GH�PDV �� vQ�JHQHUDO��DSDU�FD�R�PXO LPH�GH�IRUPH� LQGLYLGXDOH�GLIHULWH��FX�H[LVWHQ �diferiW �� DSDUHQW� I U � QLFL� R� OHJ WXU � GH� OD� R� IRUP � OD� DOWD�� GDU� FDUH�� DQDOL]DWH� FRPSDUDWLY�� VH�FRQVWDW �F �DX�DFHHDúL�HVHQ ��&HHD�FH�QX�H[SOLF �DFHDVW �DILUPD LH�HVWH�F �

a) IRUPHOH�LQGLYLGXDOH�VXQW�JHQHUDWH�GH�FDX]H�FDUH�VH�PDQLIHVW �GH�UHJXO �vQ�FRQGL LL�GLIHrite; b) IRUPHOH�LQGLYLGXDOH�GH�PDQLIHVWDUH�GLIHU �GH�OD�R�XQLWDWH�OD�DOWD��vQ�IXQF LH�GH�PRGXO�FXP�

VH� DVRFLD] � úL� VH� FRPELQ � IDFWRULL� VLVWHPDWLFL� FX� FHL� vQWkPSO WRUL�� FHL� RELHFWLYL� FX� FHL�subiectivi;

c) formele individuale de manifestare analizate la nivelul anVDPEOXOXL� SDU� DVHP Q WRDUH�vQWUH�HOH��ILLQG�JHQHUDWH�GH�FDX]H�HVHQ LDOH�FRPXQH�

d) IRUPHOH� LQGLYLGXDOH� GH� PDQLIHVWDUH� VH� VXSXQ� DFHOHLDúL� OHJL� GH� DSDUL LH� úL� GH]YROWDUH�FXQRVFXW �úL�YHULILFDW �OD�QLYHOXO�ILHF UHL�XQLW L�GH�REVHUYDUH�

e) formele individuale de maQLIHVWDUH� VH� VXSXQ� DFHOHLDúL� OHJL� VWDWLVWLFH� FDUH� OD� QLYHOXO�DQVDPEOXOXL�VH�PDQLIHVW �FD�WHQGLQ �

7) 6WDELOLUHD� SUHFLV � úL� FODU � D� VFRSXOXL� XQHL� REVHUY UL� VWDWLVWLFH�� WRWDO � VDX� SDU LDO �� QX� SUH]LQW �

LPSRUWDQ �SHQWUX�

a) delimitarea obiectului de observare; b) GHILQLUHD�XQLWD LORU�GH�REVHUYDUH� c) VWDELOLUHD�VFRSXOXL�FHUFHW ULL�VWDWLVWLFH� d) stabilirea programului propriu-]LV�DO�REVHUY ULL� e) GHOLPLWDUHD�RELHFWLYHORU�SDU LDOH�DOH�FHUFHW ULL��FDUH�vQ�FD]XO�REVHUY ULL��VH�UHIHU �FRQFUHW�

OD�YROXPXO�úL�FDOLWDWHD�GDWHORU�QHcesare.

8) Contul sintetic de bunuri:

a) are ca sold consumul intermediar; b) are ca sold consumul final; c) DUH�FD�VROG�YROXPXO�LQYHVWL LLORU�EUXWH� d) nu are sold; e) are ca sold exportul net.

���$QDOL]D L� XUP WRDUHOH� QR LXQL�� ���P VXUDUHD�� ��� DQDOL]D� úL� VLQWH]D�� ��� HVWimarea; 4) verificarea LSRWH]HORU�úL�VDX�WHVWDUHD�VHPQLILFD LLORU�����HODERUDUHD�GHFL]LLORU�

Page 12: STATISTICA - TESTE GRILA

3ULQFLSDOHOH�IXQF LL�DOH�LQGLFDWRULORU�VWDWLVWLFL�VXQW�

a) ���������úL��� b) ��������úL��� c) ��������úL��� d) ��������úL��� e) ��������úL���

10) 6H�QRWHD] �FX�(i (i = 1 80, ��P ULPHD�³H[WUDVXOXL�GH�FRQW´�VROLFLWDW�OD�����������GH����GH�FOLHQ L�OD�JKLúHXO�$-%�DO�E QFLL�$OID��9DULDELOD�XUP ULW �SUH]LQW �YDORULOH�SH�R�VFDO �

a) de rapoarte; b) de intervale; c) FRQWLQX � d) GLVFUHW � e) RUGLQDO �

11) 'DF � vQWU-R� GLVWULEX LH� XQLGLPHQVLRQDO � IRUPDW � GXS � R� YDULDELO � QXPHULF � ;� YDORULOH�LQGLYLGXDOH�VXQW�HYLGHQW�GHSODVDWH�F WUH�YDORULOH�PDUL��DWXQFL�

a) x Me Mo< < ; b) x Me Mo> > ; c) x Me Mo= = ; d) x Mo Me< < ; e) x Me Mo x− = − .

12) 9DORDUHD�PHGLDQ � vQ� FRPSDUD LH� FX� YDORDUHD�PHGLH�� LQGLFDWRUL� FDOFXOD L� SHQWUX� FDUDFWHUL]DUHD�WHQGLQ HL�FHQWUDOH�vQWU-R�VHULH�GH�UHSDUWL LH��SUH]LQW �DYDQWDMXO�XUP WRU�

a) vQ�FDOFXOXO�V X�VH�LDX�WRDWH�YDORULOH�LQGLYLGXDOH�vQUHJLVWUDWH� b) YDORDUHD�VD�QX�HVWH�LQIOXHQ DW �GH�SUH]HQ D�YDORULORU�LQGLYLGXDOH�H[WUHPH��DEHUDQWH�� c) HD�VH�SUHWHD] �XúRU�OD�HIHFWXDUHD�RSHUD LLORU�DOJHEULFH� d) GHWHUPLQDUHD�VD�VH�UHDOL]HD] �vQ�IXQF LH�GH�OLPLWD�LQIHULRDU �D�LQWHUYDOXOXL�PHGLDQ�úL�QX�vQ�

IXQF LH�GH�FHQWUXO�LQWHUYDOXOXL��HYLWkQGX-se astfel ipoteza nRUPDOLW LL�UHSDUWL LHL� e) HD�SRDWH�IL�XWLOL]DW �vQ�FRPSDUDUHD�WHQGLQ HORU�FHQWUDOH�DOH�YDULDELOHORU�GLVWLQFWH�vQ�GLIHULWH�

SRSXOD LL�VWDWLVWLFH�

13) ,QGLFDWRULL� VWDWLVWLFL� SRW� IL� RE LQX L� � SULQ� P VXUDUH� úL� HVWLPDUH�� 1R LXQHD� GH� HVWLPDUH� QX� VH�FDUDFWHUL]HD] �SULQ�IDSWXO�F �

a) HVWLPDUHD�SUHVXSXQH�R�FDUDFWHUL]DUH�VWDWLVWLF �XWLOL]kQG�XQ�PRGHO�VDX�R�LSRWH] �VWDWLVWLF �SULQ�FDUH�SH�ED]D�GDWHORU�SDU LDOH�GH�FDUH�VH�GLVSXQH�VH�GHWHUPLQ �R�VHULH�GH�LQGLFDWRUL�JHQHUDOL]DWRUL�

b) HVWH�OHJDW �vQWRWGHDXQD�vQ�VWDWLVWLF �GH�XWLOLzarea unui interval de eroare, ceea ce face ca P ULPHD�LQGLFDWRUXOXL�HVWLPDW�V �QX�DLE �R�YDORDUH�FHUW ��FL�SODVDW �vQWU-un interval;

c) HVWH�OHJDW �QHPLMORFLW�GH�QR LXQHD�GH�PRGHO�VWDWLVWLF� d) HVWH� OHJDW � vQWRWGHDXQD�GH�RE LQHUHD�YDORULL� LQGLFDWRULORU� VLQWHWLFi pe baza datelor culese

printr-R�PHWRG �GH�REVHUYDUH�WRWDO � e) HVWH�XWLOL]DW �SHQWUX�FD]XULOH� vQ�FDUH�QX�H[LVW �XQ�PRGHO�GH� WUHFHUH�GH� OD�XQ�HúDQWLRQ� OD�

SRSXOD LD� JHQHUDO �� LDU� SHQWUX� GHWHUPLQDUHD� YDORULL� XQXL� LQGLFDWRU� VH� IDF� UD LRQDPHQWH�logice, calculul direct nefiind posibil.

14) 'HVSUH� HYROX LD� PLMORDFHORU� IL[H� �OD� VIkUúLWXO� DQXOXL�� vQ� 5RPkQLD� vQ� SHULRDGD� ����-1997 se FXQRVF�GDWHOH��FRQYHQ LRQDOH��

Page 13: STATISTICA - TESTE GRILA

Anii 1994 1995 1996 1997 0RGLILFDUHD�ID �GH�DQXO�SUHFHGHQW��POG��OHL� 194,3 189,8 177,2 166,9

ùWLLQG�F �vQ������YDORDUHD�DEVROXW �D�XQXL�SURFHQW�GH�FUHúWHUH�ID �GH������D�PLMORDFHORU�IL[H�D�IRVW�GH����POG��OHL��PRGLILFDUHD�PHGLH�UHODWLY �DQXDO �vQ�SHULRDGD�����- 1997 a fost de :

a) 114,7 %; b) 182,05 mld. lei/an; c) 4,7 %; d) - 4,7 %; e) 14,7 %.

15) Ajustarea (determinarea trendului) seriilor cronologice prin metoda mediilor mobile se UHDOL]HD] �DWXQFL�FkQG�

a) IHQRPHQXO�SUH]LQW �R�HYROX LH�DSUR[LPDWLY�H[SRQHQ LDO � b) LQGLFLL�GH�GLQDPLF �FX�ED] �PRELO �SUH]LQW �YDORUL�DSURSLDWH�vQWUH�HL� c) YDULD LD�WHUPHQLORU�VHULHL�SUH]LQW �HYLGHQWH�UHJXODULW L�FLFOLFH� d) nu se pot aplica metodele analitice de ajustare; e) YDULD LD�WHUPHQLORU�VHULHL�SUH]LQW �R�HYLGHQW �OLQLDULWDWH�

16) ÌQ�DQDOL]D�GLVSHUVLRQDO �VH�XWLOL]HD] �SHQWUX�XQ�SUDJ�GH�VHPQLILFD LH� �úL�QXP UXO�JUDGHORU�GH�libertate (r-1��úL��n-r��WHVWXO�)LVKHU��'DF � rnrcalculat FF −−> ,1,α (din tabel), atunci:

a) OHJ WXUD� HVWH� VHPQLILFDWLY � úL� FDUDFWHULVWLFD� GXS � FDUH� V-a efectuat gruparea este într-DGHY U�GHWHUPLQDQW �SHQWUX�YDULD LD�FDUDFWHULVWLFLL�UH]XOWDWLYH�

b) se respinge ipoteza cu privire la eJDOLWDWHD�PHGLLORU�GH�JUXS � c) WR L� FHLODO L� IDFWRUL�GH� LQIOXHQ � �FX�H[FHS LD�DFHOXLD�GH�JUXSDUH��GHWHUPLQ � VHPQLILFDWLY�

YDULD LD�YDULDELOHL�UH]XOWDWLYH� d) IXQF LD�GH�UHJUHVLH�HVWH�OLQLDU � e) SHQWUX�WHVWDUHD�VHPQLILFD LHL�IDFWRUXOXL�GH�LQIOXHQ �DVXSUD�YDULD LHi variabilei rezultative

VH�XWLOL]HD] �7HVWXO�6WXGHQW��³W´��

17) ÌQ� GHFXUVXO� XQHL� SHULRDGH� SURGXFWLYLWDWHD� PXQFLL� D� FUHVFXW� FX� ���� LDU� vQ]HVWUDUHD� WHKQLF � D�PXQFLL�D�FUHVFXW�FX������(ILFLHQ D�XWLOL] ULL�PLMORDFHORU�IL[H�

a) a crescut cu 1,2%; b) a crescut cu 23,2%; c) D�VF ]XW�FX�������� d) D�VF ]XW�FX������ e) a crescut cu 1,8%.

18) ,QGLFHOH�PHGLX�GH�GLQDPLF �VH�FDOFXOHD] �FD�

a) PHGLH�JHRPHWULF ��LQGLIHUHQW�GH�YDORULOH�LQGLFLORU�GH�GLQDPLF �FX�ED] �PRELO � b) PHGLH�JHRPHWULF �QXPDL�GDF �LQGLFLL�GH�GLQDPLF �FX�ED] �IL[ �SUH]LQW �YDlori apropiate; c) PHGLH� JHRPHWULF � QXPDL� GDF � LQGLFLL� GH� GLQDPLF � FX� ED] � PRELO � SUH]LQW � YDORUL�

aproximativ egale între ele; d) PHGLH�DULWPHWLF �D�LQGLFLORU�GH�GLQDPLF �FX�ED] �PRELO � e) PHGLH�DUPRQLF �D�LQGLFLORU�GH�GLQDPLF �FX�ED] �PRELO �

19) Un circuit economic este considerat circuit închis pentru sectorul A când:

a) QX�H[LVW �LQWU UL�vQ�$� b) QX�H[LVW �LHúLUL�GLQ�$�

Page 14: STATISTICA - TESTE GRILA

c) QX�H[LVW �QLFL�LQWU UL�úL�QLFL�LHúLUL�SHQWUX�VHFWRUXO�$� d) fluxurile financiare sunt egale cu fluxurile reale; e) VXPD�IOX[XULORU�GH�LQWUDUH�HVWH�HJDO �FX�VXPD�IOX[XULORU�GH�LHúLUH�

20) Într-R� SRSXOD LH� VWDWLVWLF � V-au înregistrat pentru variabila X valorile x1, x2, …, xn�� 5HOD LD�

RELHFWLY � GLQWUH� DFHVWH� GDWH� FRQGXFH� OD� FRQFOX]LD� F � WHQGLQ D� FHQWUDO � SRDWH� IL� FHO� PDL� ELQH�

H[SULPDW �SULQ�PHGLD�DULWPHWLF �D�F UHL�YDORDUH�FDOFXODW �HVWH� x �� ÌQ�XUPD�YHULILF ULL�GDWHORU� úL�FDOFXOHORU� VH� FRQVWDW � F � ILHFDUH� YDORDUH� LQGLYLGXDO � vQUHJLVWUDW �� GLQ� DQXPLWH� PRWLYH�� D� IRVW�PLFúRUDW �FX������$GHY UDWD�YDORDUH�D�PHGLHL�HVWH�

a) 0,85 x ;

b) x

x0 15

6 67,

,= ;

c) 1,15 x ; d) 1,51 x ; e) HVWH�HJDO �FX�PHGLD�FDOFXODW �DQWHULRU�

21) Într-R� SRSXOD LH� VWDWLVWLF � V-DX� XUP ULW� GRX � YDULDELOH�� XQD� QXPHULF � [� úL� XQD� QHQXPHULF �$��6LVWHPDWL]DUHD�GDWHORU�GXS �FHOH�GRX �YDULDELOH�VH�SUH]LQW �vQ�IRUPD�JHQHUDO �DVWIHO�

X

A

x1

...

xj

...

xp

Total

A1 ... ... ... ... ... ... ... ... Ai ni1 ... nij ... nip ni. ... ... ... ... ... ... Ak ... ...

Total ... ... n.j ... ... n..

'LVWULEX LD�DO WXUDW �FRQ LQH�

D��GRX �GLVWULEX LL�PDUJLQDOH� E��GRX �GLVWULEX LL�PDUJLQDOH�úL�S�GLVWULEX LL�FRQGL LRQDWH�GH�$� F��GRX �GLVWULEX LL�PDUJLQDOH�úL�N�GLVWULEX LL�FRQGL LRQDWH�GH�;� G��GRX �GLVWULEX LL�PDUJLQDOH�úL�N�S�GLVWULEX LL�FRQGL LRQDWH�

e) GRX �GLVWULEX LL�PDUJLQDOH�GXS �$�úL�GXS �;��N�S�GLVWULEX LL�XQLGLPHQVLRQDOH�FRQGL LRQDWH�GH�;�úL�$�úL�R�GLVWULEX LH�ELGLPHQVLRQDO �

22) O întreprindere de transport auto-F O WRUL�DORF ����DXWREX]H�SHQWUX�WUDVHXO�0-1�D�F UXL�GLVWDQ �este D. Datele referitoare la vitezele medii înregistrate de autovehicule într-R�]L�VXQW�XUP WRDUHOH�

Viteza medie (km/h) 40 60 70 Nr. de autovehicule 3 5 2

ÌQ�PHGLH�XQ�DXWRYHKLFXO�D�SDUFXUV�vQ�]LXD�FRQVLGHUDW �WUDVHXO�0-1�GH�GLVWDQ �'�FX�R�YLWH] �GH� a) 56 km/h; b) 53,5 km/h; c) 60 km/h; d) 70 km/h; e) 56,7 km/h.

Page 15: STATISTICA - TESTE GRILA

23) ÌQ�FD]XO�DJUHJ ULL� WUDQ]DF LLORU� vQ�6�&�1��� WUDQ]DF LLOH�HIHFWXDWH� vQWUH� VXELHFWHOH� HFRQRPLFH�GLQ�sectoare diferite:

D��VH�FRQVROLGHD] � E��VH�vQVXPHD] � c) se scad; G��XQHOH�VH�vQVXPHD] �LDU�R�DOW �FDWHJRULe se scad; H��DJUHJDUHD�QX�VH�UHIHU �OD�WUDQ]DF LL� 24) 6WUXFWXUD� FRQVXPXOXL� SRSXOD LHL� vQ� SHULRDGD� GH� ED] � HVWH�� P UIXUL� DOLPHQWDUH� ����� P UIXUL�

QHDOLPHQWDUH� ����� VHUYLFLL� ����� ÌQ� SHULRDGD� FXUHQW � SUH XULOH� DX� FUHVFXW� DVWIHO�� P UIXUL�DOLPHQWDUH�������P UIXUL�QHDOLPHQWDUH�������VHUYLFLL�������5DWD�LQIOD LHL�D�IRVW�

a) 25%; b) 23,25%; c) 125%; d) 123,25%;

f) 3,25%. 25) 3HQWUX�RFXSDUHD�XQXL� ORF�GH�PXQF �YDFDQW�GH�VWHQRGDFWLORJUDI ��V-au prezentat la concurs opt

candidate. Testul propus a constat din dactilografieUHD� XQXL� WH[W� �GH� DFHHDúL� P ULPH� úL�GLILFXOWDWH���'DWHOH�FX�SULYLUH�OD�QXP UXO�GH�HURUL�FRPLVH�úL�WLPSXO�GH�GDFWLORJUDILHUH�VH�SUH]LQW �astfel:

Candidata A B C D E F G H Nr. erori 9 8 6 4 5 10 12 7 Timp dactilo (minute) 13 11 12 15 14 9 8 10

'HSHQGHQ D�GLQWUH�FHOH�GRX �YDULDELOH�VH�P VRDU �FX�DMXWRUXO�FRHILFLHQWXOXL�GH�FRUHOD LH�DO�UDQJXULORU��DO�OXL�.HQGDOO��D�F UXL�P ULPH�HVWH� a) 0,71; b) -0,30; c) -1,00; d) -0,71; e) 1,00. 26) De la un punct de desfacere s-DX�FXOHV�GDWHOH�XUP WRDUH�

Produse 9DORDUHD�YkQ] ULORU�vQ�LDQXDULH����� (mil. lei)

��PRGLILF ULL�YROXPXOXL�IL]LF�vQ�LDQXDULH������ID �GH�LDQXDULH���������

A 18 +5 B 20 -2

0RGLILFDUHD� DEVROXW � WRWDO � D� YkQ] ULORU� vQ� LDQXDULH� ����� ID � GH� LDQXDULH� ����� FD� XUPDUH� D�PRGLILF ULL�YROXPXOXL�fizic este: a) 500 mii lei; b) 1,30 mil. lei; c) -500 mii lei; d) 38 mil. lei; e) 20,76 mil. lei.

Page 16: STATISTICA - TESTE GRILA

27) &RQVWLWXLH�HOHPHQW�DO�FRPSHQV ULL�IDFWRUXOXL�PXQF �FRPSRQHQW �D�3,%� a) profitul;

E��VXPHOH�SO WLWH�DWkW�vQ�EDQL�FkW�úL�vQ�QDWXU �

c) dividendele;

d) renta;

H��QXPDL�VDODULLOH�SO WLWH�vQ�EDQL�

28) 6H�FXQRDúWH�IDSWXO�F � vQ�VWXGLXO�GHSHQGHQ HORU�VWDWLVWLFH�GLQWUH�YDULDELOHOH�QXPHULFH�<�úL�;�VH�XWLOL]HD] � úL� LQGLFDWRUXO�PRPHQW� FHQWUDW� GH� RUGLQXO� ������ QXPLW� úL� FRYDULDQ �� QRWDW � FRY�[�\���Valoarea absoluW �PD[LP �D�DFHVWXL�LQGLFDWRU�HVWH�

a) 1; b) σ x ;

c) σσ

x

y

2

2;

d) σ y ;

e) σ σx y .

29) ÌQ�FDOFXOXO�3URGXVXOXL�,QWHUQ�%UXW��H[SRUWXO�QHW�VH�FDOFXOHD] � a) Export-Impozite;

b) Export-Import;

c) Export-Amortizarea;

d) Export+Impozite indirecte-6XEYHQ LL�

e) Export+Import.

30) $QFKHWD�VWDWLVWLF �� D��HVWH�R�PHWRG �GH�REVHUYDUH�WRWDO �

b) HVWH� R� PHWRG � GH� REVHUYDUH� SDU LDO �� FDUH� QXPDL� vQWkPSO WRU� SRDWH� V � vQGHSOLQHDVF �

FRQGL LD�GH�UHSUHzentativitate;

c) HVWH� R� PHWRG � GH� REVHUYDUH� SDU LDO �� FDUH� vQ� PRG� REOLJDWRULX� WUHEXLH� V � vQGHSOLQHDVF �

FRQGL LD�GH�UHSUH]HQWDWLYLWDWH�

d) HVWH� R� PHWRG � GH� REVHUYDUH� SDU LDO �� FDUH� VH� ED]HD] � SH� REOLJDWLYLWDWHD� FRPSOHW ULL�

chestionarelor;

H��PDL�HVWH�GHQXPLW �úi sondaj statistic.

31) 2�SRSXOD LH�VWDWLVWLF �HVWH�VWUXFWXUDW �GXS �R�DQXPLW �YDULDELO �vQ�GRX �VXESRSXOD LL�$�úL�%��ÌQ�

ILHFDUH� GLQ� FHOH� GRX � VXESRSXOD LL�� V-D� XUP ULW� DFHHDúL� YDULDELO � QXPHULF � ;�� LDU� FHOH� GRX �GLVWULEX LL�VH�SUH]LQW �JUDILF�DVWIHO�

Page 17: STATISTICA - TESTE GRILA

x

Observându-VH�JUDILFXO�DO WXUDW��VH�SRDWH�DILUPD�

a) LQGLFDWRULL� WHQGLQ HL� FHQWUDOH� SUH]LQW � YDORUL� GLIHULWH� vQ� FHOH� GRX � VXESRSXOD LL�� LDU�GLVWULEX LD�JHQHUDO �HVWH�DVLPHWULF �

b) H[LVW � YDORUL� PRGDOH� SDU LDOH� GLIHULWH�� GDU� UHOD LD� GH� Dditivitate a acestora permite GHWHUPLQDUHD�YDORULL�PRGDOH�GLQ�GLVWULEX LD�JHQHUDO �

c) YDORULOH�LQGLYLGXDOH�GLQ�FHOH�GRX �VXESRSXOD LL�DX�DFHODúL�JUDG�GH�GLVSHUVDUH� d) YDORDUHD�PRGDO �D�GLVWULEX LHL�JHQHUDOH�HVWH�FXSULQV �vQWUH�0RA�úL�0RB; e) valorile mediane ale FHORU�GRX �VXESRSXOD LL��0HA�úL�0HB) sunt identice.

32) $SOLFDUHD�XQXL�PRGHO�GH�DQDOL] �GLVSHUVLRQDO �FX�XQ�VLQJXU�IDFWRU�SHQWUX�VHULL�VLPSOH�SUHVXSXQH�

FDOFXOXO�úL�LQWHUSUHWDUHD�LQGLFDWRULORU�XUP WRUL�� ( )S y y ni ii

r

12

1

= −=∑ SHQWUX�D�HYDOXD�FD�VXUV �GH�

YDULD LH� LQIOXHQ D� vQ� H[FOXVLYLWDWH� D� IDFWRUXOXL� VLVWHPDWLF� úL� ( )S y yij ii

r

j

n

22

11

= −==∑∑ pentru a

HYDOXD�LQIOXHQ D�WXWXURU�FHORUODO L�IDFWRUL��FX�H[FHS LD�IDFWRUXOXL�VLVWHPDWLF�L]RODW��3HQWUX�D�HYDOXD�FRQWULEX LD� IDFWRUXOXL� VLVWHPDWLF� OD� YDULD LD� YDULDELOHL� GHSHQGHQWH� VH� FDOFXOHD] � XQ� LQGLFDWRU� GH�forma:

a) S

S1

2;

b) S

S2

1;

c)

( )S

y yiji

r

j

n1

2

11

−==∑∑

;

d)

( )S

y yiji

r

j

n2

2

11

−==∑∑

;

A

B

MoA MoB

ni

Page 18: STATISTICA - TESTE GRILA

e)

( ) ( )y y n

r

y y

n r

i ii

r

ij ij

n

i

r

−= ==∑ ∑∑2

1

2

11

1: .

33) 9HQLWXO�QD LRQDO�HVWH�HJDO�FX�

a) 31%�OD�SUH XULOH�SLH HL� b) 311�OD�SUH XULOH�SLH HL� c) PNN la�SUH XULOH�IDFWRULORU� d) 3,1�OD�SUH XULOH�IDFWRULORU� e) 3,1�OD�SUH XULOH�SLH HL�

34) 3HQWUX� LGHQWLILFDUHD� úL� GLPLQXDUHD� HURULORU� GH� REVHUYDUH� HVWH� QHFHVDU� FRQWUROXO� GDWHORU� FXOHVH��Acest control nu presupune:

a) FD�SULQ�VRQGDM�V �VH�UHIDF ��DQXPLWH�FDOFXOH�GH�RE LQHUH�D�YDORULORU�XQRU�LQGLFDWRUL�vQVFULúL�în formulare;

b) FD�OD�FHQWUHOH�GH�SUHOXFUDUH�V �VH�YHULILFH�GDF �DX�VRVLW�WRDWH�IRUPXODUHOH�FX�WRDWH�UXEULFLOH�completate;

c) XWLOL]DUHD� XQRU� PRGHOH� GH� YHULILFDUH� D� LSRWH]HORU� VWDWLVWLFH� úL� DSOLFDUHD� GH� WHVWH� GH�verificaUH�DOH�VHPQLILFD LLORU�LQGLFDWRULORU�

d) HIHFWXDUHD�GH�FRPSDU UL� e) VXE�QLFL�R�IRUP �XWLOL]DUHD�XQRU�SURJUDPH�LQIRUPDWLFH�VSHFLDO�HODERUDWH�

35) 'HQVLWDWHD�XQHL�UHSDUWL LL�VWDWLVWLFH�HVWH�YL]XDOL]DW �SULQ�

a) KLVWRJUDP � b) FXUED�FXPXODWLY �GH�IUHFYHQ H� c) diagrama prin benzi; d) diagrama prin coloane; e) curba de concentrare a lui Lorentz.

36) ÌQ�GRX �SRSXOD LL� VWDWLVWLFH�$� úL�%�GH�DFHODúL� YROXP�R� YDULDELO � QXPHULF �;�SUH]LQW � DFHOHDúL�

YDULDQWH��3HQWUX�FHOH�GRX �GLVWULEX LL�GH�IUHFYHQ H�V-au calculat mediile x A úL� x B . Aceste medii sunt egale deoarece:

a) YDORULOH�LQGLYLGXDOH�GLQ�$�úL�%�VXQW�LGHQWLFH� b) YDORDUHD�ORU�GHSLQGH�QX�QXPDL�GH�YDORULOH�LQGLYLGXDOH�FL�úL�GH�IUHFYHQ HOH�ORU�GLIHULWH�GH�

DSDUL LH� c) VH�FDOFXOHD] �GXS �DFHHDúL�PHWRG ��LDU�YROXPXO�SRSXOD LLORU�VWDWLVWLFH�HVWH�DFHODúL� d) IUHFYHQ HOH�GH�DSDUL LH�DOH�YDORULORU�LQGLYLGXDOH�GLQ�$�úL�%�VXQW�LGHQWLFH��GDU�GLIHULWH�GH�OD�

R�SRSXOD LH�OD�DOWD� e) vQ�$�úL�%�YDORULOH�LQGLYLGXDOH�VXQW�LGHQWLFH�úL�DX�DFHOHDúL�IUHFYHQ H�GH�DSDUL LH�

37) ,QGLFHOH�SUH urilor consumatorului este calculat ca un indice de tip:

a) Paasche; b) Laspeyres; c) Fischer; d) indice al valorii; e) indice al volumului fizic.

Page 19: STATISTICA - TESTE GRILA

38) 'RL� VWDWLVWLFLHQL� DX� DQDOL]DW� DFHOHDúL� GDWH� UHIHULWRDUH� OD� ³�� vQGHSOLQLULL� QRUPHORU´� D� ���� GH�PXQFLWRUL�GH�DFHHDúL�SURIHVLH��3HQWUX�D�FDUDFWHUL]D�WHQGLQ D�FHQWUDO �D�YDULDELOHL��XQXO�D�FDOFXODW�PHGLD� DULWPHWLF �� RE LQkQG� ������ LDU� FHO ODOW� D� FRQVLGHUDW� RSRUWXQ �PHGLD� S WUDWLF �� RE LQkQG�107% (amândoi au efectuat corect calculele). Pentru a caracteriza omogenitatea datelor este QHFHVDU �GHWHUPLQDUHD�FRHILFLHQWXOXL�GH�YDULD LH��9DORDUHD�DFHVWXLD�HVWH�

a) 19,6%; b) 25%; c) -75%; d) ����SHUVRDQ � e) 50%.

39) Într-XQ� HúDQWLRQ� GH� ��� GH� DJHQ L� HFRQRPLFL� V-DX� XUP ULW� GRX � YDULDELOH� GHSHQGHQWH� VWDWLVWLF��SURILWXO� QHW� �PLO�� OHL�� úL� QXP UXO� PHGLX� GH� VDODULD L�� 'HVSUH� GLVWULEX LD� FRPELQDW � IRUPDW � SH�SDWUX� LQWHUYDOH�HJDOH�GXS �SURILW�úL�SH� WUHL� LQWHUYDOH�GXS �QXP UXO�PHGLX�GH�VDODULD L�VH�FXQRVF�XUP WRDUHOH�GDWH��SH� vQWUHJXO�HúDQWLRQ�SURILWXO�PHGLX�D�IRVW�GH������PLO�� OHL�� LDU�FRHILFLHQWXO�GH�YDULD LH�D�IRVW�GH��������SURILWXO�PHGLX�D�IRVW�GH����PLO��OHL�OD�JUXSD�DJHQ LORU�HFRQRPLFL�FX�QU��PHGLX�GH�VDODULD L�VXE����SHUVRDQH�����PLO��OHL�OD�JUXSD���-���QU��PHGLX�GH�VDODULD L�úL����PLO��OHL�OD�JUXSD����úL�SHVWH�QU��PHGLX�GH�VDODULD L��QXP UXO�GH�DJHQ L�HFRQRPici pe cele trei grupe sunt ������úL����0 VXUD�vQ�FDUH�PRGLILFDUHD�QXP UXOXL�PHGLX�GH�VDODULD L�FRQWULEXLH�OD�YDULDELOLWDWHD�SURILWXOXL�DJHQ LORU�HFRQRPLFL�D�IRVW�GH�

a) 46,6%; b) 53,4%; c) -10%; d) 110%; e) 100%.

40) ÌQ�DQDOL]D�VHULLORU�GH�GDWH�VWDWLVWLFH�VH�XWLOL]HD] �QR LXQLOH�

1. YDULDELOLWDWHD�����LQGHSHQGHQ D�����LQWHUGHSHQGHQ D�����FRQFHQWUDUHD�� ���RPRJHQLWDWHD�����IRUPD�GH�UHSDUWL LH�����SHULRGLFLWDWHD�

3URSULHW LOH��SDUWLFXODULW LOH��VHULLORU�FURQRORJLFH�VXQW�

a) ���������úL��� b) ��������úL��� c) ��������úL��� d) ���������úL 7.

Page 20: STATISTICA - TESTE GRILA

TESTUL 3

1) 6H� GDX� GDWHOH� UHIHULWRDUH� OD� UHSDUWL LD� VDODULD LORU� XQHL� VRFLHW L� FRPHUFLDOH� GXS � YHFKLPHD� vQ�

PXQF �

Grupe (ani) 1U��VDODULD L

( ]0 5− 3

( ]5 10− 5

( ]10 15− 9

( ]15 20− 15

( ]20 25− 9

( ]25 30− 5

peste 30 3 TOTAL n=49

9HFKLPHD�PHGLH�D�XQXL�VDODULDW�vQ�FDGUXO�VRFLHW LL�FRPHUFLDOH�HVWH�

a) 12,5 ani; b) 21,5 ani; c) 9,75 ani; d) 17,5 ani; e) 24,5 ani.

2) $JUHJDWHOH�PDFURHFRQRPLFH�VH�GHWHUPLQ �OD�SUH XULOH�SLH HL�VDX�OD�SUH XULOH�IDFWRULORU��7UHFHUHD�

GH�OD�R�FDWHJRULH�GH�SUH XUL�OD�DOWD�VH�UHDOL]HD] �

a) SUH XO�IDFWRULORU� �SUH XO�SLH HL�- impozitele indirecte; b) SUH XO�IDFWRULORU� �SUH XO�SLH HL���LPSR]LWHOH�LQGLUHFWH� c) SUH XO�IDFWRULORU� �SUH XO�SLH HL�- impozitele indirecte nete; d) SUH XO�IDFWRULORU� �SUH XO�SLH HL���VXEYHQ LLOH� e) SUH XO�IDFWRULORU� �SUH XO�SLH HL�-�VXEYHQ LLOH�

3) Indicatorii de rezultate macroeconomice (agregatele macroeconomice) se pot calcula ca

LQGLFDWRUL�GH�QDWXU �EUXW �úL�GH�QDWXU �QHW ��&DOFXOXO�LQGLFDWRULORU�vQ�YDULDQWD�QHW �VH�IDFH�

a) ,QGLFDWRULL� GH� QDWXU � QHW � � ,QGLFDWRULL� GH� QDWXU � EUXW � ��$ORFD LD� SHQWUX� FRQVXPXO� GH�capital fix;

b) ,QGLFDWRULL�GH�QDWXU �QHW � �,QGLFDWRULL�GH�QDWXU �EUXW �-�6ROGXO�YDORULL�DG XJDWH�EUXWH�vQ�UDSRUW�FX�VWU LQ WDtea;

c) ,QGLFDWRULL�GH�QDWXU �QHW � �,QGLFDWRULL�GH�QDWXU �EUXW ���6ROGXO�YDORULL�DG XJDWH�EUXWH�vQ�UDSRUW�FX�VWU LQ WDWHD�

d) ,QGLFDWRULL� GH� QDWXU � QHW � � ,QGLFDWRULL� GH� QDWXU � EUXW � -� $ORFD LD� SHQWUX� FRQVXPXO� GH�capital fix;

e) ,QGLFDWRULL�GH�QDWXU �QHW � �,QGLFDWRULL�GH�QDWXU �EUXW �- Exportul net. 4) 9HQLWXO� SHUVRQDO� GLVSRQLELO� �93'�� H[SULP � YHQLWXULOH� JRVSRG ULLORU� �PHQDMHORU�� FH� SRW� IL�

XWLOL]DWH�SHQWUX�DFRSHULUHD�FKHOWXLHOLORU�SHUVRQDOH�úL�SHQWUX�HFRQRPLVLUH� 9HQLWXO�3HUVRQDO�'LVSRQLELO�VH�FDOFXOHD] �

Page 21: STATISTICA - TESTE GRILA

a) VPD = Veniturile personale + Impozitele personale; b) 93'� �9HQLWXO�1D LRQDO�-�6ROGXO�YDORULL�DG XJDWH�EUXWH�vQ�UDSRUW�FX�VWU LQ WDWHD� c) VPD = Veniturile personale - Impozitele personale; d) 93'� �9HQLWXO�1D LRQDO�- Impozitele pe veniturile firmelor + Transferurile de la Guvern

úL�ILUPH� e) 93'� �9HQLWXO�1D LRQDO���,PSR]LWHOH�SHQWUX�DVLJXU UL�VRFLDOH���'REkQ]LOH�SULPLWH�GH�SRSXOD LH�

5) ,QGLFDWRULL� PDFURHFRQRPLFL� GH� UH]XOWDWH� �DJUHJDWHOH�� VH� GHWHUPLQ � FD� LQGLFDWRUL� QRPLQDOL� �vQ�SUH XUL� FXUHQWH�� úL�VDX� FD� LQGLFDWRUL� UHDOL� �vQ� SUH XUL� FRPSDUDELOH� VDX� FRQVWDQWH��� &DOFXOXO� vQ�H[SUHVLH�UHDO �VH�HIHFWXHD] �

a) Agregat real = Agregat nominal -�$ORFD LD�SHQWUX�FRQVXPXO�GH�FDSLWDO�IL[��$&&)��

b) )Laspeyres(ilorproducatorpreturilorIndicele

realAgregatQRPLQDO$JUHJDW=

c) )PIBdeflatorul(pretuluiIndicele

realAgregatLDJUHJDWXOX

QRPLQDO$JUHJDW=

d) $JUHJDW�UHDO� �$JUHJDW�QRPLQDO�[�,QGLFHOH�SUH XOui agregatului (deflatorul PIB); e) Agregat real = Agregat nominal x Indicele Paasche.

6) 2�VHULH�GH�WLPS�VH�UHSUH]LQW �JUDILF�SULQWU-o:

a) FRUHORJUDP � b) GLDJUDP �GH�VWUXFWXU � c) FURQRJUDP ��KLVWRULRJUDP �� d) FDUWRJUDP � e) FDUWRGLDJUDP �

7) 'DF �VH�QRWHD] �� x a -�PHGLD�DULWPHWLF �� x g -�PHGLD�JHRPHWULF �� x h -�PHGLD�DUPRQLF �� x p - PHGLD�S WUDWLF ��UHOD LD�GH�RUGLQH�GLQWUH�PHGLL�HVWH�XUP WRDUHD�

a) x x x xp a h g≤ ≤ ≤ ;

b) x x x xa h g p≤ ≤ ≤ ;

c) x x x xh a g p≤ ≤ ≤ ;

d) x x x xg p a h≤ ≤ ≤ ;

e) x x x xh g a p≤ ≤ ≤ .

8) 'DF �VH�QRWHD] � x a -�PHGLD�DULWPHWLF ��[mo -�YDORDUHD�PRGDO ��[me -�YDORDUHD�PHGLDQ ��vQWU-o

VHULH�GH�UHSDUWL LH��FHL�WUHL�LQGLFDWRUL�VXQW�HJDOL�� x a =xmo = xme) atunci când:

a) seria este de tip calitativ; b) VHULD�HVWH�OHSWRFXUWLF � c) VHULD�HVWH�SODWLFHQWLF � d) VHULD�HVWH�SHUIHFW�VLPHWULF � e) seria este de tip normal.

9) 9HULILFDUHD� FRQFRUGDQ HL� GLQWUH� UHSDUWL LD� H[SHULPHQWDO � �³HPSLULF ´�� RE LQXW � vQWU-o cercetare FRQFUHW � úL� UHSDUWL LD� WHRUHWLF � SUHVXSXV � �GH� H[HPSOX� QRUPDO �� VH� HIHFWXHD] � FX� DMXWRUXO�PDL�multor teste.

Page 22: STATISTICA - TESTE GRILA

Expresia:

( )n n p

n pi i

ii

k − ⋅⋅=

∑2

1

UHSUH]LQW �VWDWLVWLFD�WHVWXOXL� a) Shapiro - Wilk; b) Lalliefors; c) Hi-S WUDW��χ2); d) Kolmogorov-Smirnov; e) Gnedenko.

10) 3HQWUX�D�GLPLQXD�HURDUHD�VLVWHPDWLF �LQWURGXV �OD�FDOFXOXO�GLVSHUVLHL�vQWU-R�VHULH�GH�UHSDUWL LH�SH�

LQWHUYDOH�� SULQ� IRORVLUHD� FHQWUHORU� GH� LQWHUYDO��:�)�6KHSSDUG� D� SURSXV� R� FRUHF LH�� DVWIHO� vQFkW�UHOD LD�GH�FDOFXO�HVWH�

a) σ ’ ( )’

2 2 2= ⋅ − −∑∑

x f

fh x hi i

i;

b) σ σ’2 22

12= − h

;

c) ( )σ ’2 1= −p p ;

d) σ ’22

2

= −

∑∑

∑∑

x fi

fi

x fi

fii i

;

e) ( )

σ ’22

100=

−∑ x x fi i.

Unde σ ’2 -� YDORDUHD� UHFDOFXODW � D� GLVSHUVLHL�� h -� P ULPHD� LQWHUYDOXOXL� GH� JUXSDUH�� xi - valorile

caracteristicii; x - media; fi -�IUHFYHQ HOH��p - media caracteristicii binare. 11) 'HWHUPLQDUHD� YROXPXOXL� HúDQWLRQXOXL� vQ� YDULDQWD�� ³DOHDWRU� VLPSOX� UHSHWDW´� VH� HIHFWXHD] �

XWLOL]kQG�UHOD LD�

a) nz

z

Nx

=⋅

+⋅

α

α

σσ

2 2

22 2

;

b) nn N

N

j j

j jj

k=

⋅ ⋅

⋅=∑

2 2

2

1

σ

σ;

c) nz z

z z

k

p p=

+

⋅ +

α β

1 2

22

12

;

Page 23: STATISTICA - TESTE GRILA

d) n

p

pp

p

p

p

=

−−

−−−

lg

lg lg

1

11

1

1

2

2

1

2

1

;

e) nz

x

=⋅α σ2 2

2∆.

12) ,QGLFLL� SUH XULORU� PHGLL� OD� SULQFLSDOHOH� SURGXVH� YkQGXWH� SH� SLD D� U QHDVF � VH� GHWHUPLQ � vQ�

varianta:

a) Laspeyres; b) Edgeworth; c) Fischer; d) Paasche; e) Marschal.

13) 3H�ED]D�XQXL�VRQGDM�Q ���VWXGHQ L��HIHFWXDW�DOHDWRU�vQ�FDGUXO�IDFXOW LL��V-au înregistrat diferite

FDUDFWHULVWLFL�� 3UHOXFUkQG� GDWHOH� UHIHULWRDUH� OD� GRX � GLQWUH� DFHVWH� FDUDFWHULVWLFL� V-DX� RE LQXW�XUP WRDUHOH�UH]XOWDWH�

Culoarea ochilor GHVFKLV vQFKLV

Culoarea deschis 17 6 23 S UXOXL închis 9 19 28

Total 26 25 51

&RHILFLHQWXO�GH�DVRFLHUH��FRQFRUGDQ ��vQWUH�FHOH�GRX �FDUDFWHULVWLFL�DUH�YDORDUHD�

a) 0,243; b) 0,713; c) 0,980; d) 0,01; e) 0,901.

14) 9DORDUHD�UDSRUWXOXL�GH�FRUHOD LH�HVWH�HJDO �FX�YDORDUHD�FRHILFLHQWXOXL�GH�FRUHOD LH�DWXQFL�FkQG�

a) UHSDUWL LD�HVWH�XQLPRGDO � b) UHSDUWL LD�HVWH�VLPHWULF � c) OHJ WXUD�GLQWUH�YDULDELOH�HVWH�OLQLDU � d) OHJ WXUD�GLQWUH�YDULDELOH�HVWH�LQYHUV � e) OHJ WXUD�GLQWUH�YDULDELOH�HVWH�GLUHFW �

15) Produsul Intern Brut a fost 109.515 mld. lei în anul 1996, respectiv de 249.750 mld. lei în 1997,

VF GHUHD� �UHFDOFXODW � vQ� SUH XUL� FRPSDUDELOH�� ILLQG� � GH� -������ 5DWD� LQIOD LHL� vQ� DQXO� �����comparativ cu 1996 a fost:

a) 244,16%; b) 109,20%;

Page 24: STATISTICA - TESTE GRILA

c) 344,16%; d) 57,20%; e) 144,16%.

16) ,QGLFLL�SUH XULORU�GH�FRQVXP�DO�SRSXOD LHL�vQ�DQXO������ID �GH������DX�IRVW�

• OD�P UIXUL�DOLPHQWDUe 251,4%; • OD�P UIXUL�QHDOLPHQWDUH�������� • la servicii 276,5%.

Ponderile celor trei grupe în totalul cheltuielilor au fost: • P UIXUL�DOLPHQWDUH����� • P UIXUL�QHDOLPHQWDUH����� • servicii 12%;

&XQRVFkQG� IDSWXO� F � vQ� ����� ID � GH� ����� FkúWLJXO� VDODULDO� PHGLX� QRminal net a fost de ��������GLQDPLFD�VDODULLORU�UHDOH�D�IRVW�vQ�����������HJDO �FX�

a) 77,6%; b) 112,5%; c) 177,6%; d) 100,0%; e) 47,6%.

17) /D�R�ILUP ��vQ�GHFXUVXO�XQHL�SHULRDGH��V-DX�vQUHJLVWUDW�XUP WRDUHOH�GDWH�

• LQGLFHOH�vQ]HVWU ULL�WHKQLFH�D�PXQFLL������ • modificarea prRFHQWXDO �D�HILFLHQ HL�FDSLWDOXOXL�IL[�-5%; • LQGLFHOH�QXP UXOXL�GH�VDODULD L������

0RGLILFDUHD�SURGXF LHL�HVWH�HJDO �FX�

a) 100%; b) 0,9576; c) -7,5%; d) +12,3%; e) 112,3%.

18) ,QGLFHOH�VLQWHWLF��GH�JUXS��VWDELOLW�FD�PHGLH�DUPRQLF �D�LQGLFLORU�LQGLYLGXDOL�HVWH�

a) x f

f

x f

f1 1

1

0 0

0

∑∑

∑∑

: ;

b) ( )( )

x f f

x f f1 1 0

0 1 0

++

∑∑

;

c) x f

x f

x f

x f0 1

0 0

1 1

1 0

∑∑

∑∑

⋅ ;

d) x f

ix f

x

1 1

1 11

∑∑

;

e) q

q

q

q

q

qn n n

n0

1

0 1: −

−= .

Page 25: STATISTICA - TESTE GRILA

19) Într-R�VHULH�GH�LQGLFL��SHQWUX�IDFWRUXO�FDOLWDWLY��[���YDULDQWD�³ED] �PRELO ´�úL�³SRQGHUH�YDULDELO ´�

este:

a) x f

x f

x f

x f

x f

x f

x f

x fi i

i i

n n

n n

1 0

0 0

2 1

1 1

1

1 1

1

1 1

∑∑

∑∑

∑∑

∑∑

− −

− −; ; ...; ; ...; ;

b) x f

x f

x f

x f

x f

x f

x f

x fi

i i

n n

n n

1 1

0 0

2 2

1 1

1

1 1 1 1

∑∑

∑∑

∑∑

∑∑− − − −

; ; ...; ; ...; ;

c) x f

x f

x f

x f

x f

x f

x f

x fi i

i i

n n

n n

0 0

1 1

1 1

2 2

1 1 1 1∑∑

∑∑

∑∑

∑∑

− − − −; ; ...; ; ...; ;

d) x f

x f

x f

x f

x f

x f

x f

x fi i

i i

n n

n n

1 1

0 1

2 2

1 2 1 1

∑∑

∑∑

∑∑

∑∑− −

; ; ...; ; ...; ;

e) x f

x f

x f

x f

x f

x f

x f

x fi

i

n

n

1 1

1 1

1 2

1 2

1

1

1

1

∑∑

∑∑

∑∑

∑∑

; ; ...; ; ...; .

20) 5HIHULWRU�OD�DFWLYLWDWHD�HFRQRPLF �D�XQHL�VRFLHW L�FRPHUFLDOH�VH�FXQRVF�XUP WRDUHOH�GDWH�

Unitatea 9DORDUHD�SURGXF LHL��PLO��OHL� 3HU��GH�ED] 3HU��FXUHQW

Modificarea valorii pe seama modiILF ULL�

SUH XULORU��PLO��OHL� A 1200 1850 350 B 875 1600 275

0RGLILFDUHD�UHODWLY �D�YDORULL�OD�QLYHOXO�vQWUHJLL�VRFLHW L��FDX]DW �GH�PRGLILFDUHD�YROXPXOXL�IL]LF�DO�SURGXF LHL�vQWUH�FHOH�GRX �SHULRDGH�D�IRVW�HJDO �FX�

a) -12,5%; b) +100,0%; c) +36,1%; d) +136,1%; e) -112,5%.

21) ÌQ� VWDELOLUHD� WUHQGXOXL� �³DMXVWDUHD´� VHULHL� SHQWUX� LGHQWLILFDUHD� WHQGLQ HL� FHQWUDOH�� PHWRGD�

PRGLILF ULL�PHGLL�DEVROXWH�VH�DSOLF �DWXQFL�

a) FkQG�HYROX LD�HVWH�H[SRQHQ LDO � b) FkQG�PRGLILF ULOH�FX�ED] �PRELO �VXQW�DSUR[Lmativ egale; c) FkQG�VHULD�HVWH�IRUPDW �GLQWU-XQ�QXP U�LPSDU�GH�WHUPHQL� d) FkQG�VHULD�HVWH�IRUPDW �GLQ�P ULPL�UHODWLYH� e) FkQG�VHULD�HVWH�GH�PRPHQWH�LQHJDO�GLVWDQ DWH�

22) 0HWRGD�LQIOXHQ HORU�L]RODWH��³UHVWXOXL�QHGHVFRPSXV´��QX�VH�SRDWH�DSOLFD�DWXQFL�FkQG�

a) x x f f1 0 1 0= =; ;

b) x x f f1 0 1 0< <; ;

c) x x f f1 0 1 0< >; ;

d) x x f f1 0 1 0> <; ;

e) x x f f1 0 1 0> =; .

Page 26: STATISTICA - TESTE GRILA

23) 6H�FXQRVF�XUP WRDUHOH�GDWH�

Ramuri economice 'LQDPLFD�9$%�ID �GH������

(%) Structura VAB pe ramuri

(%) Industrie 95,0 36,8 $JULFXOWXU ���6LOYLFXOWXU 101,4 20,8 &RQVWUXF LL 78,2 7,9 Servicii 88,8 34,5

0RGLILFDUHD�SRSXOD LHL�RFXSDWH�vQ������ID �GH������D�IRVW�GH�-2%. 'LQDPLFD�SURGXFWLYLW LL�VRFLDOH�D�PXQFLL�������������D�IRVW�HJDO �FX�

a) 94,76%; b) 102,51%; c) 104,76%; d) 2,51%; e) 194,76%.

24) Cunoscând valorile observate (Yi��úL�FHOH�DMXVWDWH��UHFDOFXODWH�SULQWU-un model analitic ( �Yi ):

�Yi : 98; 109; 121; 145; 152 Yi: 99; 108; 119; 147; 152 &RHILFLHQWXO�GH�GHWHUPLQD LH�DO�PRGHOXOXL�GH�UHJUHVLH�SULQ�FDUH�V-a realizat ajustarea este egal cu:

a) 1,215; b) 0,095; c) 0,875; d) 0,962; a) 0,715.

25) Pentru estimarea fondului de salarizare necesar într-R�OXQ � OD�R�6&�FX�����GH�DQJDMD L��GLQ�FDUH�

���� DQJDMD L� SHUPDQHQW� úL� ��� �� FRODERUDWRUL�� V-a organizat un sondaj aleator stratificat SURSRU LRQDO��I U �UHYHQLUH��GH�YROXP�����GLQ�FROHFWLYLWDWHD�JHQHUDO ��'LQ�SUHOXFUDUHD�GDWHORU��GLQ�HúDQWLRQ�D�UH]XOWDW�XQ�VDODULX�PHGLX�DO�DQJDMD LORU�FX�FRQWUDFW�GH�PXQF �GH���PLO��OHL�úL�XQ�VDODULX�PHGLX�DO�DQJDMD LORU�vQ�UHJLP�GH�FRODERUDUH�GH���PLO� lei, iar dintr-R�FHUFHWDUH�DQWHULRDU �VH�úWLH�F �IDFWRUXO�ÄUHJLPXO�GH�DQJDMDUH´� LQIOXHQ HD] �YDULD LD�VDODULXOXL� vQ�SURSRU LH�GH��������)RQGXO�GH�salarizare estimat pentru întreaga S.C. (pentru o probabilitate de 0,9973, z � � =3), este:

a) (3,32 mil. lei; 4,28 mil. lei); b) (2568 mil. lei; 3504 mil. lei); c) (2656 mil. lei; 3424 mil. lei); d) (3,21 mil. lei; 4,38 mil. lei); e) (2800 mil. lei; 3280 mil. lei).

26) 2�FUHúWHUH�D�HILFLHQ HL�DFWLYLW LL�HFRQRPLFH�QX�VH�UHDOL]HD] �GDF � a) LQGLFHOH�GH�GLQDPLF �D�HILFLHQ HL�IRORVLULL fondurilor fixe este supraunitar; b) GLQDPLFD�SURGXF LHL�PDUI �GHYDQVHD] �GLQDPLFD�FDSLWDOXOXL�IL[� c) LQGLFHOH�GH�GLQDPLF �D�QHFHVDUXOXL�GH�PLMORDFH�IL[H�HVWH�VXSUDXQLWDU� d) indicele de dinaPLF �D�SURGXFWLYLW LL�PXQFLL�HVWH�VXSUDXQLWDU� e) GLQDPLFD�SURGXF LHL�PDUI �GHYDQVHD] �GLQDPLFD�QXP UXOXL�GH�VDODULD L�

Page 27: STATISTICA - TESTE GRILA

27) ÌQ�OXQD�LDQXDULH�������vQ�GRX �ILOLDOH�DOH�XQHL�ILUPH�V-DX�vQUHJLVWUDW�XUP WRDUHOH�GDWH�

- vQ�ILOLDOD�$��FHL�����DQJDMD L�UHSUH]HQWkQG�����GLQ�WRWDOXO�DQJDMD LORU�ILUPHL�PDX�UHDOL]DW�R�

SURGXF LH�GH�������PLO��OHL;

- în filiala B s-a realizat o productivitate medie a muncii de 3,1 mil. lei.

ùWLLQG�F �vQ�OXQD�IHEUXDULH�SURGXFWLYLWDWHD�PHGLH�D�PXQFLL�SH�DQVDPEOX�FHORU�GRX �ILOLDOH�D�IRVW�GH�

����PLOLRDQH� OHL�� LDU�QXP UXO� WRWDO�GH�DQJDMD L�D� IRVW�GH������PRGLILFDUHD�DEVROXW �D�SURGXF LHL� vQ�

OXQD�IHEUXDULH�ID �GH�LDQXDULH�SH�DQVDPEOXO�ILUPHL��GDWRUDW �PRGLILF ULL�QXP UXOXL�WRWDO�GH�DQJDMD L�

a fost:

a) 178,44 mil. lei;

b) 195,96 mil. lei;

c) 138 mil. lei;

d) 170,4 mil. lei;

e) 374,4 mil lei.

28) ÌQ�DQDOL]D�VWDWLVWLF �D�VH]RQDOLW LL�XQHL�6&5��LQGLFLL�GH�VH]RQDOLWDWH�VH�GHWHUPLQ �DWXQFL�FkQG�

a) IHQRPHQXO�DUH�R�HYROX LH�SH�WHUPHQ�OXQJ�DVHP Q WRDUH�XQHL�SURJUHVLL��JHRPHWULFH�

b) vQ� VHULD� FURQRORJLF � VH� FRQVWDW � F �PRGLILF ULOH� DEVROXWH� FX� ED] �PRELO � VXQW� DSUR[LPDWLY�

egale;

c) s-a utilizat pentru deteUPLQDUHD�WUHQGXOXL�R��PHWRG �PHFDQLF �

d) s-D�XWLOL]DW�SHQWUX�GHWHUPLQDUHD�WUHQGXOXL�R�PHWRG �DQDOLWLF �

e) FRPSRQHQWHOH�GH�WUHQG��RVFLODWRULH�úL�DOHDWRDUH�VH�FRPSXQ�GXS �XQ�PRGHO�PXOWLSOLFDWLY�

29) ,QGLFDWRUXO�VWDWLVWLF�ÄHQHUJLD�LQIRUPD LRQDO �2QLFHVFX´��HVWH�XWLOL]DW�vQ�DQDOL]D�VWDWLVWLF �D�

a) REOLFLW LL�

b) WHQGLQ HL�FHQWUDOH�

c) YDULD LHL�

d) FRQFHQWU ULL�GLYHUVLILF ULL�

e) EROWLULL�DSODWL] ULL�

30) ÌQ�FRQVWUXF LD�FRQWXULORU�PDFURHFRQRPLFH�GLQ�FDGUXO�6&1��QX�DUH�VROG�

a) FRQWXO�GH�UHSDUWL LH�D�YHQLWXULORU�

b) contul de creare a veniturilor;

c) FRQWXO�GH�SURGXF LH�

d) contul sintetic de bunuri;

Page 28: STATISTICA - TESTE GRILA

e) contul de modificare a patrimoniului.

31) 'DF �GLVWULEX LD�XQXL�ORW�GH�PLQJL��FRQIHF LRQDWH�GLQ�DFHODúL�PDWHULDO���vQ�IXQF LH�GH�GLPHQVLXQH��

HVWH�QRUPDO �úL�SHUIHFW�VLPHWULF ��DWXQFL�GLVWULEX LD�ORWXOXL�GXS �YROXP�HVWH�

a) SHUIHFW�VLPHWULF �

b) DVLPHWULF ��vQ�FDUH�SUHGRPLQ �YDORULOH�PDUL�

c) DVLPHWULF ��vQ�FDUH�SUHGRPLQ �YDORULOH�PLFL�

d) vQ�IRUP �GH�Ä8´�

e) QX�VH�SRDWH�SUHFL]D�IRUPD�GLVWULEX LHL�

32) ÌQ�GHWHUPLQDUHD�DJUHJDWHORU�PDFURHFRQRPLFH��LQGLFDWRULL�FDUH�H[SULP �Srodusul domestic iau în

calcul:

a) UH]XOWDWXO�DFWLYLW LL�SURGXFWLYH�D�WXWXURU�DJHQ LORU�GLQ�LQWHUiRUXO� ULL��QD LRQDOL�VDX�VWU LQL�

b) UH]XOWDWXO�DFWLYLW LL�SURGXFWLYH�D�WXWXURU�DJHQ LORU�QD LRQDOL�FDUH�úL-DX�GHVI úXUDW�DFWLYLWDWHD�

SH�WHULWRULXO� ULL�VDX�vQ�VWU LQ WDWH�

c) UH]XOWDWXO�DFWLYLW LL�SURGXFWLYH�D�DJHQ LORU�QD LRQDOL�FDUH�úL-DX�GHVI úXUDW�DFWLYLWDWHD�QXPDL�

SH�WHULWRULXO� ULL�

d) UH]XOWDWXO� DFWLYLW LL� SURGXFWLYH� D� DJHQ LORU� QD LRQDOL� FDUH� úL-DX� GHVI úXUDW� DFWLYLWDWHD� SH�

WHULWRULXO� ULL��FHO�SX in 11 luni, în cadrul unui an;

e) SURGXF LD�PHQDMHORU�SHQWUX�FRQVXPXO�SURSULX�

Page 29: STATISTICA - TESTE GRILA

TESTUL 4

1) ÌQ�6LVWHPXO�&RQWXULORU�1D LRQDOH��LPSR]LWHOH�LQGLUHFWH�QHWH�IDF�RELHFWXO�

a) GHELWXOXL�FRQWXOXL�³3URGXF LH´� b) FUHGLWXOXL�FRQWXOXL�´3URGXF LH´� c) VROGXOXL�FRQWXOXL�³3URGXF LH´� d) soldului contului “Venituri”; e) debitului contului de “Modificare a patrimoniului sectorului firme”.

2) 3UHVXSXQHP�F �VXQWH L�LQWHUHVD L�vQ�HIHFWXDUHD�WHVWXOXL�VWDWLVWLF�

H m

H ma

0 200

200

:

:

=>

úL�XWLOL]D L� UHJXOD�GH�GHFL]LH��³6H� UHVSLQJH�+0� GDF �PHGLD�HúDQWLRQXOXL�GH�����GH�XQLW L� HVWH�PDL�PDUH�GH����´��'HYLD LD�VWDQGDUG�vQ�SRSXOD LH�HVWH�GH�����3UREDELOLWDWHD�FRPLWHULL�XQHL�HURUL�GH�JHQXO�întâi este:

a) 13,36%; b) 6,68%; c) 43,32%; d) 0,4332; e) 3,34%.

3) 6DODULD LL� XQHL� VRFLHW L� FRPHUFLDOH� DX� XQ� VDODULX� PHGLX� GH� ���� PLL� OHL�� 3DWURQXO� KRW U úWH� V �

P UHDVF �VDODULXO�ILHF UXL�DQJDMDW�GH������RUL��1RXO�VDODULX�PHGLX�YD�IL�

a) 750 mii lei; b) 780 mii lei; c) 975 mii lei; d) 576,9 mii lei; e) 880 mii lei.

4) ,QFOXGHUHD� UHVXUVHORU�PLQHUDOH� vQ�DYX LD�QD LRQDO � VH� UHDOL]HD] �SULQ�FRQVWLWXLUHD�XQRU trepte de

DWUDJHUH�vQ�FLUFXLWXO�HFRQRPLF�DO�DFHVWRU�UHVXUVH��GLQ�SXQFW�GH�YHGHUH�DO�JUDGXOXL�GH�FXQRDúWHUH�D�DFHVWRUD� úL� DO�SRVLELOLW LORU�GH�H[SORDWDUH��1XP UXO�GH� WUHSWH� vQ� FDUH� VH�FXSULQG�DFHVWH� UHVXUVH�minerale sunt:

a) 2; b) 4; c) 3; d) 5; e) 8.

5) 1XP UXO�DQJDMD LORU�XQHL�FRPSDQLL�FDUH�DEVHQWHD] �OXQHD�DUH�DSUR[LPDWLY�R�GLVWULEX LH�3RLVVRQ��

LDU�QXP UXO�PHGLX�GH�DEVHQ L�GLQ�DFHDVW �]L�D�V SW PkQLL�HVWH������3UREDELOLWDWHD�FD�PDL�SX LQ�GH���DQJDMD L�V �DEVHQWH]H�vQWU-R�]L�GH�OXQL�D�V SW PkQLL�HVWH�

a) 25,10%; b) 19,31%; c) 2,6%;

Page 30: STATISTICA - TESTE GRILA

d) 51,84; e) 26,74%.

6) )LH�R�FROHFWLYLWDWH�VWDWLVWLF �VLVWHPDWL]DW �vQ�r�JUXSH�GXS �YDORULOH�FDUDFWHULVWLFLL�GH�JUXSDUH�;�úL�

în m�JUXSH�GXS �YDORULOH�YDULDELOHL�DQDOL]DWH�<�úL�SHQWUX�FDUH�V-au calculat dispersiile: σ 2 =

GLVSHUVLD� WRWDO �� σ i2 � GLVSHUVLLOH� GH� JUXS � � i r= 1, ), σ 2

�PHGLD� GLVSHUVLLORU� GH� JUXS �� δ 2 = dispersia dintre grupe.

&RQWULEX LD�IDFWRUXOXL�GH�JUXSDUH�;�OD�YDULD LD�JHQHUDO �D�YDULDELOHL�<�VH�P VRDU �FX�LQGLFDWRUXO�

a) R22

2= σ

σ;

b) R22

2= δ

σ;

c) R22

21= − δ

σ;

d)

( )R

n

n

y y n

n

i ii

r

ii

r

jj

m

j

jj

m2

2

1

1

1

2

1

=

−=

=

=

=

σ .

.

.

.

: ;

e)

( ) ( )R

y y n

n

y y n

n

j ij

m

i

r

ij

ijj

m

i

r

j jj

m

jj

m2 11

2

11

2

1

1

=

− −==

==

=

=

∑∑

∑∑

∑:

.

.

.

���/HJ WXULOH�GLQWUH�IHQRPHQHOH�HFRQRPLFR-VRFLDOH�GH�PDV �VXQW�

a) OHJ WXUL�IXQF LRQDOH� b) OHJ WXUL�FDUH�VH�VXSXQ�DF LXQLL�OHJLORU�VWRFKDVWLFH� c) OHJ WXUL�FH�SRW�IL�SXVH�vQ�HYLGHQ �OD�QLYHOXO�ILHF UHL�XQLW L�vQ�SDUWH� d) OHJ WXUL�FDUH�VH�VXSXQ�DF LXQLL�OHJLORU�GLQDPLFH� e) OHJ WXUL�XQLYRF�GHWHUPLQDWH�

���6H�FRQVLGHU �XQ�WDEHO�GH�FRQWLQJHQ ��FRUHOD LH��vQ�IRUPD�VD�JHQHUDO :

( )[ ]{ }x y n j J k Kj k jk, ; ,∈ ∈

&RYDULDQ D�GLQWUH�YDULDELOHOH�;�úL�<��&RY�;�<���FDOFXODW �SH�ED]D�WDEHOXOXL�HVWH�

a) ( ) ( )( )Cov X Yn

x x y y njk

k jj

, .= − −∑∑1;

b) Cov X Yn

x y n xyj k jkkj

( , ) = −∑∑1;

Page 31: STATISTICA - TESTE GRILA

c) ( ) ( )( )Cov X Yn

x x y yjk

kj

, = − −∑∑1;

d) Cov X Yn

x x

y yn

j

kij

kj

( , ) =−

−∑∑1;

e)

( )( )Cov X Y

x x y y n

n

j j ijkj

x y( , ) =

− −∑∑

σ σ.

9) 'DF � vQ� WDEHOXO� GH� FRQWLQJHQ � GHILQLW� OD� SUREOHPD� ��� QRW P� Ux x

jj

x=

−σ

� úL� Vy y

kk

y=

−σ

,

atunci: a) Cov X Y Cov U Vx y( , ) ( , )= σ σ ;

b) Cov X Y Cov U Vx y( , ) ( , )≠ σ σ ;

c) Cov X YCov U V

x y( , )

( , )=σ σ

;

d) Cov X Y Cov U V x y( , ) ( , )− = σ σ ;

e) Cov X Y Cov U VU V( , ) ( , )= σ σ . 10) 3UHFL]LD�HVWLP ULL�SDUDPHWULORU�SRSXOD LHL�JHQHUDOH�SH�ED]D�GDWHORU�GH�VRQGDM�GHSLQGH�GH�HURULOH�

GH�vQUHJLVWUDUH�úL�GH�HURULOH�GH�UHSUH]HQWDWLYLWDWH��3HQWUX�D�PD[LPL]D�SUHFL]LD�HVWLP ULORU�

a) HVWH� VXILFLHQW� V � VH� HOLPLQH� VXUVHOH� HURULORU� GH� vQUHJLVWUDUH� SULQ� GLIHULWH� PRGDOLW L� GH�verifLFDUH�D�YHULGLFLW LL�GDWHORU�FXOHVH�

b) HVWH�VXILFLHQW�V �DFRUG P�XQLW LORU�SRSXOD LHL�VWDWLVWLFH�úDQVH�HJDOH�GH�D�IL�LQFOXVH�vQ�HúDQWLRQ� c) HVWH� QHFHVDU� V � HOLPLQ P� HURULOH� GH� UHSUH]HQWDWLYLWDWH� SULQ� UHVSHFWDUHD� SULQFLSLLORU�

VHOHF LHL�DOHDWRDUH� d) este necesar� V � HOLPLQ P� HURULOH� GH� vQUHJLVWUDUH�� VXUVHOH� HURULORU� VLVWHPDWLFH� GH�

UHSUH]HQWDWLYLWDWH�úL�V �PLQLPL] P�HURULOH�DOHDWRDUH�GH�UHSUH]HQWDWLYLWDWH� e) HVWH� QHFHVDU� V � HOLPLQ P� HURULOH� GH� vQUHJLVWUDUH� úL� �QRQU VSXQVXULOH�� OD� vQWUHE ULOH� GLQ�

chestionare.

11) ClasifiFDUHD�DFWLYLW LORU�HFRQRPLFR-VRFLDOH�GLQ�HFRQRPLD�QD LRQDO � VH� UHDOL]HD] �SH�FDWHJRULL��GLYL]LXQL��JUXSH�úL�VDX�FODVH�

a) 2�FDWHJRULH�HVWH�PDL�RPRJHQ �GHFkW�R�GLYL]LXQH��JUXS �VDX�FODV � b) *UXSD�GH�DFWLYLW L�SUH]LQW �FHD�PDL�PDUH�RPRJHQLWDWH�vQ�UDSRUW�FX�FHOelalte; c) 2�JUXS �HVWH�PDL�RPRJHQ �GHFkW�R�FDWHJRULH�VDX�GLYL]LXQH��GDU�PDL�HWHURJHQ �GHFkW�R�FODV � d) &ODVD�GH�DFWLYLW L�HVWH�PDL�HWHURJHQ �GHFkW�R�FDWHJRULH��GLYL]LXQH�VDX�JUXS � e) 'LYL]LXQHD� HVWH� PDL� RPRJHQ � GHFkW� R� JUXS � VDX� FODV �� GDU� PDL� HWHURJHQ � GHFkW� R

FDWHJRULH�GH�DFWLYLW L�

&RQGL LD� QHFHVDU � FD� H[SUHVLD� ( ) ( )F y xi ii

β β β β0 1 0 12, = − −∑ V � ILH� PLQLP � HVWH� DFHHD� FD�

GHULYDWHOH�VDOH�SDU LDOH�vQ�IXQF LH�GH�β0�úL�β1�V �ILH�HJDOH�FX�]HUR�

Page 32: STATISTICA - TESTE GRILA

dF

d

dF

d

β

β

0

1

0

0

=

=

12) 6ROX LD�DFHVWXL�VLVWHP�GH�HFXD LL�HVWH�FXSOXO�GH�YDORri (b0, b1)�FRUHVSXQ] WRU�SDUDPHWULORU��β0, β1)

definit prin:

a) ( )

bCov x y

x1 2

=,

σ�úL�b y b x0 1= − ;

b) ( )

bCov x y

n x y1 =

,

σ σ�úL�b y b x0 1= − ;

c) b y b x1 0= − �úL�( )

bCov x y

x0 2

=,

σ;

d) b b y1 0= = ;

e) ( )

b bCov x y

x1 0 2

= =,

σ.

13) 6H� úWLH� F � ( ) ( )σ σy ii

y x i iir

y yn

y Y2 2 2 21 1= − = −∑ ∑; .� úL� ( )σ Y i

inY y2 21= −∑ � unde

�Y b b xi i= +0 1 ��'DF �U�HVWH�FRHILFLHQWXO�GH�FRUHOD LH�GLQWUH�YDULDELOHOH�<�úL�;�DWXQFL�

a) ( )σ σy x y r.2 2 21= − �úL�σ σ σy y x Y

2 2 2< +. ;

b) ( )σ σy x y r.2 2 21> − �úL�σ σ σy y x Y

2 2 2= +. ;

c) ( )σ σy x y r.2 2 21= − �úL�σ σ σy y x Y

2 2 2= +. ;

d) ( )σ σy x y r.2 2 21> − �úL�σ σ σy y x Y

2 2 2< +. ;

e) ( )σ σy x y r.2 2 21< − �úL�σ σ σy y x Y

2 2 2> +. .

14) 2� YDULDELO � FRPSOH[ �<� HVWH� H[SULPDW � vQ� IXQF LH� GH� IDFWRULL� D�E�F�G�H�I�J�K� D� F URU� LQIOXHQ �

WUHEXLH� L]RODW ��5HOD LD� GLQWUH�<� úL� IDFWRULL� V L� ILLQG�PXOWLSOLFDWLY �� SHUPLWH� R� GHVFRPSXQHUH� vQ�

trepte de forma:

Page 33: STATISTICA - TESTE GRILA
Page 34: STATISTICA - TESTE GRILA

b) 'DF �S�HVWH� SDU�� HVWH� QHFHVDU� V � FDOFXO P�PHGLL�PRELOH� SDU LDOH� GH� RUGLQXO���� DSRL� SH�ED]D� DFHVWRUD�� PHGLL� PRELOH� SDU LDOH� GH� RUGLQXO� ��� ú�D�P�G��� SkQ � DMXQJHP� OD� PHGLLOH�finale (valorile ajustate) plasate în dreptul termenilor reali;

c) 'DF �S�HVWH�LPSDU��VH�SLHUG�SULQ�DMXVWDUH�XQ�QXP U�GH�p +

1

2 termeni reali;

d) 'DF �S�HVWH�SDU��VH�SLHUG�SULQ�DMXVWDUH�XQ�QXP U�GH�S�WHUPHQL�UHDOL� e) 1XP UXO�YDORULORU�DMXVWDWH�HVWH�DFHODúL��LQGLIHUHQW�GH�QDWXUD�OXL� p N∈ .

17) ,QGLFHOH�PHGLX�GH�GLQDPLF �SHQWUX�XQ�RUL]RQW�de timp 1,T �VH�FDOFXOHD] �FD�PHGLH�JHRPHWULF �D�

LQGLFLORU�GH�GLQDPLF �FX�ED] �PRELO �GLQ�RUL]RQWXO�1,T ��FX�FRQGL LD�FD�DFHúWLD�V �SUH]LQWH�YDORUL�DSURSLDWH��V �ILH�RPRJHQL���$FHDVW �FRQGL LH�

a) HVWH�IDFXOWDWLY � b) este LPSRUWDQW �úL�WUHEXLH�UHVSHFWDW �GHRDUHFH�LQGLFHOH�PHGLX�VH�SRDWH�FDOFXOD�úL�vQ�IXQF LH�

doar de termenii extremi (y1� úL� \T�� I U � V � VH� LQ � VHDPD� GH� HYROX LD� IHQRPHQXOXL� vQ�interiorul orizontului de timp;

c) QX�HVWH�QHFHVDU �GHRDUHFH�HD�H[FOXGH�QHFHVLWDWHD�UHSUH]HQWDWLYLW LL�PHGLHL�FDOFXODWH�vQWU-o serie de date statistice;

d) QX� HVWH� QHFHVDU � GHRDUHFH� vQ� RULFH� VHULH� FURQRORJLF � � PHGLD� JHRPHWULF � VW � OD� ED]D�GHWHUPLQ ULL�LQGLFHOXL�PHGLX�GH�GLQDPLF �

e) WUHEXLH�UHVSHFWDW �QXPDL�DWXQFL�FkQG�RUL]RQWXO�GH�WLPS�1,T al seriei cronologice nu este mai mic de 5 ani.

18) 3HQWUX� GHWHUPLQDUHD� DJUHJDWHORU� PDFURHFRQRPLFH� VH� XWLOL]HD] � GDWH� GLQ� XUP WRDUHOH� FRQWXUL�

QD LRQDOH�����FRQWXO�VLQWHWLF�GH�EXQXUL�����FRQWXO�PRGLILF ULL�SDWULPRQLXOXL�����FRQWXO�GH�FUHDUH�D�vHQLWXULORU�����FRQWXO�SURGXF LH�����FRQWXO�GH�UHSDUWL LH�D�YHQLWXULORU�����FRQWXO�GH�UHGLVWULEXLUH�D�YHQLWXULORU�����FRQWXO�GH�ILQDQ DUH�D�PRGLILF ULL�SDWULPRQLXOXL�����FRQWXO�XWLOL] ULL�YHQLWXULORU�

&DUH�GLQWUH�YDULDQWHOH�GH�PDL�MRV�HVWH�IDOV �

a) Soldul contului 4) este produsul intern brut; b) 3URGXVXO�LQWHUQ�EUXW�OD�SUH XO�IDFWRULORU�HVWH�VROGXO�FRQWXOXL���� c) 9HQLWXO�QD LRQDO�HVWH�VROGXO�FRQWXOXL����

$IODUHD�QXP UXOXL�GH�termeni din care se FDOFXOHD] �PHGLLOH�mobile (ordinul de

filtraj = p∈ N)

P este par

Calcularea unei a doua sume mobile

(de ordinul 2)

Divizarea prin 2 P

Calculul sumelor mobile

Aflarea valorilor DMXVWDWH�úL�WUDVDUHD�trendului pe grafic

P este impar

Divizarea prin 2 P

Page 35: STATISTICA - TESTE GRILA

d) 9HQLWXO�QD LRQDO�GLVSRQLELO�HVWH�VROGXO�FRQWXOXL���� e) 9HQLWXO�QD LRQDO�GLVSRQLELO�HVWH�UHVXUV �SHQWUX�FRQWXO���.

19) Pe baza tabelului de date punctuale prezentat mai jos:

i 1 2 3 4 5 6 7 8 xi 1 2 1 3 2 1 1 2

FDOFXOD L�FXDUWLOHOH�Q1, Q2�úL�Q3. Valorile acestora sunt:

a) Q1=1; Q2=2; Q3=3; b) Q1=1; Q2=(1,2); Q3=2; c) Q1=3; Q2=(1,2); Q3=2; d) Q1=1; Q2=3; Q3=2; e) altele decât cele prezentate în variantele anterioare;

20) Într-o colectivitate s-DX�FXOHV�GDWHOH�SHQWUX�GRX �YDULDELOH�VWDWLVWLFH��RE LQkQGX-se: { } { }1;2;3;6;5;1;1;48,1 ==iix

{ } { }70;100;50;70;80;40;90;1008,1 ==iiy

ÌQ�SULYLQ D�RPRJHQLW LL�FHORU�GRX �VHULL��VH�SRDWH�DILUPD�

a) VHULD�DOF WXLW �GXS �YDULDELOD�;�HVWH�PDL�RPRJHQ �GHFkW�FHD�GXS �<� b) VHULD�IRUPDW �GXS �<�HVWH�PDL�RPRJHQ �GHFkW�FHD�GXS �;� c) VHULD�DOF WXLW �GXS �YDULDELOD�;�HVWH�PDL�RPRJHQ ��GHRDUHFH�YDORULOH�VXQW�PDL�PLFL� d) QX�VH�SRDWH�FRPSDUD�RPRJHQLWDWHD�FHORU�GRX �VHULL��ILLQG�YRUED�GH�YDriabile diferite; e) ILLQG�YRUED�GH�DFHHDúL�FROHFWLYLWDWH��RPRJHQLWDWHD�FHORU�GRX �VHULL�HVWH�DFHHDúL�

21) $QDOL]D L�XUP WRDUHOH�FDWHJRULL�GH�SHUVRDQH�GH����DQL�úL�SHVWH��GLQWU-R�SHULRDG �GH�UHIHULQ � ���SHUVRDQH�FDUH�QX�OXFUHD] ��QHDYkQG�XQ�ORF�GH�PXQF �����SHUVRDQH�FDUH�VXQW� vQ�F XWDUHD�

XQXL� ORF� GH�PXQF �� ���SHUVRDQH� FRQFHGLDWH����� SHUVRDQH�FDUH� VXQW� GLVSRQLELOH� V � vQFHDS � LPHGLDW�F XWDUHD�XQXL�ORF�GH�PXQF �����SHUVRDQH�vQ�F XWDUHD�SULPXOXL�ORF�GH�PXQF �����SHUVRDQH�FDUH��GXS �R�vQWUHUXSHUH�YROXQWDU �D�DFWLYLW LL��VROLFLW �UHOXDUHD�DFHVWHLD�����SHUVRDQH�VH]RQLHU�RFXSDWH�DIODWH�vQ�RFXSDUHD�XQXL�SHUPDQHQW�ORF�GH�PXQF � ÌQ� GHWHUPLQDUHD� QXP UXOXL� GH� úRPHUL� vQ� VHQVXO� GHILQL LHL� GDWH� GH� %LURXO� ,QWHUQD LRQDO� DO�0XQFLL��GHILQL LD�VWDQGDUG��VH�FXSULQGH�

a) �����úL��� b) 1,���úL��� c) �����úL��� d) �����úL��� e) �����úL���

���� /X P� vQ� FRQVLGHUDUH� WDEHOXO� GH� FRQWLQJHQ � �FRUHOD LH�� ( )[ ]{ }x y n j J k Kj k jk, ; ,∈ ∈ úL�

GLVWULEX LLOH� FRQGL LRQDWH� DOH� OXL� <� GH� ;� ( ){ }y n k Kk jk, , ,j fixat ∈ �� 3HQWUX� DFHVWHD� GLQ� XUP � VH�

FXQRVF�PHGLLOH�úL�GLVSHUVLLOH�

y xn

n yjj

jk kk

( ).

= ∑1úL� [ ]σ y j

jk j jk

k

xn

y y x n2 21( ) ( )

.= −∑ , cu n nj jk

k. = ∑ efectivul

�IUHFYHQ D��PDUJLQDO� ��DVRFLDW �YDULDQWHL�xj.

Dispersia variabilei Y (σ y2 ��vQ�IXQF LH�GH�HOHPHQWH�SUH]HQWDWH�vQ�LSRWH] �VH�SUH]LQW �DVWIHO�

Page 36: STATISTICA - TESTE GRILA

a) [ ]σ σy jj

y j jj

jnn x

nn y x y2 2 21 1= + −∑ ∑. .( ) ( ) ;

b) [ ]σ y jj

jn

n y x y2 21< −∑ . ( ) ;

c) σ σy jj

y jnn x2 21< ∑ . ( ) ;

d) [ ]σ σy jj

y j jj

jn

n xn

n y x y2 2 21 1= − −∑ ∑. .( ) ( ) ;

e) [ ]σ σy jj

y j jj

jnn x

nn y x y2 2 21 1> + −∑ ∑. .( ) ( ) �FX�FRYDULDQ D�GLQWUH�<�úL�FHLODO L�IDFWRUL�

GH�LQIOXHQ �FX�H[FHS LD�IDFWRUXOXL�;� 23) Luându-se în considerare elementele prezentate în ipoteza pUREOHPHL� ����� SURSRU LD� YDULD LHL�

PHGLLORU�FRQGL LRQDWH�vQ�GLVSHUVLD�JHQHUDO �D�YDULDELOHL�<�HVWH�QXPLW �JUDG�GH�GHWHUPLQD LH�úL�HVWH�

QRWDW �FX�Ry x.2 ��&DUH�GLQ�XUP WRDUHOH�DILUPD LL�QX�HVWH�DGHY UDW �

a) 0 12≤ ≤Ry x. ;

b) Ry x.2 0= �GDF �WRDWH�PHGLLOH�FRQGL LRQDWH�DOH�OXL�\�vQ�IXQF LH�GH�[�VXQW�HJDOH�vQWUH�HOH�

c) Ry x.2 1= GDF �ILHF UHL�YDORUL�[j�vL�FRUHVSXQGH�R�XQLF �YDORDUH�D�YDUDELOHL�\�

d) Ry x.2 0= � GDF � PHGLLOH� FRQGL LRQDWH� DOH� OXL� \� vQ� IXQF LH� GH� [� VXQW� GLVWLQFWH� GRX � FkWH�

GRX �

e) Ry x.2 �H[SULP �P VXUD�vQ�FDUH�IDFWRUXO�GH�LQIOXHQ �H[SOLF �YDULD LD�YDULDELOHL�\�

24) (URULOH�DOHDWRDUH�GH�UHSUH]HQWDWLYLWDWH�vQWkOQLWH�vQ�FD]XO�RUJDQL] ULL�RULF UXL�WLS�GH�VRQGDM�QX pot

fi evitate ci diminuate:

a) GHRDUHFH� XQLW LORU� GLQ� SRSXOD LLOH� VWDWLVWLFH� OL� VH� DFRUG � DFHHDúL� úDQV � GH� DSDUL LH� vQ�HúDQWLRDQH�

b) GHRDUHFH� vQ� HúDQWLRDQH� VH�FXSULQG�QXPDL�S U L�GLQ�SRSXOD LL� VWDWLVWLFH�úL�SULQ�XUPDUH�QX�pot reproduce identic, decât întâmpO WRU��VWUXFWXULOH�SRSXOD LLORU�GLQ�FDUH�DFHVWHD�DX�IRVW�extrase;

c) DWXQFL�FkQG�FRQWUROXO�GDWHORU�FXOHVH�VH�UHDOL]HD] �SULQ�FHOH�PDL�DGHFYDWH�PHWRGH d) DWXQFL�FkQG�VH�XWLOL]HD] �ED]H�GH�VRQGDM��DFWXDOL]DWH�FRUHVSXQ] WRU� e) DWXQFL�FkQG�VH�IRUPHD] �GLQ�DFHHDúL�SRSXOD LH�WRDWH�HúDQWLRDQHOH�SRVLELOH��FKLDU�GDF �HOH�

DX�DFHODúL�YROXP� 25) 3HQWUX� FRPSDUDUHD� SUH XULORU� SURGXVHORU� GLQWU-R� DU � FX� FHOH� GLQWU-R� DOW � DU � VH� XWLOL]HD] � XQ�

LQGLFH�GH�JUXS�GH�SUH �

Page 37: STATISTICA - TESTE GRILA

a) de tip Laspeyres; b) de tip Paasche; c) de tip Fischer; d) IRUPDW�GXS �PHWRGD�VXEVWLWXLULL�vQO Q XLWH� e) IRUPDW�GXS �PHWRGD�UHVWXOXL�QHGHVFRPSXV�

26) Estimatorul unui parametru θ�VH�QRWHD] � �θ ��$FHVW�HVWLPDWRU�HVWH�QHGHSODVDW�GDF �

a) GLIHUHQ D�GLQWUH�PHGLD�VD�úL�YDORDUHD�SDUDPHWUXOXL�HVWH�GLIHULW �GH�]HUR�( )M ( �θ θ− ≠ 0 ;

b) GDF �PHGLD�VD�HVWH�HJDO �FX�YDORDUHD�SDUDPHWUXOXL�( )M ( � )θ θ= ;

c) GLVSHUVLD� VD� HVWH� PLQLP � �D( � )θ → 0 FkQG� YROXPXO� HúDQWLRQXOXL� WLQGH� F WUH� YROXPXO�SRSXOD LHL�JHQHUDOH��n N→ );

d) dispersia sa este miniP �SHQWUX�XQ�YROXP�IL[DW�DO�HúDQWLRQXOXL� e) GLVSHUVLD�HVWLPDWRUXOXL�HVWH�PD[LPDO �

27) ÌQ�FDOFXOXO�SURGXFWLYLW LL�VRFLDOH�D�PXQFLL�VH�LD�vQ�FRQVLGHUDUH�

a) SRSXOD LD�RFXSDW �WRWDO � b) SRSXOD LD�DFWLY � c) SRSXOD LD�RFXSDW �WRWDO �GLQ�FDUH�VH�VFDGH�SRSXOD LD�GLQ�DUPDW � d) SRSXOD LD� RFXSDW � WRWDO � GLPLQXDW � FX� SRSXOD LD� RFXSDW � vQ� DUPDW � úL� FX� VDODULD LL�

RUJDQL]D LLORU�SROLWLFH�úL�REúWHúWL� e) SRSXOD LD�RFXSDW �WRWDO �GLPLQXDW �FX�VDODULD LL�RUJDQL]D LLORU�SROLWLFH�úL�REúWHúWL�

28) 3HQWUX� D� VWXGLD� HYHQWXDOD� LQIOXHQ a culorii DPEDODMXOXL� DVXSUD� XQXL� QRX� WLS� GH� V SXQ� VH�VWXGLD] �XQ�HúDQWLRQ�GH�����PHQDMH��6H�WULPLW�ILHF UXL�PHQDM�GLQ�HúDQWLRQ�SDWUX�EXF L�GH�V SXQ�GH�DFHHDúL�FRPSR]L LH��GLQ�WLSXO�DQDOL]DW��GDU�DPEDODWH�vQ�FXORUL�GLIHULWH��URúX��DOE��EOHX�úL�YHUGH���Pentru a testD�SUHIHULQ D�PHQDMHORU�R�OXQ �PDL�WkU]LX�ILUPD�SURGXF WRDUH�RIHU �JUDWXLW����EXF L�FX�FXORDUHD� GRULW � D� DPEDODMXOXL�� ÌQ� XUPD� VLVWHPDWL] ULL� GDWHORU� REVHUYDWH� V-D� RE LQXW� XUP WRDUHD�serie:

Culoarea 5RúX Alb Bleu Verde TOTAL Nr. menaje 51 74 30 45 200

Pentru o probabilitate 0,1%:

a) VH� UHVSLQJH� LSRWH]D� SRWULYLW� F UHLD� FXORDUHD� DPEDODMXOXL� QX� DU� LQIOXHQ D� YROXPXO�

YkQ] ULORU�GHRDUHFH� χ χcalc. ,, ,20 1%;3220 04 16 3= > = ;

b) VH�DFFHSW �LSRWH]D�SRWULYLW�F UHLD�FXORDUHD�DPEDODMXOXL�QX�DU�LQIOXHQ D�YROXPXO�YkQ] ULORU�deoarece 3,1604,20 2

3%;1,02

. =>= χχ calc ;

c) nu se poate lua nici o decizie deoarece 3,1623%;1,0

2. == χχ calc ;

d) VH� UHVSLQJH� LSRWH]D� DEVHQ HL� LQIOXHQ HL� FXORULL� DPEDODMXOXL� DVXSUD� YROXPXOXL� YkQ] ULORU�GLQ�WLSXO�GH�V SXQ�DQDOL]DW�GHRDUHFH� 3,1610 2

3%;1,02

. =<= χχcalc ;

e) nu se poate lua o decizie deoarece testul χ2 nu poate fi utilizat. 29) 1XP UXO�PD[LP� GH� HúDQWLRDQH� GH� DFHODúL� YROXP� Q� FDUH� SRW� IL� IRUPDWH� SULQ� DFHODúL� SURFHGHX�

DOHDWRU�vQ�YDULDQW �QHUHSHWDW ��I U �UHYHQLUH���GLQWU-R�SRSXOD LH�VWDWLVWLF �GH�YROXP�1�HVWH�

a) nN; b) Nn;

Page 38: STATISTICA - TESTE GRILA

c) ANn ;

d) CNn ;

e) n!.

30) 6H�QRWHD] � HVWLPDWRUXO� SDUDPHWUXOXL�θ cu �θ � LDU�PHGLD� úL� GLVSHUVLD� HVWLPDWRUXOXL� FX� [ ]M �θ � úL�

respectiv cu [ ]D �θ . Estimatorul �θ este abVROXW�FRUHFW�GDF �

a) este nedeplasat ( )M ( � )θ θ= �úL�FRQYHUJHQW��D( � )θ → 0 �GDF � n N→ );

b) M ( � )θ θ→ �úL�D( � )θ → 0 când n N→ ;

c) [ ]D �θ este minim , dar nenul ��SHQWUX�XQ�YROXP�IL[DW�DO�HúDQWLRQXOXL�

d) ( )M ( � )θ θ− ≠ 0 úL��D( � )θ → 0 ��GDF �n N→ ;

e) ( )M ( � )θ θ= , indiferent de valoarea dispersiei estimatorului (pentru orice [ ]D �θ ).

31) Statisticianul enJOH]� <XOH� ������� SUHFL]HD] � FRQGL LLOH� SH� FDUH� WUHEXLH� V � OH� vQGHSOLQHDVF �

LQGLFDWRULL�VLQWHWLFL�DL�UHSDUWL LLORU�VWDWLVWLFH�úL�DQXPH�

1) V �ILH�GHILQLW�vQ�PRG�RELHFWLY� 2) V �GHSLQG �GH�WRDWH�REVHUYD LLOH�GLQ�VHULH� 3) V �DLE �R�VHPQLILFD LH�FRQFUHW � 4) V �ILH�VLPSlu de calculat; 5) V �ILH�SX LQ�VHQVLELO�OD�IOXFWXD LLOH�GH�VHOHF LH� 6) V �VH�SUHWH]H�XúRU�OD�FDOFXOH�DOJHEULFH�

$FHVWH�FRQGL LL�vQ�WRWDOLWDWH�

a) sunt respectate de medie; b) sunt respectate de dispersie; c) VXQW�UHVSHFWDWH�GH�FRYDULDQ � d) sunt respectate de valoarea �PRGDO � e) QX�VXQW�UHVSHFWDWH�GH�QLFL�XQ�LQGLFDWRU�DO�WHQGLQ HL�FHQWUDOH�VDX�DO�YDULD LHL�

32) Media ( x �� D� XQXL� HúDQWLRQ�GH�PDUH�YROXP� � �n�� SRDWH� IL� FRQVLGHUDW � F �XUPHD] �R� GLVWULEX LH�

QRUPDO �GH�PHGLH� x 0 �úL�DEDWHUH�PHGLH�S WUDWLF ��HURDUH�PHGLH��σn

, în cazul unui sondaj simplu

cu revenire. Pentru o probabilitate 1-α intervalul de estimare (sau de încredere) a parametrului

0x este:

x x zn

− ≤0 ασ

Pentru ca preciziD� HVWLPD LHL� V � ILH�PDL�PLF � VDX� HJDO � FX� N�� �SUHFL]LH� IL[DW � vQ� YDORDUH�

UHODWLY ��GLQ� 0x �YROXPXO�HúDQWLRQXOXL�HVWH�

a) nz

k x≤ ⋅α σ2

2

2

02

;

Page 39: STATISTICA - TESTE GRILA

b) ( )nz

kCV≥ ⋅α

2

22�XQGH�&9� �FRHILFLHQWXO�GH�YDULD LH�

c) nk x

=σ 2

20

;

d) nz k

x= α σ2 2 2

0

;

e) PDL�PDUH�GH����GH�XQLW L� 33) 8Q� FRQWURORU� GH� FDOLWDWH� úWLH� F � SUREDELOLWDWHD� FD� SH� XQ� QRX� DXWRPRELO� V � J VHDVF � GHIHFWH�

YL]LELOH�GH�VXSUDID ��]JkULHWXUL��HVWH�GH��‰. Probabilitatea ca dintr-un lot de 2500 de automobile V �J VHDVF �H[DFW��2 automobile cu defecte vizibile este:

a) 7,5%; b) 3,66%; c) 92,5%; d) 7,32%; e) 15%.

34) Într-un proces de verificare a ipotezelor statistice nivelul de încredere reprezint probabilitatea:

a) α; b) 1-α; c) β; d) 1-β; e) α+β.

35) &RQWXO�³�3URGXF LH´�DO�VHFWRUXOXL�ILUPH�VH�SUH]LQW �VLQWHWLc astfel: 1. Cheltuieli pentru produse LQWHUPHGLDUH�úL�GH�LQYHVWL LL�GLQ�LPSRUW 2. Amortizarea capitalului fix 3. Impozite indirecte brute

���ÌQFDV UL�GLQ�YkQ]DUHD�GH�EXQXUL�F WUH�DOWH�VHFWRDUH -�YkQ] UL�GH�EXQXUL�GH�FRQVXP�F WUH�PHQDMH -�YkQ] UL�GH�SURGXF LH�LQWHUPHGLDU �F WUH�VHFWRUXO�SXEOLF -�YkQ] UL�SULQ�H[SRrt

���6XEYHQ LL�GH�H[SORDWDUH 5. Salarii ���'REkQ]L�úL�UHQWH 7. Profitul din DFWLYLWDWHD�GH�SURGXF LH

���,QYHVWL LL�EUXWH��LQFOXVLY�LPSRUWXULOH� -�LQYHVWL LL�EUXWH�vQ�EXQXUL�GH�FDSLWDO -�LQYHVWL LL�EUXWH�vQ�VWRFXUL

3H�ED]D�HOHPHQWHORU�DFHVWXL�FRQW�VH�SRW�FDOFXOD�PDL�PXO L�LQGLFDWRUL��&DUH�UHOD LH�GLQ�FHOH�SUH]HQWDWH�PDL�MRV�HVWH�IDOV �

a) 9DORDUHD�DG XJDW �OD�SUH XO�SLH HL� �9DORDUHD�DG XJDW �QHW �OD�SUH XO�IDFWRULORU�����������impozitele indirecte nete (3-4) + amortizarea capitalului fix (2);

b) 9DORDUHD� DG XJDW � EUXW � OD� SUH XO� IDFWRULORU� � YDORDUHD� DG XJDW � OD� SUH XO� IDFWRULORU�(5+6+7) + amortizarea (2);

c) 9DORDUHD�DG XJDW �QHW �OD�SUH XO�SLH HL� �9DORDUHD�DG XJDW �EUXW �OD�SUH XO�SLH HL�- amortizarea; d) Soldul contului: (1+2+3+4+5+6+7)-(8+9)=0; e) Soldul contului: (1+2+3+4+5+6+7)-(8+9)≠ 0.

Page 40: STATISTICA - TESTE GRILA

36) 6 � VH� SUHFL]H]H� FDUH� GLQ� VHULLOH� GH� UHSDUWL LH� FDUDFWHUL]DWH� SULQ� XUP WRDUHOH� VHWXUL� GH� YDORUL�SUH]LQW �R�DVLPHWULH�SR]LWLY �

a) x = 31 2, ; Me=31,2; Mo=31,2;

b) x = 2850; Me=3150; Mo=3300;

c) x = 151 25, ; Me=138,75; Mo=112,58;

d) x = 180 ��0H �����0R ����úL����� e) x = 0; Me=0; Mo=0.

����,QGLFLL�DQXDOL�DL�SUH XULORU�GH�FRQVXP�OD�P UIXrile alimentare în perioada 1991-1994 au fost:

Anul 1991 1992 1993 1994 Indice (an precedent = 100) 286,2 336,6 348,9 236,2

Sursa: Anuarul Statistic al României, 1995, pag. 411 ,QGLFHOH�PHGLX�DO�SUH XULORU�GH�FRQVXP�OD�P UIXULOH�DOLPHQWDUH�vQ�DFHDVW �SHULRDG �D�IRVW� a) 1,985; b) 298,50%; c) 301,975; d) 261,2%; e) 2,612.

����'DF � vQWU-R� VHULH�GH� UHSDUWL LH� UHOD LD�RELHFWLY �GLQWUH�GDWH� �[i�� FRQGXFH� OD�GHFL]LD� FD� WHQGLQ D�

FHQWUDO �V-R�FDUDFWHUL] P�FX�PHGLD�JHRPHWULF �� xg ) atXQFL�DEDWHUHD�PHGLH�S WUDWLF �ID �GH�WHQGLQ D�

FHQWUDO �HVWH�DFHD�YDORDUH��gx

σ pentru care avem:

a) log logσ xi

gig n

x

x=

∑1

2

;

b) ( )σ x i gi

g nx x= −∑1 2

;

c) σ xi gi

g n x x= −

∑1 1 1

2

;

d) ( )σ x i gi

g nx x= −∑1

;

e) σ xi

gig n

x

x=

∑1

.

����&LUFXLWXO�HFRQRPLF�UHIOHFW �vQ�HVHQ �WUDQ]DF LLOH�GLQWUH�VXELHFWHOH�HFRQRPLFH��ÌQ�FDGUXO�DFHVWRUD�XQ�ORF�LPSRUWDQW�vO�RFXS �WUDQ]DF LLOH�GH�SLD ��$FHVWHD�VXQW� a) transferuri curente (impozite, pensii, ajutoare sociale, etc.); E��VXEYHQ LL� c) transferuri de patrimoniu; d) transferuri unilaterale; e) transferuri bilaterale.

Page 41: STATISTICA - TESTE GRILA

����*UDILFHOH�VWDWLVWLFH�vQ�FRRUGRQDWH�SRODUH�VH�XWLOL]HD] �vQ�PRG�FXUHQW�SHQWUX�YL]XDOL]DUHD� D��RULF UHL�VHULL�GH�GDWH�VWDWLVWLFH� E��VHULLORU�GH�UHSDUWL LH� c) eYROX LHL�WUHQGXOXL�GLQ�HYROX LD�XQXL�IHQRPHQ� G��HYROX LHL�XQXL�IHQRPHQ�DIHFWDW�GH�RVFLOD LL�VH]RQLHUH� H��WHQGLQ HL�OHJ WXULL�GLQWUH�YDULDELOH�úL�DOHJHUHD�PRGHOXOXL�GH�UHJUHVLH�

Page 42: STATISTICA - TESTE GRILA

TESTUL 5

���5DWD�úRPDMXOXL�VH�FDOFXOHD] �FX�UHOD LD�

a) neocupatiocupati

ocupati

+;

b) munca de forta

neocupati;

c) ocupati

neocupati;

d) ani 15 de mare mai in varsta populatia

neocupati;

H��QLFL�XQD�GLQWUH�UHOD LLOH�SUHFHGHQWH� ���6H�FXQRVF�XUP WRDUHOH�GDWH�SULYLQG��QXP UXO�GH�IDFWXUL���vQWRFPLWH�GH�6�&���$QRQLPXV��65/�vQ�luna noiembrie 1997:

Data Nr. facturi Data Nr. facturi Data Nr. facturi 1 6 11 10 21 14 2 10 12 14 22 12 3 12 13 6 23 11 4 10 14 18 24 10 5 8 15 13 25 8 6 9 16 9 26 4 7 10 17 14 27 12 8 11 18 12 28 9 9 12 19 17 29 12

10 9 20 12 30 16

I II III Grupe de zile�GXS �

nr. de facturi

Nr. zile Grupe de ]LOH�GXS �

nr. de facturi

Nr. zile Intervale de timp

Nr. facturi

0 - 5 1 0 -5 1 0 - 6 55 6 - 11 13 6 - 10 16 7 - 14 90

11 - 15 13 11 - 15 10 15 - 22 103 15 - 20 3 16 - 20 3 23 - 30 82

A. IV B. V

Intervale ale QXP UXOXL�

zilnic de facturi

Nr. de zile

Intervale ale QXP UXOXL�

de facturi

Nr. de zile

( 0 - 5 ] 1 [ 0 - 5 ) 1 ( 5 - 10 ] 13 [ 5 - 10 ) 9 (10 - 15 ] 13 [10 - 15 ) 17 (15 – 20] 3 [15 – 20) 3

3RSXOD LD�VWDWLVWLF �VWXGLDW �HVWH�VWUXFWXUDW �úL�SUH]HQWDW �vQ�

Page 43: STATISTICA - TESTE GRILA

a) Tabelul I; b) Tabelul II; c) Tabelul III; d) Tabelul IV; e) Tabelul V.

3) Cadranul II al Tabelului Input- Output cuprinde:

D��YDORDUHD�DG XJDW �EUXW �

E��SURGXF LD�ILQDO �

F��SURGXF LD�LQWHUPHGLDU �

G��FRHILFLHQ LL�Fheltuielilor totale;

H��FRHILFLHQ LL�FKHOWXLHOLORU�GLUHFWH�

4) 3HQWUX�����GH�VDODULD L�DL�XQHL�VRFLHW L�FRPHUFLDOH��IRQGXO�GH�VDODUL]DUH�D�IRVW��vQWU-R�OXQ ��GH�����PLOLRDQH� OHL�� ùWLLQG� F � FHL� PDL� PXO L� GLQWUH� VDODULD L� DX� DYXW� XQ� VDODULX� GH� ���� PLL� OHL�� Lar FRHILFLHQWXO�GH�DVLPHWULH�DO�UHSDUWL LHL�GXS �VDODULX�D�IRVW�GH�-������FRHILFLHQWXO�GH�YDULD LH�D�IRVW��

a) 24,5%; b) 200%; c) -25,52%; d) 37,5%; e) 26,67%.

5) 'LVWULEX LD�XQXL�ORW�GH�DXWRPRELOH�GXS �FRQVXPXO�GH�FDUEXUDQW�OD�����NP�SDUFXUúL�HVWH�

IQWHUYDOH�GH�YDULD LH�D�FRQVXPXOXL��O� Nr. automobile 6,2 - 6,6 4 6,6 - 7,0 12 7,0 - 7,4 44 7,4 - 7,8 90 7,8 - 8,2 107 8,2 - 8,6 86 8,6 - 9,0 36 9,0 - 9,4 15 9,4 - 9,8 6

Total 400 Utilizând testul χ2� SHQWUX� YHULILFDUHD� FDUDFWHUXOXL� UHSDUWL LHL� Hmpirice, pentru

χ α = = =0 05 62 12 5916, ; ,l se poate afirma:

a) χ χcalc tab2 2> ;

b) QX� VH� DFFHSW � LSRWH]D� FRQIRUP� F UHLD� vQWUH� GLVWULEX LD� HPSLULF � úL� FHD� WHRUHWLF � H[LVW �FRQFRUGDQ �

c) χ calc2 3 44= , ;

d) χ calc2 8 12= , ;

e) χ calc2 12 5916= , .

Page 44: STATISTICA - TESTE GRILA

6) 2�FRPSDQLH�FDUH�SURGXFH�XQ�QRX�WLS�GH�vQJU ú PkQW�DJULFRO�HVWH�LQWHUHVDW �vQ�VWXGLHUHD�UHOD LHL�GLQWUH�SURGXF LD�GH�URúLL��<��úL�FDQWLWDWHD�GH�vQJU ú PkQW�DSOLFDW��;���2�VXSUDID �HVWH�GLYL]DW �vQ�RSW�SDUFHOH�GH�P ULPL�HJDOH�SH�FDUH�VXQW�DSOLFDWH�FDQWLW L�GLIHULWH�GH�vQJU ú PkQW��3URGXF LLOH�GH�URúLL��NJ��úL�FDQWLW LOH�GH�vQJU ú PkQW�DSOLFDW��NJ���vQUHJLVWUDWH�SHQWUX�ILHFDUH�SDUFHO �VXQW�

xi 1 1,5 2 2,5 3 3,5 4 4,5 yi 25 31 27 28 36 35 32 34

(FXD LD�GH�UHJUHVLH�SHWQUX�GHVFULHUHD�GHSHQGHQ HL�GLQWUH�FHOH�GRX �YDULDELOH�HVWH� a) � , ,y x= −24 45 2 38 ; b) � , ,y x= +2 38 24 45 ; c) � , ,y x= +24 45 2 38 ; d) � ,y x= +32 2 01 ; e) � ,y x= −32 2 01 ;

���'LPLQXHD] �DYX LD�QD LRQDO �

a) rezervele de devize; b) rezervele de aur; F��UH]HUYHOH�GH�PRQHG �QD LRQDO �GH LQXWH�GH�DOWH� UL� G��EXQXULOH�QD LRQDOH�DIODWH�SH�WHULWRULXO�DOWRU� UL� H��FUHDQ HOH�DVXSUD�DOWRU� UL�

8) Într-R�UHSDUWL LH�GH�IUHFYHQ H��IUHFYHQ D�UHODWLY �FXPXODW �FUHVF WRU�D�JUXSHL i�DUDW � a) QXP UXO�XQLW LORU�VWDWLVWLFH�FDUH�DX�YDORULOH�FDUDFWHULVWLFLL�PDL�PLFL�VDX�HJDOH�FX�xi;

E��SRQGHUHD�XQLW LORU�VWDWLVWLFH�GLQ�JUXSD�i�vQ�WRWDOXO�FROHFWLYLW LL�VWXGLDWH� c) QXP UXO�XQLW LORU�VWDWLVWLFH�FDUH�DX�YDORULOH�FDUDFWHULVWLFLL�PDL�PDUL�VDX�FHO�SX LQ�HJDle cu xi; d) ponderea unit LORU� VWDWLVWLFH� FDUH� DX� QLYHOXO� FDUDFWHULVWLFLL�PDL�PLF� VDX� HJDO� FX� xi, în

WRWDOXO�FROHFWLYLW LL�VWXGLDWH� e) SRQGHUHD� XQLW LORU� VWDWLVWLFH� FDUH� DX� QLYHOXO� FDUDFWHULVWLFLL�PDL�PDUH� VDX� HJDO� FX� xi, în

WRWDOXO�FROHFWLYLW LL�VWXGLDWH.

9) 8Q� DQDOLVW� ILQDQFLDU� HVWH� LQWHUHVDW� vQ� D� GHWHUPLQD� VDODULXO�PHGLX� DFRUGDW� DQJDMD LORU� ILUPHL�� (O�FXOHJH� GDWH� SULYLQG� VDODULXO� PHGLX� SH� ILHFDUH� GLQ� FHOH� SDWUX� ILOLDOH� DOH� ILUPHL� úL� IRQGXO� GH�salarizare:

Filiala Salariul mediu

(mii lei) Fondul de salarizare

(mil. lei) 1 540 45,90 2 620 33,48 3 480 16,80 4 700 19,60

6DODULXO�PHGLX�SH�vQWUHDJD�ILUP �HVWH� a) 573,168 mii lei; b) 585,5 mii lei; c) 825,325 mii lei; d) 460,5 mii lei; e) 632,375 mii lei.

Page 45: STATISTICA - TESTE GRILA

����5HSDUWL LD�YHQLWXULORU�HVWH�HYLGHQ LDW �vQ�FRQWXO� D��SURGXF LH� E��ILQDQ DUH� c) modificarea patrimoniului; d) redistribuirea venitului; e) contul sintetic de bunuri. 11) 8Q�IDEULFDQW�GH�DXWRPRELOH�GHWHUPLQ �F �����GLQ�UH]HUYRDUHOH�GH�EHQ]LQ �PRQWDWH�SH�PRGHOXO�

����� VXQW� GHIHFWH�� 'DF � �� PDúLQL� VRVHVF� SHQWUX� UHYL]LH�� SUREDELOLWDWHD� FD� �� GLQ� �� PDúLQL� V �necesite înlocuirea rezervorului este:

a) 22,69%; b) 9,72%; c) 12%; d) 30%; e) 70%. ����$QDOL]D L�XUP WRDUHOH�PRGDOLW L�GH�FRQWURO� 1) controlul de volum; 2) controlul cantitativ-numeric; 3) controlul financiar-contabil; 4) FRQWUROXO� ORJLF�� ��� FRQWUROXO� &XU LL� GH� FRQWXUL�� ��� WHVWH� GH� YHULILFDUH� D� VHPQLILFD LHL� LQGLFDWRULORU�FDOFXOD L� ÌQ� WRDWH� HWDSHOH� FHUFHW ULL� VWDWLVWLFH� HVWH� QHFHVDU � YHULILFDUHD� DXWHQWLFLW LL� GDWHORU� úL�eliminarea�HURULORU�GH�REVHUYDUH��FDOFXO�úL�HVWLPDUH��ÌQ�DFHVW�VHQV�HVWH�QHFHVDU� D�������������úL��� E�������������úL��� F�������������úL��� G�������������úL��� H�������������úL��� ����)DF�SDUWH�GLQ�IRU D�GH�PXQF � a) persoanele casnice; b) pensionarii; F��úRPHULL� G��SHUVRDQHOH�I U �XQ�ORF�GH�PXQF �FH�UHQXQ �V �PDL�FDXWH�ORF�GH�PXQF � H��QLFL�XQD�GLQ�FDWHJRULLOH�PHQ LRQDWH� 14) 3HQWUX� GLVWULEX LD� XQHL� YDULDELOH� DOHDWRDUH�� ;�� VH� FXQRDúWH� F � ( )P xi ≤ =151 33 0 5, , , valoarea

quartilei întâi este 105,86 iar�YDORDUHD�TXDUWLOHL�WUHL�HVWH��������6HULD�GH�GLVWULEX LH� D��HVWH�SURIXQG�DVLPHWULF �VSUH�YDORULOH�PLFL�DOH�YDULDELOHL� E��DUH�R�DVLPHWULH�PRGHUDW �SR]LWLY � F��DUH�R�DVLPHWULH�PRGHUDW �QHJDWLY � d) nu se poate preciza felul asimetriei; e) este profXQG�DVLPHWULF �VSUH�YDORULOH�PDUL�DOH�YDULDELOHL�

Page 46: STATISTICA - TESTE GRILA

15) 8Q�DQDOLVW�GH�PDUNHWLQJ�XUP UHúWH�vQ���OXQL�HIHFWXO�UHFODPHORU�DVXSUD�YHQLWXULORU�GLQ�YkQ] UL��(O�vQUHJLVWUHD] � FKHOWXLHOLOH� FX� UHFODPD� �;�� �PLOLRDQH� OHL�� úL� YHQLWXULOH� GLQ� YkQ] UL� �<�� �VXWH�milioane lei)��ÌQ�XUPD�SUHOXFU ULL�GDWHORU�RE LQH�

x y x x yii

ii

ii

i ii

= = = =∑ ∑ ∑ ∑15 10 55 372; ; ; ; ( )i = 1 5, �� ÌQ� LSRWH]D� XQHL� GHSHQGHQ H� � OLQLDUH��

HFXD LD�GUHSWHL�GH�UHJUHVLH�HVWH� a) � , ,y x= −0 7 0 1 ; b) � , ,y x= − +0 1 0 7 ; c) � ,y x= −2 0 7 ; d) � , ,y x= +3 7 5 5 ; e) � ,y x= 0 7 . ����$QDOL]D L�XUP WRDUHOH�QR LXQL� ��� DXWRQRPLH�� ��� FRQILGHQ LDOLWDWH����� WUDQVSDUHQ �� ��� VSHFLDOL]DUH����� SURSRU LRQDOLWDWH�� ���GHRQWRORJLH� SURIHVLRQDO �� ��� LQGHSHQGHQ � SROLWLF �� ��� HODERUDUHD� GHFL]LLlor; 9) argumentarea DF LXQLORU�GXS �GHFODQúDUHD�ORU������SUHOXFUDUHD�GDWHORU������REVHUYDUH� $FWLYLWDWHD�VWDWLVWLFLL�SXEOLFH�WUHEXLH�V �VH�GHVI úRDUH�UHVSHFWkQG�XUP WRDUHOH�SULQFLSLL� D�������������������úL��� E�������������������úL��� c) 3, 4, 5, 6,������úL��� G�������������������úL���� H��������������������úL���� ����5HFHQV PkQWXO�FD�PHWRG �GH�REVHUYDUH�VWDWLVWLF �

a) QX�SUHVXSXQH�FXOHJHUHD�GDWHORU�GH�OD�WRDWH�XQLW LOH�SRSXOD LHL�VWDWLVWLFH�ELQH�GHOLPLWDW � b) are exclusiv un caracter demografic; F��VH�vQFDGUHD] �vQ�VIHUD�REVHUY ULORU�FX�FDUDFWHU�SHUPDQHQW� G��VH�RUJDQL]HD] �FX�R�DQXPLW �SHULRGLFLWDWH�

e) VH�RUJDQL]HD] �RUL�GH�FkWH�RUL�6WDWLVWLFD�218�GHFODQúHD] �UHFHQV PLQWH�vQ� ULOH�PHPEUH� 18) ÌQ�PRG�VLQWHWLF�RIHUWD�QD LRQDO �GH�EXQXUL�úL�VHUYLFLL�HVWH�H[SULPDW �GH� a) VN; b) PNNpp; c) PNBpp; d) PNBpf; e) PIBpf.

����)LH�;�úL�<�GRL�YHFWRUL�FX�Q�FRPSRQHQWH� ( )X xi= ’�úL� ( )Y yi= ’cu i n= 1, . 'LVWDQ D�OXL�0LQNRYVNL�HVWH�GDW �GH�UHOD LD�

( )d X Y x yi ip

i

n p, = −

=

∑1

1

cu p N∈ * .

'DF �S� ���VH�RE LQH�GLVWDQ D�DEVROXW ��LDU�GDF �S� ���VH�RE LQH�GLVWDQ D�HXFOLGLDQ � 3ULQ�H[WHQVLH�V �FRQVLGHU P�R�SRSXOD LH�VWDWLVWLF �FX�Q�XQLW L�OD�FDUH�VH�REVHUY �YDULDELOHOH�x1, x2, ... , xr��0DWULFHD�GLVWDQ HORU�GLQWUH�XQLW L��FDOFXODWH�SHQWUX�ILHFDUH�SHUHFKH��xi, yi), cu elemente

de forma ( )d d x xij i j= , :

D��QX�SUH]LQW �LQWHUHV�SHQWUX�DQDOL]D�VWDWLVWLF �

Page 47: STATISTICA - TESTE GRILA

b) SUH]LQW �LQWHUHV�SHQWUX�DQDOL]D�YDULD LHL�úL�D�GHRVHELULORU��GLVLPLODULW LORU��GLQWUH�XQLW L� c��QX�SUH]LQW �LQWHUHV�SHQWUX�VWUXFWXUD�GDWHORU�FXOHVH� d) are toate elementele nenule;

e) DUH�FRPSRQHQWH�QXOH�SH�DPEHOH�GLDJRQDOH�úL�HOHPHQWHOH�VLPHWULFH�ID �GH�GLDJRQDOH�

20) 2�YDULDELO �DOHDWRDUH�;�XUPHD] �R�UHSDUWL LH�QRUPDO �GH�SDUDPHWULL� x �úL�σ 2 �GDF �DUH�GHQVLWDWHD�GH�UHSDUWL LH�

a) ( )1

2

1

22 2

2

σ π σexp − −

x x ;

b) ( )1 1

2 2

2

σ σexp − −

x x ;

c) ( )1

2

1

2 2

2

σ π σexp − −

x x ;

d) ( )1

2

1

2 2

2

σ π σexp − +

x x ;

e) ( )

2

22

1exp

2

1xx

σπσ.

21) 6H� FXQRDúWH� IDSWXO� F � PHGLD� H[SULP � WHQGLQ D� FHQWUDO � LDU� SH� DQVDPEOX� DEDWHULOH� YDORULORU�

LQGLYLGXDOH� ID � GH� HD� VH� FRPSHQVHD] � UHFLSURF�� &DUH� YDULDQW � GH� U VSXQV� QX� IRUPDOL]HD] �DILUPD LD�HIHFWXDW �

a) ( )x xii

n− =

=∑

1

0 ;

b) 1 1

01 x xi hi

n−

=

=∑ ;

c) x xi pi

n2 2

1

0−

=

=∑ ;

d) x

xi

gi

n

=∏ =

1

1 ;

e) x x x xh p g= = = .

unde: x �PHGLD�DULWPHWLF

xh �PHGLD�DUPRQLF

x p �PHGLD�S WUDWLF

xg �PHGLD�JHRPHWULF �

Page 48: STATISTICA - TESTE GRILA

22) Trecerea de la venituO�QD LRQDO�OD�YHQLWXO�GLVSRQLELO�VH�UHDOL]HD] �vQ�FDGUXO�FRQWXOXL�

a) repartizarea veniturilor; b) modificarea patrimoniului; F��ILQDQ DUH� d) redistribuirea veniturilor; H��QX�VH�UHDOL]HD] �vQ�FDGUXO�XQXL�DQXPLW�FRQW�PDFURHFRQRPLF�

23) Cifra de afaceri�D�XQHL�VRFLHW L�FRPHUFLDOH�D�FUHVFXW�vQ�SHULRDGD�LDQ�������- dec. 1996 cu 10% GH� OD� R� OXQ � OD� DOWD�� ÌQ� SURJUDPXO� VRFLHW LL� FRPHUFLDOH� HVWH� SUHY ]XW� FD� FLIUD� GH� DIDFHUL� vQ�perioada ian. 1990 -�GHF�������V �vQUHJLVWUH]H�XQ�LQGLFH�PHGLX�DQXDO�GH�������3HQWru perioada ian. 1996 - dec. 1998 indicele mediu anual care trebuie realizat este:

a) anti loglog , log ,79 1 3 45 11

24

;

b) anti loglog , log ,1 3 11

2

;

c) 120%; d) 95%; e) 118,1%.

24) 3HQWUX� DSUHFLHUHD� P VXULL� vQ� FDUH� XQ� IDFWRU� VHPQLILFDWLY� GH� LQIOXHQ � GHWHUPLQ � R� YDULDELO �GHSHQGHQW ��VH�FDOFXOHD] �DWkW�FRHILFLHQWXO�GH�FRUHOD LH�FkW�úL�UDSRUWXO�GH�FRUHOD LH��9DORULOH�FHORU�GRL�LQGLFDWRUL�ILLQG�LGHQWLFH�DWXQFL�OHJ WXUD�VWDWLVWLF �GLQWUH�FHOH�GRX �YDULDELOH�HVWH�

D��OLQLDU � E��KLSHUEROLF � F��SDUDEROLF � d) logiVWLF � H��H[SRQHQ LDO �

25) 8Q�úRPHU�FDUH�FDXW �XQ�ORF�GH�PXQF �vQWU-R�DQXPLW �LQGXVWULH�FXOHJH�LQIRUPD LL�GHVSUH�VDODULXO�RIHULW�GH�ILUPHOH�GLQ�DFHDVW �LQGXVWULH��3UHVXSXQHP�F �GLVWULEX LD�VDODULXOXL�RIHULW�DQJDMD LORU�GH�FDOLILFDUH�VLPLODU �SRDWH�IL�DSUR[LPDW �FX�R�GLVWULEX LH�QRUPDO �GH�PHGLH�����PLL� OHL�úL�DEDWHUH�PHGLH�S WUDWLF �GH�����PLL� OHL�� ÌQ�SOXV��SUHVXSXQHP�F �PXQFLWRUXOXL� L�VH�RIHU ������PLL� OHL�GH�F WUH�SULPD�ILUP �FRQWDFWDW ��3URSRU LD�RIHUWHORU�VDODULDOH�FDUH�DU�SXWHD�V �VH�VLWXH]H�SHVWH�DFHVW nivel este:

a) 4,01%; b) 8,02%; c) 54,01%; d) 91,98%; e) 45,99%.

26) 6H� FXQRDúWH� IDSWXO� F � vQWU-R� UDPXU � GH� DFWLYLWDWH� YDULDELOD� �VDODULXO� PHGLX� EUXW�� �<�� HVWH�GHSHQGHQW �SULQWUH�DOWHOH�GH��JUDGXO�PHGLX�GH�vQGHSOLQLUH�DO�QRUPHORU���;1��úL��JUDGXO�PHGLX de vQ]HVWUDUH� WHKQLF � D�PXQFLL�� �;2��� &RQWULEX LD� FHORU� GRL� IDFWRUL�;1 úL�;2� OD� YDULD LD� VDODULXOXL�PHGLX�EUXW��<��HVWH�HYDOXDW �SULQ�

a) R r ry x x y x y x/ , / /1 2 1 2

2 2 2= + ;

b) Rr r r r r

ry x x

y x y x y x y x x x

x x

/ ,/ / / /

1 21 2 1 1 2

1 2

2 22

2

2

1=

+ −

−;

Page 49: STATISTICA - TESTE GRILA

c) R r r r r ry x x y x y x y x y x x x/ , / / / /1 2 1 2 1 1 22 2

22= + − ;

d) rx x1 20= ;

e) Rr r

ry x x

y x y x

x x

/ ,/ /

1 21 2

1 2

2 2

21=

+

−.

����&RQVLGHU P�GDWHOH�

Ramura 9DORDUHD�DG XJDW �EUXW ��POG��OHL� (ILFLHQ D�PLMORDFHORU�IL[H 1 3000 0,5 2 1000 0,8

(ILFLHQ D�PLMORDFHORU�IL[H�SH�WRWDO�D�IRVW�

a) 0,5751; b) 0,6500; c) 0,5517; G��QX�SRDWH�IL�FDOFXODW � e) 1,3.

28) ÌQ� HYROX LD� VD� vQGHOXQJDW �� VWDWLVWLFD� V-a dezvoltat continuu atât sub aspectul obiectului de VWXGLX�� GDU�PDL� DOHV� DO� SHUIHF LRQ ULL� úL� GLYHUVLILF ULL�PHWRGHORU� GH� DERUGDUH� DOH� RELHFWXOXL�� ÌQ�WRDWH�PRPHQWHOH�GH]YROW ULL�VWDWLVWLFD�VH�RFXS �GH�DFHOe fenomene:

D��FDUH�VH�SURGXF�OD�R�DQXPLW �XQLWDWH�GH�REVHUYDUH� b) care se produc în mod identic; c) exclusiv tehnice;

d) care se produc într-XQ� QXP U� PDUH� GH� FD]XUL�� SUH]LQW � vQ� SURGXFHUHD� ORU� DQXPLWH�UHJXODULW L�úL�FDUH�SRW�IL�GHQXPLWH�IHQRPHQH�GH�PDV ;

H��FDUH�DX�OD�RULJLQH�XQ�VLQJXU�IDFWRU�GH�LQIOXHQ �

29) 8Q�HOHPHQW�LPSRUWDQW�DO�XQXL�SURJUDP�GH�REVHUYDUH�HVWH�WLPSXO�REVHUY ULL��$FHVWD� D��HVWH�WLPSXO�OD�FDUH�VH�UHIHU �GDWHOH�VDX�WLPSXO�vQUHJLVWU ULL�GDWHORU�

b) nu este altceva decât timpul la care se reIHU � GDWHOH� FXOHVH�� FDUH� SRDWH� IL� XQ� VLQJXU�PRPHQW��SHQWUX�vQUHJLVWU ULOH�VWDWLFH��VDX�R�SHULRDG ��SHQWUX�vQUHJLVWU ULOH�GLQDPLFH��

F��QX�HVWH�DOWFHYD�GHFkW�SHULRDGD�vQ�FDUH�VH�vQUHJLVWUHD] �GDWHOH�VWDWLVWLFH� d) HVWH�SULYLW�úL�SULQ�XUPDUH�SUHFL]DW�FD�WLPS�OD�FDUH�VH�UHIHU �GDWHOH�FXOHVH�úL�FD�LQWHUYDO�GH�

WLPS�vQ�FDUH�VH�UHDOL]HD] �vQUHJLVWUDUHD�GDWHORU� e) nu este altceva decât data la care operatorii statistici trebuie s prezinte datele culese.

����'LVSHUVLD��FDOFXODW �SULP�PHWRGD�PRPHQWHORU��HVWH�

a) momeQWXO�LQL LDO�GH�RUGLQXO�GRL� b) PRPHQWXO�LQL LDO�GH�RUGLQXO�SDWUX�vPS U LW�OD�PRPHQWXO�LQL LDO�GH�RUGLQXO�GRL�OD�S WUDW�

F��PRPHQWXO�FHQWUDW�GH�RUGLQXO�GRL�OD�S WUDW� d) PRPHQWXO�LQL LDO�GH�RUGLQXO�GRL�PLQXV�PRPHQWXO�LQL LDO�GH�RUGLQXO�vQWkL�OD�S WUDW� e) momentul�FHQWUDW�GH�RUGLQXO�GRL�PLQXV�PRPHQWXO�LQL LDO�GH�RUGLQXO�XQX�OD�S WUDW�

31) Scala de interval:

D��DUH�WRDWH�FDUDFWHULVWLFLOH�VFDOHORU�RUGLQDOH�úL�GH�UDSRUW� b) DUH� WRDWH� FDUDFWHULVWLFLOH� VFDOHL� RUGLQDOH� úL� vQ� SOXV�� GLVWDQ D� VDX� GLIHUHQ D� GLQWUH� GRX �

numere�DOH�VFDOHL�DUH�VHPQLILFD LH�FRQFUHW �

Page 50: STATISTICA - TESTE GRILA

c) HVWH�R�VFDO �QXPHULF �úL��vQ�SOXV��UDSRUWXO�GLQWUH�GRX �SXQFWH�DOH�VFDOHL�HVWH�LQGHSHQGHQW�GH�XQLWDWHD�GH�P VXU �

G��SUH]LQW �PXOWH�GLQ�FDUDFWHULVWLFLOH�VFDOHL�RUGLQDOH� H��PDL�HVWH�QXPLW �úL�VFDO �GH�UDSRUW�VDX�VFDO �GLVFUHW �

32) Într-R�UHSDUWL LH�QRUPDO �YDORDUHD�ID �GH�FDUH�����GLQ�YDORULOH� LQGLYLGXDOH�VXQW�PDL�PLFL�� LDU�75% din valorile individuale sunt mai mari este:

a) cuartila a doua; b) cuartila a treia; c) cuartila întâi; G��YDORDUHD�PRGDO � e) valoarea�PHGLDQ �

33) 2�DJHQ LH�GH� vQFKLULDW�DXWRPRELOH�KRW U úWH� V -VL�YkQG �DXWRPRELOHOH�GXS �XWLOL]DUHD�DFHVWRUD�timp de un an. Managerul firmei presupune c �GLVWDQ D�SDUFXUV �GH�PDúLQL�LQIOXHQ HD] �FRVWXO�GH�vQWUH LQHUH�DO�DXWRYHKLFXOHORU�úL�GHFL�SUH XO�GH�YkQ]DUe al acestora. Pentru a verifica presupunerea VD��VH�vQUHJLVWUHD] ��SHQWUX�����GH�PDúLQL��GLVWDQ D�SDUFXUV �vQ�XOWLPXO�DQ��PLL�NP��úL�FRVWXO�GH�vQWUH LQHUH��VXWH�PLL�OHL���6H�DOF WXLHVF�DVWIHO���JUXSH�GXS �GLVWDQ D�SDUFXUV ��VXE����PLL�NP�����- 60 mii km, 60 -����PLL�NP�úL����VDX�SHVWH����PLL�NP�� ÌQ�XUPD�VLVWHPDWL] ULL�GDWHORU�� VH�RE LQ�XUP WRDUHOH�LQIRUPD LL�

&RVWXO�vQWUH LQHULL��VXWH�PLL�OHL�

*UXSH�GXS �GLVWDQ D SDUFXUV ��PLL�NP�

5 - 7 7 - 9 9 - 11 11 - 13

Total

sub 40 16 32 12 - 60 40 - 60 10% 25% 35% 30% 100%

ÌQ� JUXSD� D� WUHLD� GXS � GLVWDQ D� SDUFXUV � ���-80 mii km) s-au înregistrat date pentru 40 de PDúLQL��FRVWXO�PHGLX�GH�vQWUH LQHUH�ILLQG�����������OHL��FX�XQ�FRHILFLHQW�GH�YDULD LH�GH����������LDU�vQ�JUXSD�D�SDWUD� ���� úL�SHVWH����PLL�NP�� V-au îQFDGUDW�����GLQ�PDúLQL�� FKHOWXLHOLOH� WRWDOH�DX� IRVW������������OHL��LDU�DEDWHUHD�PHGLH�S WUDWLF ����PLL�OHL� 'LVWDQ D�SDUFXUV �LQIOXHQ HD] �YDULD LD�FKHOWXLHOLORU�GH�vQWUH LQHUH�vQ�SURSRU LH�GH� a) 51,04%; b) 71,44%; c) 48,96%; d) 69,97%; e) 28,56%. 34) ÌQ� XWLOL]DUHD� PHWRGHL� WDEHOXOXL� GH� FRUHOD LH� SHQWUX� DQDOL]D� OHJ WXULORU� GLQWUH� IHQRPHQH�� GDF �

IUHFYHQ HOH�VXQW�DSUR[LPDWLY�HJDO�UHSDUWL]DWH�vQ�LQWHULRUXO�WDEHOXOXL��DWXQFL� D��OHJ WXUD�HVWH�QHOLQLDU � E��OHJ WXUD�HVWH�OLQLDU �GLUHFW � F��OHJ WXUD�HVWH�LQYHUV � G��OHJ WXUD�HVWH�GLUHFW � H��OHJ WXUD�HVWH�VODE �VDX�QX�H[LVW �OHJ WXU între variabile. 35) Într-R� VHULH� VWDWLVWLF �� vQWUH� SULQFLSDOHOH� WLSXUL� GH� PHGLL� �PHGLD� DULWPHWLF �� PHGLD� DUPRQLF ��

PHGLD�S WUDWLF ��PHGLD�JHRPHWULF ��H[LVW �XUP WRDUHD�UHOD ie:

a) x x x xh g p≤ ≤ ≤ ;

b) x x x xg h p≤ ≤ ≤ ;

Page 51: STATISTICA - TESTE GRILA

c) x x x xh p g≤ ≤ ≤ ;

d) x x x xh g p≤ ≤ ≤ ;

e) x x x xh g p= = = ��GDF �VHULD�HVWH�SHUIHFW�VLPHWULF � 36) 3HQWUX� R� VHULH� GH� GLVWULEX LH� GH� IUHFYHQ H� FX� WHQGLQ � GH� QRUPDOLWDWH�� DEDWHUHD� PHGLH� OLQLDU �

( d x ��ID �GH�DEDWHUHD�WLS��σ x ) este:

a) d x x> σ ;

b) d x x= σ ;

c) d x x≈ 4

5σ ;

d) d x x≈ 2

3σ ;

e) d x x≈ σ 2 . 37) VHQLWXO�EUXW�GLVSRQLELO�OD�QLYHOXO�HFRQRPLHL�QD LRQDOH�VH�FDOFXOHD] � a) VN+Amortizarea; E��91�6ROGXO�YHQLWXULORU�GLQ�WUDQVIHUXUL�vQ�UDSRUW�FX�VWU LQ WDWHD� c) b) + Amortizarea; d) a) -�6ROGXO�YHQLWXULORU�GLQ�WUDQVIHUXUL�vQ�UDSRUW�FX�VWU LQ WDWHD� e) PIB - b). 38) 8Q�GLVWULEXLWRU�GH�VXFXUL�OLYUHD] �FDUWRDQH�GH�FkWH���VWLFOH�úL�FXQRDúWH�SUREDELOLWDWHD��S ������FD�

R� VWLFO � V � VH� VSDUJ � SH� GXUDWD� WUDQVSRUWXOXL�� 'DF � VH� WUDQVSRUW � ����� GH� FDUWRDQH�� QXP UXO�FDUWRDQHORU�vQ�FDUH�VH�YRU�J VL�GRX sau mai multe sticle sparte este de aproximativ:

a) 85; b) 14; c) 3960; d) 41; e) 40. ����&DUH�GLQ�REVHUY ULOH�VWDWLVWLFH�SUHFL]DWH�PDL�MRV�QX�DX�XQ�FDUDFWHU�SHUPDQHQW� D��EXJHWHOH�GH�IDPLOLH��VDX�DQFKHWHOH�LQWHJUDWH�vQ�JRVSRG ULL�� b) rapoartele statistice; c) statisticile fiscale; G��vQUHJLVWU ULOH�F V WRULLORU��QDWDOLW LL��PRUWDOLW LL��HWF�� H��UHFHQV PLQWHOH�VWDWLVWLFH�

Page 52: STATISTICA - TESTE GRILA

TESTUL 6

1) ÌQWUH�3,%�úL�31%�H[LVW �QXPDL�UHOD LD�

a) >; b) <; c) =; d) ≥ ; e) ≤ ≥ .

2) Într-o serie de reparWL LH�SH�LQWHUYDOH�IRUPDW �GXS �R�DQXPLW �YDULDELO ��YDORDUHD�VD�PRGDO �HVWH�

LQIOXHQ DW �GH�

a) OLPLWHOH�LQIHULRDUH�úL�VXSHULRDUH�DOH�LQWHUYDOHORU�H[WUHPH�

b) GH�IUHFYHQ HOH�GH�DSDUL LH�DOH�LQWHUYDOHORU�HJDOH�VDX�QHHJDOH�

c) GH�P ULPHD�HJDO �VDX�QHHJDO �D�LQWHUYDOHORU�GH�YDULD LH�

d) GH�OLPLWD�LQIHULRDU �D�LQWHUYDOXOXL�PRGDO�

e) GH�OLPLWD�LQIHULRDU ��GH�IUHFYHQ HOH�LQWHUYDOXOXL�PRGDO��SUHPRGDO�úL�SRVWPRGDO�

3) Într-XQ�VSLWDO������GLQ�SDFLHQ LL�LQWHUQD L�P QkQF �UHJLP�I U �VDUH��$OF WXLQG�JUXSXUL�GH�FkWH���

SDFLHQ L��SUREDELOLWDWHD�FD�H[DFW���SDFLHQ L�V � LQ �UHJLP�I U �VDUH�HVWH�

a) 0,015625; b) 0,2344; c) 0,9375; d) 0,50; e) 0,0468.

4) 3UHFL]D L�FDUH�QX�HVWH�SULQFLSDO �IXQF LH�D�LQGLFDWRULORU�VWDWLVWLFL�

a) GH�P VXUDUH� b) GH�DQDOL] �VDX�VLQWH] � c) GH�YHULILFDUH�D�LSRWH]HORU�úL�VDX�GH�WHVWDUH�D�VHPQLILFD LHL�SDUDPHWULORU�XWLOL]D L� d) de fundamentare a deciziilor; e) de estimare.

5) 3URGXVXO� JOREDO� EUXW� FUHúWH� vQWU-R� SHULRDG � FX� ���� LDU� SRQGHUHD� FRQVXPXOXL� LQWHUPHGLDU� vQ�

produsul global brut scade de la 64% la 60%. Produsul intern brut:

a) FUHúWH�FX�������� b) scade cu 28,8%; c) FUHúWH�FX������� d) FUHúWH�FX����� e) FUHúWH�FX�������

Page 53: STATISTICA - TESTE GRILA

6) ÌQ�WHVWDUHD�LSRWH]HL�VWDWLVWLFH�SULYLWRDUH�OD�SDUDPHWUXO�³PHGLD�SRSXOD LHL´�

H m m

H m ma

0 0

0

:

:

=<

FkQG�GDWHOH�SURYLQ�GH�OD�XQ�HúDQWLRQ�GH�YROXP�UHGXV��UHJLXQHD�FULWLF �HVWH�GDW �GH�

a) z z< − α ;

b) z z< − α / 2 ;

c) t t n< − α , ;

d) t t n< − α / ,2 ;

e) t t n< − −α , 1 .

7) &DUH�GLQ�XUP WRDUHOH�DILUPD LL�SULYLQG�PHGLD�DULWPHWLF �HVWH�DGHY UDW �

a) VXPD� S WUDWHORU� WXWXURU� DEDWHULORU� LQGLYLGXDOH� DOH� WHUPHQLORr seriei de la media lor DULWPHWLF �HVWH�]HUR�

b) P ULPHD� PHGLHL� DULWPHWLFH� HVWH� FXSULQV � vQWUH� [min� úL� [max� GRDU� GDF � VHULD� SUH]LQW � R�WHQGLQ �FODU �GH�VLPHWULH�

c) SHQWUX�R�VHULH�GH�GLVWULEX LH�GH�IUHFYHQ H��PHGLD�DULWPHWLF ��FDOFXODW �SH�ED]D�IUHFYHQ HORU�reGXVH�GH�F�RUL�HVWH�PDL�PLF �GHFkW�PHGLD�VHULHL�LQL LDOH�GH�F�RUL�

d) PHGLD�SURGXVXOXL�D�GRX �YDULDELOH�DOHDWRDUH��HVWH�HJDO �FX�SURGXVXO�PHGLLORU�FHORU�GRX �variabile;

e) SHQWUX�R� VHULH� GH� GLVWULEX LH� GH� IUHFYHQ H��PHGLD� FDOFXODW � SH� ED]D� IUHFYHQ HORU� UHODWLYH�eVWH�HJDO �FX�PHGLD�DULWPHWLF �GHWHUPLQDW �SH�ED]D�IUHFYHQ HORU�DEVROXWH�

8) $QDOL]D� IHQRPHQXOXL� GH�FRQFHQWUDUH� �� GLYHUVLILFDUH�QX�DUH� VHQV�DWXQFL� FkQG�JUXSDUHD� XQLW LORU�

FROHFWLYLW LL�V-a efectuat:

a) pe variante; b) SH�LQWHUYDOH�HJDOH�GH�YDULD LH� c) GXS �R�FDUDFWHULVWLF �GH�VSD LX� d) GXS �R�FDUDFWHULVWLF �DOWHUQDWLY � e) GXS �R�FDUDFWHULVWLF �QHQXPHULF �

9) 7LPSXO�REVHUY ULL�VDX�DO�FXOHJHULL�GDWHORU�VH�DOHJH�

a) vQWRWGHDXQD�vQ�SHULRDGD�vQ�FDUH�SRSXOD LD�VWDWLVWLF �SUH]LQW �XQ�PDUH�JUDG�GH�VWDELOLWDWH� b) vQ�IXQF LH�GH�VFRSXO�FHUFHW ULL�úL�DO�REVHUY ULL�VWDWLVWLFH��GXS �FD]��FkQG�SRSXOD LD�VWDWLVWLF �

SUH]LQW � VDX� QX� XQ� JUDG� PDUH� GH� VWDELOLWDWH� �GH� H[HPSOX� UHFHQV PkQWXO� SRSXOD LHL��REVHUYDUHD�FRWD LLORU�OD�EXUV �D�XQRU�DF LXQL��HWF���

c) vQ�IXQF LH�GH�SRVLELOLW LOH�LQIRUPDWLFH�GH prelucrare a datelor culese; d) DWXQFL�FkQG�VH�GRUHúWH�V �VH�MXVWLILFH�R�DQXPLW �DF LXQH�GHMD�GHFODQúDW � e) OD�vQWkPSODUH��I U �FULWHULL�SUHFL]DWH�úL�DQDOL]DWH�DSULRULF�

10) Într-R� FROHFWLYLWDWH� VWDWLVWLF �� GDF � GLYHUVLILFDUHD� HVWH� PD[LP � �úL�� HYLGHQW� FRQFHQWUDUHD este PLQLP ��DWXQFL�FRHILFLHQWXO�GH�FRQFHQWUDUH�&RUUDGR-Gini este:

Page 54: STATISTICA - TESTE GRILA

a) G=1;

b) Gn

= 1;

c) Gn

= 1;

d) G=0;

e) G n= . 11) ÌQ�FRQWXO�PDFURHFRQRPLF�³9HQLWXUL´��UHVXUVHOH�VH�IRUPHD] �GLQ�

a) $PRUWL]DUH�úL�3,1pp; b) PIBpp�úL�VXEYHQ iile de exploatare; c) PIBpp�úL�LPSR]LWHOH�LQGLUHFWH� d) Amortizare, PIBpp�úL�VXEYHQ LLOH�GH�H[SORDWDUH� e) $PRUWL]DUHD��LPSR]LWH�LQGLUHFWH�úL�LPSR]LWH�SH�LPSRUWXUL�

12) 6 �VH�SUHFL]H]H�FDUH�GLQ�XUP WRDUHOH�DILUPD LL�QX�HVWH�DGHY UDW �

a) vQ�RULFH�UHSDUWL LH�VLPHWULF ��XQLPRGDO �� x Me Mo= = ; b) într-R�UHSDUWL LH�XQLPRGDO ��XúRU�DVLPHWULF ��PHGLDQD�VH�SODVHD] �vQWUH�PHGLH�úL�PRG� c) într-R�UHSDUWL LH�XQLPRGDO ��XúRU�DVLPHWULF ��PHGLD�VH�SODVHD] �vQWUH�PRG�úL�PHGLDQ � d) într-R�UHSDUWL LH�XQLPRGDO �SR]LWLY�vQFOLQDW �F tre valorile mici x Me Mo< < ; e) într-R� UHSDUWL LH� XQLPRGDO � SR]LWLY� vQFOLQDW � F WUH� YDORULOH� PDUL�� PRGXO� VH� VLWXHD] � OD�

VWkQJD�PHGLDQHL�úL�D�PHGLHL� 13) 8Q� DQDOLVW� HFRQRPLF� VWXGLD] � GLVWULEX LD� ILUPHORU� GXS � SURFHQWXO� GLQ� YHQLWXUL� FKHOWXLW� SHQWUX�

cercetare-GH]YROWDUH��3HQWUX�D�YHULILFD�LSRWH]D�QRUPDOLW LL�HPSLULFH�RE LQXWH��HO�XWLOL]HD] �WHVWXO�

χ2�úL�RE LQH��SHQWUX�XQ�QXP U�GH�JUDGH�GH�OLEHUWDWH��O ����YDORDUHD� χ calc2 18 30= , . Probabilitatea

PD[LP �FX�FDUH�VH�JDUDQWHD] �UH]XOWDWXO�HVWH�

a) 75%; b) 90%; c) 95%; d) 99%; e) 97,5%.

14) &DUH�GLQ�XUP WRDUHOH�DILUPD LL�UHIHULWRDUH�OD�FRHILFLHQWXO�GH�YDULD LH�QX�HVWH�DGHY UDW �

a) HVWH�XQ�LQGLFDWRU�VLQWHWLF�DO�vPSU úWLHULL� b) HVWH�H[SUHVLD�UHODWLY �D�DEDWHULL�PHGLL�S WUDWLFH� c) YDORUL�PLFL�DOH�FRHILFLHQWXOXL�GH�YDULD LH�VHPQLILF �XQ�JUDG�PDUH�GH� UHSUH]HQWDWLYLWDWH�D�

mediei caracteristicii studiate; d) YDORUL�PLFL�DOH�FRHILFLHQWXOXL�GH�YDULD LH�UHIOHFW �R�WHQGLQ �DFFHQWXDW �GH�VLPHWULH�D�GLVWULEX LHL� e) YDORUL�PLFL�DOH�FRHILFLHQWXOXL�GH�YDULD LH� UHIOHFW �RPRJHQLWDWHD�FROHFWLYLW LL�GLQ�SXQFWXO�

de vedere al caracteristicii studiate. 15) 2� FDUDFWHULVWLF � LPSRUWDQW � GH� FDOLWDWH� SHQWUX� VXFXULOH� GH� IUXFWH� vPEXWHOLDWH� HVWH� SURSRU LD� GH�

FRQFHQWUDW� QDWXUDO� SH� FDUH� R� FRQ LQ�� ÌQWU-XQ� SURFHV� GH� IDEULFD LH� D� XQHL� P UFL� GH� VXFXUL��presupunem c �SURFHQWXO�GH�FRQFHQWUDW�QDWXUDO�HVWH�DSUR[LPDWLY�QRUPDO�GLVWULEXLW��FX�PHGLD�����úL� FRHILFLHQWXO� GH� YDULD LH� ���� 6WLFOHOH� FDUH� FRQ LQ�PDL� SX LQ� GH� ���� � FRQFHQWUDW� QDWXUDO� VXQW�

Page 55: STATISTICA - TESTE GRILA

UHVSLQVH� FDOLWDWLY�� 'DF � ������� GH� VWLFOH� VXQW� YHULILFDWH�� OD� FRQWUROXO� FDOLWDtiv pot fi respinse aproximativ:

a) 2112 sticle; b) 4224 sticle; c) 1056 sticle; d) 124 sticle; e) 248 sticle.

16) 3HQWUX�FDUDFWHUL]DUHD�SURFHVHORU�GH�SURGXF LH��VXELHFWHOH�HFRQRPLFH�VH�DJUHJ �

a) SH�VHFWRDUH�LQVWLWX LRQDOH� b) GXS �IRUPD�MXULGLF � c) pe ramuri; d) QX�HVWH�QHFHVDU �R�DJUHJDUH�VSHFLDO �SHQWUX�DFHVW�VFRS� e) DWkW�SH�VHFWRDUH�LQVWLWX LRQDOH�FkW�úL�SH�UDPXUL�

17) 0HGLD�DULWPHWLF �D�S WUDWHORU�DEDWHULORU�LQGLYLGXDOH�GH�OD�WHQGLQ D�ORU�FHQWUDO �VH�QXPHúWH�

a) DEDWHUH�PHGLH�DEVROXW � b) DEDWHUH�PHGLH�S WUDWLF � c) dispersie; d) PHGLDO � e) moment centrat de ordin trei.

18) Într-R� úFRDO � JHQHUDO � VH� RUJDQL]HD] � XQ� WHVW� GH� YHULILFDUH� D� DSWLWXGLQLORU� HOHYLORU� SHQWUX�

LQIRUPDWLF ��'LVWULEX LD�HOHYLORU�GXS �SXQFWDMXO�RE LQXW�HVWH�DSUR[LPDWLY�QRUPDO ��3ULPLL�����GLQ�FHL�PDL�SX LQ� vQFOLQD L� VSUH�DFHDVW �GLVFLSOLQ �RE LQ�SkQ � OD����SXQFWH�� LDU� FHL�PDL�SHUIRUPDQ L�����RE LQ���� úL�SHVWH����GH�SXQFWH��'DF �YDORDUHD�PHGLDQ �HVWH�GH����GH�SXQFWH�� LDU�FHL�PDL�PXO L�GLQWUH�HOHYL�RE LQ����GH�SXQFWH��FRHILFLHQWXO�OXL�%RZOH\�HVWH�

a) 0,4; b) 0,53; c) 0,07; d) - 0,4; e) - 0,53.

19) PenWUX�VWXGLXO�FDOLW LL�SURGXF LHL�IDEULFDWH�vQ�VHULH��vQWU-R�XQLWDWH�HFRQRPLF ��VH�REVHUY �SHULRGLF�XQ�ORW�GH�����H[HPSODUH�SUHOHYDWH�GLQ�SURGXVHOH�DIODWH�OD�VIkUúLWXO�ODQ XOXL�GH�IDEULFD LH��3RSXOD LD�VWDWLVWLF �LQYHVWLJDW �HVWH�

a) SURGXF LD�WRWDO �UHDOL]DW � b) ansamblul loturilor de produse; c) lotul format prin prelevare; d) SURGXF LD�QHWHUPLQDW � e) SURGXF LD�UHDOL]DW ��IDFWXUDW �úL�OLYUDW �EHQHILFLDULORU�

20) 'DF � VH� XUP UHúWH� FXQRDúWHUHD� FRPSRUWDPHQWXOXL� vQ� GRPHQLXO� YHQLWXULORU�� FKHOWXLHOLORU� úL�

RSHUD LXQLORU�ILQDQFLDUH��VXELHFWHOH�HFRQRPLFH�VH�DJUHJ �GXS �FULWHULXO�

a) DFWLYLW LL�GHSXVH� b) LQVWLWX LRQDO� c) GH�UDPXU �

Page 56: STATISTICA - TESTE GRILA

d) IRUPD�MXULGLF �GH�RUJDQL]DUH� e) a)+b)+c)+d).

21) 6DODULD LL�XQHL�ILUPH�DX�VDODULXO�PHGLX�����PLL�OHL��FX�R�DEDWHUH�PHGLH�S WUDWLF �D�VDODULLORU�����

mii lei. PatroQXO� ILUPHL� KRW U úWH� V � P UHDVF � ILHFDUH� VDODULX� LQGLYLGXDO� GH� ���� RUL�� 'LVSHUVLD�QRLORU�VDODULL�ID �GH�VDODULXO�PHGLX�YD�IL�

a) 150;

b) 22500;

c) 29250;

d) 253,5;

e) 38025.

22) ÌQ� PRGHOXO� GH� DQDOL] � GLVSHUVLRQDO � XQLIDFWRULDO �� GLVSHUVLD� FRUHFWDW � GLQWUH� JUXSH� VH� RE LQH�

UDSRUWkQG�YDULDQ D�VLVWHPDWLF ��GLQWUH�FHOH�U�JUXSH��OD�QXP UXO�JUDGHORU�GH�OLEHUWDWH��QRWDW�FX�³O´��Acest num r este:

a) l=n-1; b) l=n-r; c) l=r-1; d) l=n-r-1; e) l=n-2.

23) ÌQ�FD]XO�LQGLFDWRULORU�GH�WLS�FDOLWDWLY��DJUHJDUHD�VH�UHDOL]HD] �SULQWU-o:

a) RSHUD LH�GH�DGXQDUH� b) oSHUD LH�GH�DGXQDUH�VDX�VF GHUH� c) numai printr-R�PHGLH�DULWPHWLF � d) numai prin calculul unei medii armonice; e) SULQ�FDOFXOXO�XQHL�P ULPL�PHGLL�

24) ,GHQWLILFD L�FDUH�GLQWUH�DILUPD LLOH�XUP WRDUH�UHIHULWRDUH�OD�RELHFWXO�REVHUY ULL�HVWH�IDOV �

a) 2ELHFWXO� REVHUY ULL� HVWH� PXO LPHD� GH� IHQRPHQH� GH� PDV � GHVSUH� FDUH� XUPHD] � V � VH�FXOHDJ �GDWHOH�VWDWLVWLFH�

b) 2ELHFWXO�REVHUY ULL�HVWH�R�PXO LPH�GH�XQLW L�VLPSOH�VDX�FRPSOH[H�GH�REVHUYDUH� c) 3RSXOD LD� VXSXV �REVHUY ULL� WUHEXLH�GHOLPLWDW �FD�YROXP�� vQ� WLPS� úL� vQ�VSD LX�� LQGLIHUHQW�

GDF �HD�HVWH�VWDWLF �VDX�GLQDPLF � d) 1X�vQWRWGHDXQD�RELHFWXO�REVHUY ULL�FRLQFLGH�FX�RELHFWXO�FHUFHW ULL� e) &KLDU�GDF �RELHFWXO�REVHUY ULL�HVWH�ELQH�GHILQLW��GXS �FULWHULL�FODUH��HVHQ LDOH��VWDELOH�QX�VH�

SRDWH�DVLJXUD�VXE�QLFL�R�IRUP �FRPSDUDELOLWDWHD�GDWHORU�Ge la o observare la alta. 25) &RUHF LD�OXL�6KHSSDUG�VH�DSOLF �GLVSHUVLHL�FkQG�

a) seria este pe variante; b) VHULD�HVWH�SH�LQWHUYDOH�QHHJDOH�GH�YDULD LH� c) VHULD�HVWH�SH�LQWHUYDOH�HJDOH�GH�YDULD LH� d) FkQG�GLVWULEX LD�HVWH�DSUR[LPDWLY�QRUPDO �úL�SUH]LQW �XQ�QXP U�PDUH�de intervale egale; e) FkQG�VHULD�HVWH�ELPRGDO �

Page 57: STATISTICA - TESTE GRILA

26) 3UHFL]D L�FDUH�HOHPHQWH�GLQ�FHOH�SUH]HQWDWH�PDL�MRV�QX�HVWH�R�IXQF LH�VSHFLILF �PHWRGHL�JUXS ULL���FODVLILF ULL��vQ�DFWLYLWDWHD�VWDWLVWLF �

a) VLVWHPDWL]DUHD�GDWHORU� LQGLYLGXDOH�SULQ� UHVWUkQJHUHD�QXP UXOXL�GH�variante ale variabilei de grupare;

b) IDFLOLWDUHD�FDOFXOXOXL�WXWXURU�LQGLFDWRULORU�SULPDUL�úL�GHULYD L� c) VWUXFWXUDUHD�SRSXOD LHL�VWDWLVWLFH�vQ�FODVH����JUXSH�RPRJHQH� d) SUH]HQWDUHD�úL�GHVFULHUHD�VWUXFWXULL�SRSXOD LHL�VWDWLVWLFH� e) FDUDFWHUL]DUHD�OHJ WXULORU�VWDWLstice dintre variabilele analizate.

27) Programul propriu-]LV� DO� REVHUY ULL� HVWH� IRUPDW� GLQ� WRWDOLWDWHD� FDUDFWHULVWLFLORU� �YDULDELOHORU��SHQWUX�FDUH�XUPHD] �V �VH�FXOHDJ �GDWHOH�GH�OD�XQLW LOH�SRSXOD LHL�VWDWLVWLFH��(O�VH�FRQFUHWL]HD] �

a) vQ� vQWUHE UL� FDUH� VXnt înscrise în formulare statistice la care se primesc obligatoriu U VSXQVXUL�FX�SULYLUH�OD�QLYHOXO��GH�GH]YROWDUH�VDX�IRUPD�ORU�GH�PDQLIHVWDUH�

b) într-R�OLVW �GH�YDULDELOH�GHVSUH�FDUH�VH�FXOHJ�GDWHOH�GLQ�GRFXPHQWHOH�SH�FDUH�XQLW LOH�GH�REVHUYDUH�GRUHVF�V �OH�SXQ �OD�GLVSR]L LH�

c) vQ�vQWUHE UL�vQVFULVH�vQ�FKHVWLRQDUH�VDX�DOWH�IRUPXODUH�VWDWLVWLFH�DGUHVDWH�OD�WRDWH�VDX�OD�R�SDUWH�GLQ�XQLW LOH�SRSXOD LHL�úL�DOH�F URU�SRVLELOH�U VSXQVXUL�UHIOHFW �IRUPHOH�LQGLYLGXDOH�de manifestare ale fenomenelor;

d) vQWUHE UL�LQFOuse în chestionare sau în alte formulare statistice numai atunci când ele sunt DGUHVDWH� GLUHFW� WXWXURU� XQLW LORU� GH� REVHUYDUH� VDX� OD� R� SDUWH� GLQ� DFHVWHD� úL� DOH� F URU�SRVLELOH�U VSXQVXUL�UHIOHFW �IRUPHOH�LQGLYLGXDOH�DOH�IHQRPHQHORU�GH�PDV �LQYHVWLJDWH�

e) în variantele variabilelor precizate.

28) 3HQWUX�GLVWULEX LD�XQHL�YDULDELOH�DOHDWRDUH�;�VH�FXQRDúWH�YDORDUHD�GLVSHUVLHL����������úL�YDORDUHD�momentului centrat de ordinul 4: 20876491.

&RHILFLHQWXO�OXL�)LVFKHU�SHQWUX�P VXUDUHD�EROWLULL�DUH�YDORDUHD�

a) γ 2 0 782= − , ;

b) γ 2 2 218= , ;

c) γ 2 5 218= , ;

d) γ 2 0 45= , ;

e) γ 2 2 218= − , .

29) 6H�H[FOXG�GLQ�FDOFXOXO�LQGLFDWRULORU�PDFURHFRQRPLFL�GH�UH]XOWDWH�WUDQ]DF LLOH�

a) intersectoriale; b) bilaterale; c) unilaterale; d) intrasectoriale; e) de SLD �

30) &RQWXO�PDFURHFRQRPLF�3URGXF LH�DUH�FD�VROG�

a) PINpp; b) PIBpf; c) PIBpp; d) VN; e) PNBpf.

Page 58: STATISTICA - TESTE GRILA

31) 'LVWULEX LD� HOHYLORU� GLQ� FODVD� ,� D� XQHL� úFROL� JHQHUDOH� GXS � QXP UXO�PDWHULLORU� OD� FDUH� DX� DYXW�media zece este:

Nr. materii 0 1 2 3 4 5 Nr. elevi 10 30 80 70 50 20

VaORDUHD�PHGLDQ �D�VHULHL�HVWH�

a) 2 materii; b) 2,5 materii; c) 3 materii; d) 2,7 materii; e) 70 elevi.

32) 'LVWULEX LD�XQHL�YDULDELOH�DOHDWRDUH�;�HVWH�SHUIHFW�VLPHWULF ��GH�PHGLH� x = 20 ��'DF �VH�DGDXJ �GRX �XQLW L�VWDWLVWLFH�FX�YDORULOH�YDULDELOHL�VWXGLDWe x1 ���úL�[2 �����DWXQFL�QRXD�GLVWULEX LH�

a) DUH�DVLPHWULH�SR]LWLY � b) HVWH�SHUIHFW�VLPHWULF � c) DUH�DVLPHWULH�QHJDWLY � d) DUH�ILH�DVLPHWULH�SR]LWLY ��ILH�DVLPHWULH�QHJDWLY � e) QX�SUH]LQW �DVLPHWULH�

33) 1X�VXQW�FXSULQVH�vQ�YDORDUHD�SURGXF LHL�

a) serviciile statului; b) EXQXULOH�GH�FDSLWDO�GLQ�SURGXF LH�SURSULH� c) autoconsumul; d) FKLULD�DXWRLPSXV ��LSRWHWLF �� e) EXQXULOH�SURGXVH�úL�FRQVXPDWH�SHQWUX�SURGXFHUHD�DOWRU�EXQXUL�úL�VHUYLFLL�

34) Atunci când datele provin dintr-XQ� HúDQWLRQ� GH� YROXP� UHGXV� �Q�� úL� VH� WHVWHD] � LSRWH]D� QXO �prLYLQG�SDUDPHWUXO�PHGLD�vQWUHJLL�FROHFWLYLW L�

H m m

H m ma

0 0

0

:

:

=>

UHJLXQHD�FULWLF �HVWH�GDW �GH�

a) z z> α ;

b) z z> α / 2 ;

c) t t n> −α ; 1 ;

d) t t> α / 2 ;

e) t t n> − − −α 2 1; .

35) Aplicând modelul analizei GLVSHULVRQDOH� XQLIDFWRULDOH�� VH� DFFHSW � LSRWH]D� FRQIRUP� F UHLD�IDFWRUXO�GH�JUXSDUH�HVWH�VHPQLILFDWLY�GDF ��OD�XQ�SUDJ�GH�VHPQLILFD LH�α��VH�vQGHSOLQHúWH�FRQGL LD�

a) F Fcalc n r< − −α , ,1 1 ;

b) F Fcalc r n r< − −α , ,1 ;

c) F Fcalc r n< − −α , ,1 1 ;

d) F Fcalc r n> − −α , ,1 1 ;

e) F Fcalc r n r> − −α , ,1 .

Page 59: STATISTICA - TESTE GRILA

36) 2�JUXS �GH����GH�VWXGHQ L�VXV LQH�OD�GRX �GLVFLSOLQH�FkWH�XQ�WHVW�SHQWUX�YHULILFDUHD�FXQRúWLQ HORU��

Testele au punctaje diferite, iar rezultatele sunt:

- la testul A: x Aii

2

1

259000=

=∑ ; x Ai

i

==∑ 450

1

25;

- la testul B: xBii

2

1

25425=

=∑ ; xBi

i

==∑ 100

1

25;

*UXSD�GH�VWXGHQ L�HVWH�PDL�RPRJHQ �GLQ�SXQFWXO�GH�YHGHUH�DO�FXQRúWLQ HORU�DFXPXODWH�

a) la disciplina A; b) la disciplina B; c) OD�DPEHOH�GLVFLSOLQH�SUH]LQW �DFHODúL�JUDG�GH�RPRJHQLWDWH� d) nu sunt sufLFLHQWH�GDWH�SHQWUX�D�IL�VWXGLDW �RPRJHQLWDWH�VHULLORU� e) QX�VH�SRW�FRPSDUD�RPRJHQLW LOH�OD�FHOH�GRX �GLVFLSOLQH��GHRDUHFFH�SXQFWDMHOH�WHVWHORU�DX�

fost diferite. 37) 3UREDELOLWDWHD�FD�R�FRPSDQLH�GH�DVLJXU UL�V �ILH� LQXW �V �SO WHDVF �R�SROL �SHQWUX�R�SUREOHP �

PHGLFDO � PDMRU � HVWH� ������� 'DF � XQ� JUXS� GH� ����� GH� SHUVRDQH� DVLJXUDWH� VXQW� VHOHFWDWH�vQWkPSO WRU�� SUREDELOLWDWHD� FD� DFHDVW � FRPSDQLH� V � SO WHDVF � FHO� SX LQ� R� SROL � SHUVRDQHORU�selectate este:

a) 0,8196; b) 0,1804; c) 0,1353; d) 0,8647; e) 0,001.

38) Valoarea individual �³]HUR´�D�YDULDELOHL�³P ULPHD�H[WUDVXOXL�GH�FRQW´�DUH�VHPQLILFD LH�FRQFUHW �

pe scala:

a) RUGLQDO � b) de rapoarte; c) de intervale; d) GLVFUHW � e) FRQWLQX �

39) 3HQWUX� SDWUX� ILOLDOH� DOH� XQHL� VRFLHW L� FRPHUFLDOH� VWUXFWXUD�FLIUHL� GH�DIDFHUL� UHDOL]DWH� úL� LQGLFLL�

UHDOL] ULL programului la cifra de afaceri au fost:

Filiala Structura cifrei de afaceri realizate (%)

,QGLFHOH�UHDOL] ULL�

programului cifrei de afaceri A 20 1,1 B 40 1,2 C 30 1,25 D 10 1,5

Page 60: STATISTICA - TESTE GRILA

,QGLFHOH�UHDOL] ULL�SURJUDPXOXL�FLIUHL�GH�DIDFHUL�SH�vQWUHDJD�VRFLHWDWH�FRPHUFLDO �D�IRVW�

a) 1,2625; b) 1,225; c) 1,2542; d) 1,2168; e) 1,2465.

Page 61: STATISTICA - TESTE GRILA

TESTUL 7

1) ([SUHVLD� VLQWHWL] ULL� YDORULORU� LQGLYLGXDOH� DOH� XQHL� YDULDELOH� VWDWLVWLFH� vQWU-un singur nivel

UHSUH]HQWDWLY��D�WRW�FHHD�FH�HVWH�HVHQ LDO��RELHFWLY�úL�VWDELO�vQ�DSDUL LD�úL�PDQLIestarea fenomenelor GH�PDV �HVWH�GDW �GH�

a) YDORDUHD�ORU�PHGLDQ � b) valoarea lor medial ; c) valoarea lor medie; d) FRHILFLHQWXO�ORU�GH�YDULD LH� e) FDOFXOXO�XQHL�P ULPL�UHODWLYH�GH�LQWHQVLWDWH

2) 3HULRDGD�GH�WLPS�FkW�IXQF LRQHD] �XQ�DQXPLW�WLS�GH�EDWHULL�HVWH�QRUPDO�GLVWULEXLW �FX�R�PHGLH�GH�

���GH�RUH�úL�R�GHYLD LH�VWDQGDUG�GH����RUH��3UREDELOLWDWHD�FD�R�EDWHULH�V �IXQF LRQH]H�vQWUH����úL����de ore este:

a) 0,5918; b) 0,4082; c) 0,8164; d) 0,1836; e) 0,7959.

3) 'DF � vQWU-R�VHULH�GH�GLVWULEX LH�YDORULOH� LQGLYLGXDOH�VH�VLPSOLILF �GH�N�RUi, atunci dispersia noii

serii este:

a) de k2�RUL�PDL�PLF �ID �GH�GLVSHUVLD�VHULHL�LQL LDOH� b) GH�N�RUL�PDL�PDUH�GHFkW�GLVSHUVLD�VHULHL�LQL LDOH� c) HJDO �FX�GLVSHUVLD�VHULHL�LQL LDOH� d) de k2�RUL�PDL�PDUH�ID �GH�GLVSHUVLD�VHULHL�LQL LDOH� e) GH�N�RUL�PDL�PLF �GHFkW�GLVSHUVLD�VHULHL�LQL LDOH�

4) ÌQ�PRGHOXO�GH�DQDOL] �GLVSHUVLRQDO �XQLIDFWRULDO ��VH�XWLOL]HD] �WHVWXO�³)´�GDW�GH�UHOD LD�

a)

( ) ( )F

y y n

r

y y

n rcalc

i ii

r

ij ij

m

i

r

=−

−= ==∑ ∑∑2

1

2

11

1: ;

b)

( )

( )F

y y n

y ycalc

i ii

r

ijj

m

i

r=

=

==

∑∑

2

1

2

11

;

c)

( ) ( )F

y y n

r

y y

ncalc

i ii

r

jj

m

i

r

=−

−= ==∑ ∑∑2

1

2

11

1 1: ;

Page 62: STATISTICA - TESTE GRILA

d)

( ) ( )F

y y n

r

y y

ncalc

i ii

r

ij ij

m

i

r

=−

−= ==∑ ∑∑2

1

2

11

1 1: ;

e)

( ) ( )F

y y n

n r

y y n

rcalc

ij i ij

m

i

r

i ii

r

=

−== =∑∑ ∑

2

11

2

1

1: .

5) În teVWDUHD� LSRWH]HL� VWDWLVWLFH�SULYLQG�PHGLD�SRSXOD LHL��FkQG�GDWHOH�SURYLQ�GH� OD�XQ�HúDQWLRQ�GH�YROXP�UHGXV��Q��úL�

H m m

H m ma

0 0

0

:

:

=≠

UHJLXQHD�FULWLF �HVWH�GDW �GH�

a) z z< − α sau z z> α ;

b) z z< − α / 2 sau z z> α /2 ;

c) t t n< − α / ,2 sau t t n> α / ,2 ;

d) t t n< − −α , 1 sau t t n> −α , 1;

e) t t n< − −α / ,2 1sau t t n> −α / ,2 1

6) ÌQ�FDGUXO�XQXL�VWXGLX�GH�SLD �HIHFWXDW�vQ�OXQD�LDQXDULH������V-D�XUP ULW�SULQWUH altele opinia a 100

GH� FRQVXPDWRUL� DVXSUD� FDOLW LL� XQXL� DQXPLW� SURGXV� XWLOL]DW� vQ� PRG� FXUHQW�� 6H� QRWHD] � FX� ;�

YDULDELOD�RSLQLH�úL�FX�[i opinia consumatorului i ( i = 1100, ) intervievat. �����3RSXOD LD�VWDWLVWLF �QRWDW �FX�P �HVWH�IRUPDW �GLQ:

a) WR L�FRQVXPDWRULL� b) consumatorii români; c) FHL�����GH�FRQVXPDWRUL�LQWHUYLHYD L� d) FRQVXPDWRULL�SRWHQ LDOL� e) consumatorii din zona de sud-HVW�D� ULL�

���9DULDELOD�;��GHILQLW �vQ�SUREOHPD������HVWH�

a) FDOLWDWLY �FRQWLQX � b) FDOLWDWLY �GLVFUHW � c) QRPLQDO � d) de timp; e) QXPHULF �

8) &DUH�GLQ�XUP WRDUHOH�DILUPD LL�QX�HVWH�DGHY UDW �SHQWUX�R�VHULH�VWDWLVWLF �

a) vQWUH�TXDUWLOD���úL�TXDUWLOD���VH�J VHVF�����GLQ�REVHUYD LL��VLWXDWH�vQ�FHQWUXO�GLVWULEX LHL� b) YDORDUHD�TXDUWLOHL���HVWH�HJDO �FX�PHGLDQD��GRDU�SHQWUX�R�VHULH�VLPHWULF � c) YDORDUHD�PHGLDQHL�HVWH�vQWRWGHDXQD�HJDO �FX�YDORDUHD�TXDUWLOHL��� d) SHQWUX�R�VHULH�VLPHWULF ��DEDWHUHD�LQWHUTXDUWLOLF �HVWH�QXO � e) SHQWUX�R�VHULH�VLPHWULF ��DEDWHUHD�LQWHUTXDUWLOLF �FXSULQGH�����GLQ�REVHUYD LL�

Page 63: STATISTICA - TESTE GRILA

9) 3HQWUX�R�GLVWULEX LH�VLPHWULF �

a) abaterile�LQGLYLGXDOH�VH�FRPSHQVHD] �GRDU�OD�QLYHOXO�vQWUHJLL�FROHFWLYLW L� b) abaterile individuale sunt nule; c) DEDWHUHD�PD[LP �SR]LWLY �HVWH�HJDO �FX�DEDWHUHD�PD[LP �QHJDWLY � d) DEDWHULOH�LQGLYLGXDOH�VH�FRPSHQVHD] �DWkW�SH�WRWDO��FkW�úL�OD�QLYHOXO�FHQWUDOL]DW�DO�XQLW LORU� e) VXPD�DEDWHULORU�LQGLYLGXDOH�HVWH�HJDO �FX�DPSOLWXGLQHD�YDULD LHL�

10) *UDGXO�GH�OLEHUWDWH�HVWH�XQ�FRQFHSW�VWDWLVWLF�FH�GHVHPQHD] �

a) QXP UXO�GH�HOHPHQWH�GLQWU-o colectivitate; b) num rul de elemente dintr-o colectivitate minus unul; c) num rul de elemente necesare pentru a defini starea unui ansamblu; d) num rul de elemente independente necesare pentru a defini starea unui ansamblu; e) QXP UXO�GH�UHOD LL�LQGHSHQGHQWH�FDUH�OHDJ �HOHPHQWHOH�XQXL�DQVDPEOX�

11) 'RX � YDULDELOH� VWDWLVWLFH� DX� IRVW� PRGHODWH� vQWU-R� SRSXOD LH� VWDWLVWLF � FX� Q� XQLW L� FX� DMXWRUXO�HFXD LHL�OLQLDUH�GH�IRUPD��� �y x= +5 64 ��ùWLLQG�F �

( ) ( )x x y yii

n

ii

n− = − =

= =∑ ∑

2

1

2

1

30 1960; � �� SHQWUX� Q ��� XQLW L� VWDWLVWLFH�� DWXQFL� LQWHUYDOXO� GH�

încredere pentru panta liniei de regresie, la o probabilitate de 95% este:

a) (63,53 ; 64,47); b) (4,53 ; 5,47); c) (58,92 ; 66,65); d) (61,35 ; 66,65); e) (58,92 ; 69,08).

12) 'LVSHUVLD�XQHL�FDUDFWHULVWLFL�GH�WLS�DOWHUQDWLY�HVWH�PD[LP �FkQG�

a) QXP UXO�GH�U VSXQVXUL�DILUPDWLYH�HVWH�HJDO�FX�QXP UXO�GH�U VSXQVXUL�QHJDWLYH� b) WRDWH�XQLW LOH�FROHFWLYLW LL�vQUHJLVWUHD] �U VSXQVXUL�DILUPDWLYH� c) WRDWH�XQLW LOH�FROHFWLYLW LL�vQUHJLVWUHD] �U VSXQVXUL�QHJDWLYH� d) WRDWH�XQLW LOH�FROHFWLYLW LL�vQUHJLVWUHD] �ILH�U VSXQVXUL�QHJDWLYH��ILH�U VSXQVXUL�SR]LWLYH� e) nu se poate preciza în ce caz dispersia unei caracteristiFL�DOWHUQDWLYH�HVWH�PD[LP �

13) 'HQVLWDWHD�GH�UHSDUWL LH�D�YDULDELOHL�DOHDWRDUH�QRUPDOH��GH�PHGLH�x = 20 9, úL�GLVSHUVLH�������HVWH�GHVFULV �GH�

a) f exi( )

,

= ⋅−1

2

20 9

35

2

π;

b) ( )

f ex

x

i

i

( ),

,

,= ⋅

−⋅

−1

17 5 2

1

2 17 520 9

22

π;

c) ( )

f ex

x

i

i

( ),

,

,= ⋅

−⋅

−1

17 5 2

1

2 17 520 9 2

π;

d) ( )

f ex

x

i

i

( ),

,= ⋅

−⋅

−1

4,18 2

1

2 4 1820 9 2

π;

e) ( )

f ex

x

i

i

( ),5

,

,= ⋅

−⋅

−1

4 18 2

1

2 1720 9 2

π.

Page 64: STATISTICA - TESTE GRILA

14) 0HGLD�DUPRQLF �VH�GHILQHúWH�FD�

a) PHGLD�DULWPHWLF �FDOFXODW �GLQ�LQYHUVHOH�YDORULORU�LQGLYLGXDOH��vQUHJLVWUDWH� b) YDORDUHD�LQYHUV ��D�PHGLHL�DULWPHWLFH�D�WHUPHQLORU�VHULHL� c) YDORDUHD� LQYHUV � D� PHGLHL� DULWPHWLFH� FDOFXODW � GLQ� LQYHUVHOH� S WUDWHORU� YDORULORU�

individuale înregistrate; d) YDORDUHD�LQYHUV �D�PHGLHL�DULWPHWLFH�FDOFXODW �GLQ�LQYHUVHOH�YDORULORU�LQGLYLGXDOH� e) YDORDUHD�FDUH��GDF �DU�vQORFXL�WHUPHQLL�VHULHL��QX�DU�PRGLILFD�VXPD�ORU�

15) ,QGLFDWRUXO� ³HQHUJLD� LQIRUPD LRQDO � 2QLFHVFX´� HVWH� XWLOL]DW� vQ� DQDOL]D� VWDWLVWLF � SHQWUX�caracterizarea:

a) asimetriei; b) dispersiei; c) QRUPDOLW LL�GLVWULEX LHL� d) FRQFHQWU ULL� e) WHQGLQ HL�FHQWUDOH�

16) 'LUHFWRUXO�XQXL�SRVW�GH�UDGLR�FRPDQG �R�FHUFHWDUH�VWDWLVWLF �vQ�VFRSXO�GHWHUPLQ ULL�DXGLHQ HL�GH�FDUH�VH�EXFXU �SRVWXO�V X��&HUFHW WRUXO�FXOHJH�SH�XQ�HúDQWLRQ�GDWH�SULYLQG�QXP UXO�GH�RUH�DXGLDWH�úL�DIO �F �����GLQ�SHUVRDQH�DVFXOW �SRVWXO�GH�UDGLR�PDL�SX LQ�GH�GRX �RUH������vQWUH���úL���RUH������vQWUH���úL���RUH������vQWUH���úL���RUH��LDU�UHVWXO�SHVWH���RUH��1XP UXO�PHGLX�GH�RUH�GH�DXGL LH�SH�R�SHUVRDQ �GLQ�HúDQWLRQ�HVWH�

a) 4,8 ore; b) 4,7 ore; c) 6 ore; d) 4,2 ore; e) 4,6 ore.

17) 6 � VH� SUHFL]H]H� FDUH� GLQ� XUP WRDUHOH� GLVWULEX LL� GH� SUREDELOLWDWH� GHVFULH� R� YDULDELO � DOHDWRDUH�Poisson:

a) ( )px xi

i i

x xi i=⋅ −

−10

100 9 0 110!

! !, , (xi=0, 1, 2, … , 10);

b) ( )

pe

xi

x

i

i

=−0 5 0,

!

,5

(xi=0, 1, 2, 3, … );

c) ii xxi Cp −⋅⋅= 6

6 8,02,0 (xi=0, 1, 2, … , 6);

d) ( )

px e

ii

x

x

i

i=

−!

,0 5 (xi=0, 1, 2, 3, … )

e)

( )f ex

x

i

i

( )

,

,

,= ⋅

−−⋅1

31 2

20 9

2 9 61

2

π.

18) 3HQWUX� R� FROHFWLYLWDWH� GH� Q� XQLW L� VLVWHPDWL]DWH� FRQFRPLWHQW� vQ� U� JUXSH� GXS � YDORULOH�caracteriVWLFLL�;� �FRQVLGHUDW � FDUDFWHULVWLF � HVHQ LDO � GH� LQIOXHQ �� úL� vQ�P� JUXSH� GXS � YDORULOH�FDUDFWHULVWLFLL�DQDOL]DWH�<��LQIOXHQ D�IDFWRUXOXL�;�HVWH�P VXUDW �GH�

a) vPSU úWLHUHD�YDORULORU�LQGLYLGXDOH�GLQ�ILHFDUH�JUXS �vQ�MXUXO�PHGLHL�GH�JUXS � b) vPSU úWLHUHD�YDORULORU�LQGLYLGXDOH�GLQ�ILHFDUH�JUXS �vQ�MXUXO�PHGLHL�JHQHUDOH�D�FROHFWLYLW LL� c) vPSU úWLHUHD�PHGLLORU��GH�JUXS �vQ�MXUXO�PHGLHL�JHQHUDOH�D�FROHFWLYLW LL�

Page 65: STATISTICA - TESTE GRILA

d) vPSU úWLHUHD�YDORULORU�LQGLYLGXDOH�vQ�MXUXO�PHGLHL�PHGLLORU�GH�JUXS � e) vPSU úWLHUHD�PHGLHL�PHGLLORU�GH�JUXS �ID �GH�PHGLD�JHQHUDO �D�FROHFWLYLW LL�

19) ÌQ�PRGHOXO�GH�DQDOL] �GLVSHUVLRQDO �XQLIDFWRULDO �YDULDQ D�IDFWRULDO ��VLVWHPDWLF ��HVWH�

a) ( )y yij ij

m

i

r−

==∑∑

2

11

;

b) ( )y y ni ii

r−

=∑

2

1

;

c)

( )y y n

r

i ii

r−

−=∑

2

1

1;

d)

( )y y

n

ijj

m

i

r−

−==∑∑ 2

11

1;

e) ( )y yijj

m

i

r−

==∑∑

2

11

.

20) În testarea ipotezei statistice

H m

H ma

0 100

100

:

:

≥<

XWLOL]kQG�WHVWXO�]�VH�RE LQH�YDORDUHD�WHVWXOXL�] -1,11. Nivelul de încredere al testului este:

a) 86,65%; b) 36,65%; c) 13,35%; d) 26,70%; e) 73,30%.

21) Într-un proces de testare a ipotezelor statistice, eroarea de genul al doilea este:

a) HURDUHD�SH�FDUH�R�IDFHP�DFFHSWkQG�LSRWH]D�QXO �FkQG�HD�HVWH�DGHY UDW � b) HURDUHD�SH�FDUH�R�IDFHP�DFFHSWkQG�LSRWH]D�DOWHUQDWLY �FkQG�HD�HVWH�IDOV � c) HURDUHD�SH�FDUH�R�IDFHP�DFFHSWkQG�LSRWH]D�QXO �FkQG�HD�HVWH�IDOV � d) eroarea pe FDUH�R�IDFHP�HOLPLQkQG�LSRWH]D�QXO �FkQG�HD�HVWH�DGHY UDW � e) HURDUHD�SH�FDUH�R�IDFHP�HOLPLQkQG�LSRWH]D�DOWHUQDWLY �DWXQFL�FkQG�HD�HVWH�IDOV �

22) ÌQ� XWLOL]DUHD�PHWRGHL� UHJUHVLHL� SHQWUX� VWXGLXO� GHSHQGHQ HL� GLQWUH� YDULDELOH��PRGHOXO� GH� IRUPD��

yx

= + +α β ε1 este un model:

a) liniar; b) H[SRQHQ LDO� c) logaritmic; d) hiperbolic; e) parabolic.

Page 66: STATISTICA - TESTE GRILA

23) 'LVSHUVLD�YDORULORU�XQHL�YDULDELOH�DOHDWRDUH�;��ID �GH�R�FRQVWDQW �D�HVWH�PLQLP �FkQG�

a) a = 0;

b) a x= ; c) pentru orice a;

d) a xi= ∑ ;

e) a = xmax. 24) Un VLVWHP�DO�XQXL�YHKLFXO� VSD LDO� WUHEXLH�V � IXQF LRQH]H�FRQWLQXX�SHQWUX�FD�QDYD�V � UHLQWUH� vQ�

VSD LX��2�FRPSRQHQW �D�VLVWHPXOXL�IXQF LRQHD] �FRUHVSXQ] WRU�����GLQ� WLPS��3HQWUX�D�DVLJXUD�EXQD�IXQF LRQDUH�D�VLVWHPXOXL��VXQW�PRQWDWH�SDWUX�FRPSRQHQWH�VLPLODUH��vQ�DúD�IHO�vQFkW�VLVWHPXO�IXQF LRQHD] � GDF � FHO� SX LQ� R� FRPSRQHQW � OXFUHD] �� &RPSRQHQWHOH� RSHUHD] � LQGHSHQGHQW��3UREDELOLWDWHD�FD�VLVWHPXO�V �FDG �HVWH�

a) 0,05%;

b) 5%;

c) 15%;

d) 52,20%;

e) 0,5220%.

25) 3HQWUX�R�VHULH�GH�UHSDUWL LH�GH�IUHFYHQ H��PHGLD�S WUDWLF �VH�FDOFXOHD] �FD�

a) ( )

=

==r

ii

r

iii

p

n

nxx

1

1

2

;

b)

=

==r

ii

r

iii

p

n

nxx

1

1

2

;

c) ( )

=

==r

ii

r

iii

p

n

nxx

1

1

2

;

d)

=

==r

ii

r

iii

p

n

nxx

1

1

2

;

e)

=

==r

ii

r

iii

p

n

nxx

1

1 .

Page 67: STATISTICA - TESTE GRILA

26) 'RX �JUXSH�GH� VWXGHQ L�� FX�HIHFWLYH�GH���� úL� UHVSHFWLY����GH�SHUVRDQH��DX� VXV LQXW�XQ� WHVW�GH�

FXOWXU �JHQHUDO ��3ULPD�JUXS �D�RE LQXW�PHGLD������LDU�D�GRXD������1RWD�PHGLH�SH�DQVDPEOXO�FHORU�GRX �JUXSH�HVWH�

a) 8,14; b) 8,10; c) 8,12; d) 8,00; e) 8,09.

27) Într-R�FROHFWLYLWDWHD�VWDWLVWLF �VLVWHPDWL]DW �vQ�U�JUXSH�GXS �YDULD LD�FDUDFWHULVWLFLL�GH�JUXSDUH�;�úL�vQ�P�JUXSH�GXS �YDORULOH�YDULDELOHL�DQDOL]DWH�<�H[LVW �vQWRWGHDXQD�UHOD LD�

a) 222δσσ += i ;

b) 22δσ ≥ ;

c) r

i∑=2

2 σσ ;

d) 22σσ ≤ ;

e)

( )

∑∑

∑∑

= =

= =−

=r

i

m

jij

r

i

m

jijij

n

nyy

1 1

1 1

2

2σ .

28) Într-R�FROHFWLYLWDWHD�GH�����VDODULD L��VLVWHPDWL]DW �GXS �IDFWRUXO�GH�JUXSDUH�;��QXP UXO�RUHORU�OXFUDWH�� vQ���JUXSH� úL�GXS �YDULDELOD�GHSHQGHQW �� VDODULXO�� vQ���JUXSH�� DSOLFkQGX-se modelul de DQDOL] � GLVSHUVLRQDO � V-D� RE LQXW�� YDULDQ D� VLVWHPDWLF � 61 ���������� úL� YDULDQ D� WRWDO �ST �����������9DORDUHD�FDOFXODW �D�UDSRUWXOXL�)�SHQWUX�XWLOL]DUHD�WHVWXOXL�FX�DFHODúL�QXPH�HVWH�

a)Fcalc=81,875;

b) Fcalc=73,23; c) Fcalc=1,25; d) Fcalc=61,09; e) Fcalc=36,94.

29) În testarea ipotezei statistice

H m

H ma

0 100

100

:

:

≥<

VH�RE LQH�YDORDUHD�WHVWXOXL�VWDWLVWLF�] -1,11. 3UDJXO�GH�VHPQLILFD LH�DO�WHVWului este: a)0,3665;

b) 0,1335; c) 0,267 ; d) 0,06675; e) 0,43325.

Page 68: STATISTICA - TESTE GRILA

30) Într-un proces de testare a ipotezelor statistice, eroarea de genul întâi este:

a) HURDUHD�SH�FDUH�R�IDFHP�DFFHSWkQG�LSRWH]D�QXO �FkQG�HD�HVWH�DGHY UDW � b) eroarea pe care o facem acceptând ipoteza nXO �DWXQFL�FkQG�HD�HVWH�IDOV � c) HURDUHD�SH�FDUH�R�IDFFHP�DFFHSWkQG�LSRWH]D�DOWHUQDWLY �FkQG�HD�HVWH�DGHY UDW � d) HURDUHD�SH�FDUH�R�IDFHP�HOLPLQkQG�LSRWH]D�QXO �DWXQFL�FkQG�HD�HVWH�DGHY UDW � e) HURDUHD�SH�FDUH�R�IDFHP�HOLPLQkQG�LSRWH]D�DOWHUQDWLY �DWXQFL�FkQG�HD�HVWH�DGHY UDW �

31) 6 � VH� SUHFL]H]H� FDUH� GLQ� XUP WRDUHOH�PHWRGH� GH� FDUDFWHUL]DUH� D� OHJ WXULORU� GLQWUH� YDULDELOHOH�

VWDWLVWLFH�QX�VH�vQFDGUHD] �vQ�FDWHJRULD�³PHWRGHORU�VLPSOH´�

a) metoda seriilor interdependente; b) PHWRGD�JUXS ULORU� c) PHWRGD�JUDILF � d) PHWRGD�FRUHOD iei; e) PHWRGD�WDEHOXOXL�GH�FRUHOD LH�

Page 69: STATISTICA - TESTE GRILA

TESTUL 8

1) Prin AUDIT-ul financiar efectuat în luna ianuarie 1998 la S.C. “ICS” SRL s-D�FRQVWDWDW�F � vQ�

IDFWXULOH�HODERUDWH� vQ������H[LVW �DQXPLWH�HURUL� vQ�FDOFXOXO�79$-XOXL�FDUH� DX�DYXW�GUHSW� VXUV ��QHFXQRDúWHUHD� PHWRdologiei de calcul a TVA-XOXL� OD� XQHOH� SURGXVH�� DSUR[LP UL� HURQDWH��GHIHF LXQL�DOH�PLMORFXOXL�WHKQLF�GH�FDOFXO��HWF�

3RSXOD LD�VWDWLVWLF �VWXGLDW �HVWH�

a) ansamblul facturilor elaborate de S.C. “ICS” SRL; b) DQVDPEOXO�SURGXVHORU�úL�VHUYLFLLORU�UHDOL]DWH�GH�6�&��³,&6´�65/�SkQ �OD����;,,������ c) DQVDPEOXO� SURGXVHORU� úL� VHUYLFLLORU� UHDOL]DWH� GH� 6�&�� ³,&6´� 65/� GHVI FXWH� SH� SLD � úL�

IDFWXUDWH�SkQ �OD����;,,������ d) DQVDPEOXO�SURGXVHORU�úL�VHUYLFLLORU�UHDOL]DWH�SHQWUX�D�IL�GHVI FXWH�SH�SLD �GH�6�&��³,&6´�

SRL, facturate�SkQ �OD����;,,������úL�OD�FDUH�VH�SHUFHSH�79$� e) DQVDPEOXO�IDFWXULORU�HODERUDWH�GH�6�&��³,&6´�65/�SkQ �OD����;,,������SHQWUX�SURGXVHOH�

úL�VHUYLFLLOH�UHDOL]DWH�úL�GHVI FXWH�SH�SLD �

2) &DOFXOXO�DPSOLWXGLQLL�YDULD LHL�YDORULORU�LQGLYLGXDOH�DUH�VHQV�SHQWUX�

a) serii statistice numerice formate pe variante; b) VHULL�VWDWLVWLFH�IRUPDWH�GXS �R�YDULDELO �DOWHUQDWLY � c) VHULL�VWDWLVWLFH�IRUPDWH�SH�LQWHUYDOH�HJDOH�GH�YDULD LH� d) VHULL�VWDWLVWLFH�IRUPDWH�SH�LQWHUYDOH�QHHJDOH�GH�YDULD LH� e) orice tip de serie.

3) Pentru o colectivitDWH�GH�Q�XQLW L�FDUH�DX�IRVW�VWUXFWXUDWH�FRQFRPLWHQW� vQ�r�JUXSH�GXS �YDORULOH�FDUDFWHULVWLFLL�;�úL�vQ�m�JUXSH�GXS �YDORULOH�FDUDFWHULVWLFLL�<��PHGLD�FDUDFWHULVWLFLL�<�SH�vQWUHDJD�

colectivitate ( y ��QX�VH�FDOFXOHD] �FD�

a)

=

==m

jj

m

jjj

n

ny

y

1.

1.

;

b)

=

==r

ii

r

iii

n

nyy

1.

1..

;

c)

∑∑

∑∑

=

==

=

=r m

jij

r m

jijij

in

iny

y

1

1

1

1 ;

d) n

iny

y

r m

jijij∑∑

== =1 1 ;

e)

=

==r

ii

r

iii

n

nyy

1.

1..

.

Page 70: STATISTICA - TESTE GRILA

4) ÌQ� DQXO� ������ LQGLFHOH�PHGLX� OXQDU� DO� SUH XULORU� GH� FRQVXP� OD� VHUYLFLL� D� IRVW� SHQWUX� SHULRDGD�ianuarie-DXJXVW��������úL�SHQWUX�SHULRDGD�DXJXVW-decembrie 1,0319. Indicele mediu lunar pe anul 1994 a fost:

a) 1,0505; b) 1,0474; c) 1,0435; d) 1,0436; e) 104,35%.

5) 3HQWUX�GRX �YDULDELOH� VWDWLVWLFH�;�úL�<� vQWUH�FDUH� H[LVW �R�GHSHQGHQ � OLQLDU ��XWLOL]kQG�PHWRGD�

JUDILF ��V-au calculat:

σ x x y y x2 9043 2392 8 37 364= = − = =; cov( , ) , ; ; .

(FXD LD�GH�UHJUHVLH�FDUH�PRGHOHD] �GHSHQGHQ D�GLQWUH�FHOH�GRX �YDULDELOH�HVWH�

a) � , ,y x= +133 3 0 2646 ; b) xy 2646,03,133ˆ −= ; c) xy 3,1332646,0ˆ += ; d) xy 78,392,1412ˆ −= ; e) xy 78,392,1338ˆ −−= .

6) ÌQ� UHSDUWL LD� ELQRPLDO � FX� Q� REVHUYD LL�� S� - probabilitatea succesului, q - probabilitatea

LQVXFFHVXOXL��IUHFYHQ D�D�N�VXFFHVH�vQ�1�VHULL�HVWH�

a) q pn k k− ;

b) C q pnk n k k− ;

c) C p qnk n k k− ;

d) N C q pnk n k k⋅ − ;

e) N q pn k k⋅ − . 7) ÌQ�VWXGLXO�PLúF ULL�QDWXUDOH�D�SRSXOD LHL�VH�DQDOL]HD] �SULQWUH�DOWHOH�úL�YDULDELOD�³UDQJXO�Q VFXWXOXL�

YLX´��ÌQ�LDQXDULH������vQ�5RPkQLD�UHSDUWL LD�GXS �DFHDVW �YDULDELO �VH�SUH]LQW �DVWIHO�

5DQJXO�Q VFXWXOXL�YLX 1XP U�GH�QRX�Q VFX L

Primul 139958

Al doilea 64897

Al treilea 19812

Al patrulea 9657

Al cincilea 5650

$O�úDVHOHD 3966

$O�úDSWHOHD 2322

Al 8-OHD�úL�SHVWH 3722

Sursa: Anuarul statistic al României, CNS, 1994, p.126

Page 71: STATISTICA - TESTE GRILA

Datele prezentate mai sus sunt:

a) individuale; b) grupate; c) de stoc; d) de flux; e) agregate.

8) 3HQWUX�GRX �YDULDELOH�VWDWLVWLFH�GHSHQGHQWH�;�úL�<��FX�\� �I�[���DX�IRVW�FXOHVH�GDWH�GH�OD����GH�

XQLW L�VWDWLVWLFH�úL��vQ�XUPD�SUHOXFU ULL�GDWHORU��V-D�RE LQXW�FRHILFLHQWXO�GH�FRUHOD LH�U -0,82. &RHILFLHQWXO�GH�FRUHOD LH�U�

a) HVWH�VHPQLILFDWLY�VWDWLVWLF�OD�XQ�SUDJ�GH�VHPQLILFD LH�α=0,0005; b) nu este semnificativ statistic; c) este semnificativ statistic doar pentru cel mult un nivel de încredere de 1-α=0,90; d) QX�HVWH�VHPQLILFDWLY�VWDWLVWLF�OD�XQ�SUDJ�GH�VHPQLILFD LH�α=0,010; e) DUH�R�YDORDUH�FDUH�QX�SRDWH�IL�WHVWDW �SHQWUX�QLFL�XQ�SUDJ�GH�VHPQLILFD LH�

9) )UHFYHQ HOH�UHGXVH�OD�XQLWDWH�VH�FDOFXOHD] �

a) vQ�FD]XO�UHSDUWL LLORU�SH�LQWHUYDOH�QHHJDOH��SHQWUX�DVLJXUDUHD�FRPSDUDELOLW LL�IUHFYHQ HORU� b) SHQWUX�D�VWXGLD�SRQGHUHD�XQLW LORU�VWDWLVWLFH�GLQWU-R�JUXS �vQ�WRWDOXO�FROHFWLYLW LL�VWXGLDWH� c) pentru a detHUPLQD� QXP UXO� XQLW LORU� FDUH� DX� YDORDUHD� LQGLYLGXDO � VLWXDW � SkQ � OD� XQ�

anumit nivel al caracteristicii; d) SHQWUX�D�VWXGLD�VWUXFWXUD�XQHL�VHULL�GH�GLVWULEX LH� e) SHQWUX� D� VWXGLD� QXP UXO� XQLW LORU� VWDWLVWLFH� FDU� DX� YDORULOH� LQGLYLGXDOH� VLWXDWH� SHVWH� XQ�

anumit nivel al caracteristicii. 10) 3UHVXSXQHP� F �� vQ� XUPD� DSOLF ULL� PHWRGHL� GH� UHJUHVLH� OLQLDU �� V-a calculat, pentru 12 valori

SHUHFKL�� VXPD� S WUDWHORU� DEDWHULORU� YDlorilor empirice de la valorile ajustate

( )y yi ii

− ==∑ � ,2

1

120 507 . Atunci, se

2 ��HVWLPDWRUXO�GLVSHUVLHL�DEDWHULORU�vQWkPSO WRDUH�ε, este:

a) 0,0507; b) 0,04225; c) 0,04609; d) 0,2252; e) 0,2055.

11) 'LVSHUVLD�FDOFXODW �ID �GH�R�FRQVWDQW �a este, comparatLY�FX�GLVSHUVLD�FDOFXODW �ID �GH�PHGLH�

a) de a�RUL�PDL�PLF � b) mai mare de a2 ori; c) PDL�PLF ��FX�S WUDWXO�GLVWDQ HL�GLQWUH�PHGLH�úL�FRQVWDQWD�a; d) mai mare cu a2; e) PDL�PDUH��FX�S WUDWXO�GLVWDQ HL�GLQWUH�PHGLH�úL�FRQVWDQWD�a.

Page 72: STATISTICA - TESTE GRILA

12) 2�YDULDELO �DOHDWRDUH�;�DUH�R�GLVWULEX LH�QRUPDO ��GH�PHGLH����úL�GLVSHUVLH����9DORUHD�[0, pentru care P x x( ) ,≤ =0 0 8413 este:

a) 54,23; b) 45,77; c) 53; d) 59; e) 46.

13) 3HQWUX� YHULILFDUHD� QRUPDOLW LL� UHSDUWL LLORU� HPSLULFH� XWLOL]kQG� WHVWXO� χ2� �� YDORDUHD� FDOFXODW � D�

variabilei χ2 are forma:

a) ( )

i

r

iii

calc np

npn∑=

−= 1

2

2χ ;

b) ∑=

−=r

i i

iicalc np

npn

1

2

2χ ;

c) ∑=

−=r

i i

iicalc np

npn

1

2χ ;

d) ( )∑=

−=r

i i

iicalc

np

npn

12

2χ ;

e) ( )∑

=

−=r

i i

iicalc np

npn

1

22χ .

14) ÌQ�FDGUXO�PHWRGHORU�JHQHUDOH�GH�DERUGDUH� úWLLQ LILF �D� IHQRPHQHORU�HFRQRPLFR-sociale, un loc

LPSRUWDQW�vO�RFXS �DEVWUDFWL]DUHD�VXFFHVLY ��LQGXF LD�úL�GHGXF LD��$FHVWH�PHWRGH� a) nu pot fi utilizate într-XQ� GHPHUV� VWDWLVWLF� GHRDUHFH� RSHUHD] � FX� GDWH� FRQFUHWH� RE LQXWH�

SULQ�REVHUY UL�WRWDOH�úL�SDU LDOH� b) VXQW�XWLOL]DWH�vQ�VWXGLXO�VWDWLVWLF�DO�IHQRPHQHORU�GH�PDV �vQWUXFkW��SHQWUX�D�VH�UH LQH�QXPDi

FHHD�FH�HVWH�HVHQ LDO�úL�WLSLF�WUHEXLH�V �VH�HOLPLQH�DVSHFWHOH�vQWkPSO WRDUH�úL�QHHVHQ LDOH��GH� OD� SDUWLFXODUXO� RE LQXW� SULQ� REVHUYDUHD� �vQUHJLVWUDUHD�� YDORULORU� HPSLULFH� VH� WUHFH�inductiv spre ceea ce este în general valabil pentru întregul ansamblu, etc.;

c) QX�SRW�IL�XWLOL]DWH�GH�VWDWLVWLF �vQWUXFkW�vQ�RULFH�FHUFHWDUH�QX�VH�SRUQHúWH�GH�OD�LSRWH]H�FDUH�ar trebui verificate;

d) VXQW�XWLOL]DWH�QXPDL�vQ�VWXGLXO�UHSDUWL LLORU�VWDWLVWLFH�XQL-�úL�PXOWLGLPHQVLRQDOH� e) VXQW�XWLOL]DWH�QXPDL�GDF �VXQW�RUJDQL]DWH�VRQGDMH�statistice.

15) Analizate la nivelul unui ansamblu, formele individuale de manifestare ale fenomenelor de

PDV �SDU� DVHP Q WRDUH� vQWUH�HOH�� ILLQG� JHQHUDWH�GH�FDX]H� HVHQ LDOH�FRPXQH�� VH� VXSXQ�DFHOHLDúL�OHJL�GH�DSDUL LH�úL�GH]YROWDUH��$FHDVW �OHJH�DF LRQHD] �

a) stDWLF��FkQG�IHQRPHQHOH�VXQW�FLUFXPVFULVH�OD�DFHODúL�VSD LX�úL�DFHHDúL�IRUP �GH�RUJDQL]DUH��GDU�vQ�FRQGL LL�GH�WLPS�GLIHULWH�

b) GLQDPLF��FkQG�IHQRPHQHOH�VXQW�GHOLPLWDWH�vQ�DFHODúL�VSD LX��VXQW�vQUHJLVWUDWH�vQ�DFHOHDúL�XQLW L�GH�WLPS� c) atât static, când fenomenHOH�GH�PDV �VXQW�FLUFXPVFULVH�vQ�DFHOHDúL�FRQGL LL�GH�WLPS�FkW�úL�

GLQDPLF�� FkQG� IHQRPHQHOH� VXQW� GHOLPLWDWH� vQ� VSD LX� úL� RUJDQL]DWRULF�� GDU� vQUHJLVWUDWH� vQ�XQLW L�GH�WLPS�GLIHULWH�

d) exclusiv dinamic, când se face ipoteza c fenomenele au fost înregistrate lD� DFHOHDúL�PRPHQWH�GH�WLPS��YDULDELOH�ILLQG�VSD LXO�úL�IRUPD�GH�RUJDQL]DUH�

e) VWDWLF�� GHRDUHFH� GLQDPLF� QX� SRDWH� DF LRQD� vQWUXFkW� UHOD LLOH� GH� FDX]DOLWDWH� GLQWUH�fenomenele sociale nu au un caracter dinamic.

Page 73: STATISTICA - TESTE GRILA

16) 2�YDULDELO �DOHDWRDUH�;��GLVWULEXLW �QRUPDO�úL�FX�REOLFLWDWH�PRGHUDW ��DUH�����GLQ�YDORUL�VLWXDWH�

vQ�FHQWUXO�GLVWULEX LHL��FXSULQVH�vQWUH������úL�������FRHILFLHQWXO�GH�YDULD LH�HVWH�������LDU�YDORDUHD�PRGDO �������$VLPHWULD�HVWH�

a) PRGHUDW�SR]LWLY � b) PRGHUDW�QHJDWLY � c) HJDO �FX�]HUR� d) nu se poate preciza felXO�úL�P ULPHD�DVLPHWULHL� e) HJDO �FX�DPSOLWXGLQHD�VHPLLQWHUTXDUWLOLF �

17) $EDWHUHD�PHGLH�LQWHUTXDUWLOLF �VH�FDOFXOHD] �FD�

a) 13 QQ − ;

b) 2

13 QQ −;

c) 2

12 QQ −;

d) ( ) ( )

213 MeQMeQ −+−

;

e) ( )122 QQ − .

18) Pentru dou �YDULDELOH�VWDWLVWLFH��D�F URU�WHQGLQ �D�GHSHQGHQ HL�VWDWLVWLFH�\� �I�[���D�IRVW�PRGHODW �

SULQ�HFXD LD�GH�UHJUHVLH� � ,y x= −25 0 7 , se cunosc dispersiile σ x2 2603 04= , �úL�σ y

2 1896 6= , .

&RHILFLHQWXO�GH�FRUHOD LH�DUH�YDORDUHD�

a) 0,82; b) 0,96; c) -0,96; d) -0,82; e) -0,597.

19) 3UREDELOLWDWHD�FD�YDORULOH�XQHL�YDULDELOH�DOHDWRDUH�QRUPDOH�V �VH�VLWXH]H�OD�R�GLVWDQ �PDL�PDUH�GH������RUL�DEDWHUHD�PHGLH�S WUDWLF �GH�R�SDUWH�úL�GH�DOWD�ID �GH�PHGLH�HVWH�

a) 5%; b) 0,05%; c) 2,5%; d) 47,50%; e) 97,5%.

20) Un grup de����DQJDMD L�HVWH�DOHV�GLQWU-R�FRPSDQLH�vQ�VFRSXO�GH�D�GHWHUPLQD�QXP UXO�FHORU�FDUH�VXV LQ�VLQGLFDWXO�FRPSDQLHL��3UHVXSXQHP�F �����GLQ�WR L�DQJDMD LL�VXV LQ�VLQGLFDWXO�

3UREDELOLWDWHD�FD�PDL�SX LQ�GH���DQJDMD L�GLQ�FHL����V �VXV LQ �VLQGLFDWXO�HVWH�

a) 61,78%; b) 38,22%; c) 83,28%; d) 21,50%; e) 16,72%.

Page 74: STATISTICA - TESTE GRILA

21) 'DF �YDORULOH�XQHL�FDUDFWHULVWLFL�VXQW�PLFúRUDWH�FX�FRQVWDQWD�a, atunci dispersia noii serii este:

a) HJDO �FX�GLVSHUVLD�VHULHL�LQL LDOH� b) PDL�PDUH�GHFkW�GLVSHUVLD�VHULHL�LQL LDOH�FX�S WUDWXO�GLVWDQ HL�GLQWUH�PHGLH�úL�FRQstanta a; c) PDL�PLF �GHFkW�GLVSHUVLD�VHULHL�LQL LDOH�FX�S WUDWXO�GLQWUH�PHGLH�úL�FRQVWDQWD�a; d) PDL�PLF �GHFkW�GLVSHUVLD�VHULHL�LQ LDOH�FX�FRQVWDQWD�a; e) PDL�PDUH�GHFkW�GLVSHUVLD�VHULHL�LQL LDOH�FX�FRQVWDQWD�a.

22) Patronul unei firme ce vinde autoturisme presupune� F � UHOD LD� GLQWUH� QXP UXO� GH� DXWRWXULVPH�

vândute într-R�]L��<��úL�QXP UXO�GH�YkQ] WRUL�FH�OXFUHD] �vQ�VDORQXO�GH�SUH]HQWDUH�úL�vQ�VHFWRUXO�GH�SXEOLFLWDWH�D�SURGXVXOXL��;��SRDWH�IL�PRGHODW �SULQWU-R�OLQLH�GUHDSW ��'DWHOH�FXOHVH�SHQWUX���]LOH�sunt:

xi 6 6 4 2 3 yi 20 18 10 6 11

Atunci:

a) OHJ WXUD� GLQWUH� FHOH� GRX � YDULDELOH� SRDWH� IL� PRGHODW � SULQ� HFXD LD� GH� UHJUHVLH�xy 125,3125,0ˆ += ;

b) FRYDULDQ D�GLQWUH�[�úL�\�DUDW �R�OHJ WXU �SXWHUQLF �LQYHUV �vQWUH�FHOH�GRX �YDULDELOH� c) panta linie drepte de regresiH�HVWH��������LDU�SXQFWXO�GH�LQWHUFHS LH�FX�D[D�2\�HVWH�-0,125; d) FRHILFLHQWXO�GH�FRUHOD LH�HVWH�VHPQLILFDWLY�VWDWLVWLF��SHQWUX�R�SUREDELOLWDWH�GH�����

e) DSUR[LPDWLY�����GLQ�YDULD LD�YDORULORU�FDUDFWHULVWLFLL�<�vQ�MXUXO�PHGLHL� y este explLFDW �

SULQ�OHJ WXUD�OLQLDU �GLQWUH�;�úL�<� 23) 3HQWUX� LGHQWLILFDUHD� úL� GLPLQXDUHD� HURULORU� GH� REVHUYDUH� HVWH� QHFHVDU� FRQWUROXO� GDWHORU� FXOHVH��

Acest control nu presupune:

a) FD�SULQ�VRQGDM�V �VH�UHIDF �DQXPLWH�FDOFXOH�GH�RE LQHUH�D�YDORULORU�XQRU�LQGLFDWRUL�însFULúL�în formulare;

b) FD�OD�FHQWUHOH�GH�SUHOXFUDUH�V �VH�YHULILFH�GDF �DX�VRVLW�WRDWH�IRUPXODUHOH��FX�WRDWH�UXEULFLOH�completate;

c) XWLOL]DUHD�XQRU�PRGHOH�GH�YHULILFDUH�D�LSRWH]HORU�VWDWLVWLFH�úL�DSOLFDUH�GH�WHVWH�GH�YHULILFDUH�D�VHPQLILFD LLORU�YDORULORU�LQGLcatorilor;

d) HIHFWXDUHD�GH�FRPSDU UL� e) VXE�QLFL�R�IRUP �XWLOL]DUHD�XQRU�SURJUDPH�LQIRUPDWLFH�VSHFLDO�HODERUDWH�

24) Pentru calculul mediei aritmetice într-R�VHULH�QXPHULF �GH�GLVWULEX LH�GH�IUHFYHQ H�SH�LQWHUYDOH�VH�

iau în considerare: a) limitele inferioare; b) mijloDFHOH�LQWHUYDOHORU��LQGLIHUHQW�GH�UHSDUWL LLOH�GLQ�LQWHUYDOH� c) limitele superioare; d) OLPLWHOH�VXSHULRDUH�GDF �IUHFYHQ HOH�VXQW�UHODWLYH� e) PLMORDFHOH�LQWHUYDOHORU�vQ�LSRWH]D�DSULRULF �D�QRUPDOLW LL�UHSDUWL LLORU�GLQ�LQWHUYDOH�

Page 75: STATISTICA - TESTE GRILA

25) &RHILFLHQWXO� GH� GHWHUPLQD LH� R2, calculat pe baza regulii de adunare a dispersiilor, are întotdeauna valoarea:

a) R 2 1= ;

b) [ ]R 2 0 1∈ , ;

c) ( )R 2 0 1∈ , ;

d) R 2 35%≤ ;

e) R 2 50%> . 26) Inegalitatea dintre abaterile standard ale unei vaULDELOH� ;� QRUPDO� UHSDUWL]DWH� vQ� SRSXOD LLOH�

VWDWLVWLFH� ��� ��� ��� GH� DFHODúL� YROXP� úL� DFHHDúL� PHGLH� x , σ σ σ1 2 3> > � HVWH� YL]XDOL]DW � vQ�varianta:

a) b) c) d) e)

2

1

3

3

2

1

3

1

2

1

2

3

2

3

1

Page 76: STATISTICA - TESTE GRILA

27) 3HQWUX� FHOH� GRX � YDULDELOH� VWDWLVWLFH� vQWUH� FDUH� H[LVW � R� GHSHQGHQ � OLQLDU �� V-au înregistrat o PXO LPH�GH�GDWH�VWDWLVWLFH��ÌQ�XUPD�SUHOXFU ULL�DFHVWRUD�V-DX�RE LQXW�LQGLFDWRULL�

11,1 ;9,19485

;8,4099 ;6,96299 ;91,183 ;968 22

==

====

∑∑∑∑∑

iyx

xyxy

ii

iiii

'HVSUH�GHSHQGHQ D�GLQWUH�FHOH�GRX �YDULDELOH�VH�SRDWH�DILUPD�

a) GHSHQGHQ D�HVWH�LQYHUV � b) HVWLPDUHD�FRYDULDQ HL�HVWH�cov(x,y)=130,82; c) FRHILFLHQWXO�GH�FRUHOD LH�HVWH������� d) HFXD LD�GH�UHJUHVLH�HVWH� xy 2213,388ˆ += ;

e) HFXD LD�GH�UHJUHVLH�HVWH� xy 2213,314,34ˆ += . 28) 3HQWUX�XUP WRDUHOH�YDORUL�DOH�XQHL�YDULDELOH�DOHDWRDUH�;�

{ }7 111414 12 20, , , , ��FDUH�GLQ�XUP WRDUHOH�DILUPD LL�HVWH�DGHY UDW �

a) Me = 14; b) 0R� ����úL�0H� ����

c) 13=x �úL�0H� ����

d) 14=x �úL�0R� ���;

e) 14=== MeMox .

29) &RQVLGHUkQG�XUP WRDUHOH�YDORUL�DOH�XQHL�YDULDELOH�DOHDWRDUH�;��{ }5 7 4 5 20 6 4, , , , , , , indicatorul cel

PDL�SRWULYLW�SHQWUX�D�FDUDFWHUL]D�WHQGLQ D�FHQWUDO �HVWH�

a) PHGLD�DUPRQLF � b) media; c) modul; d) PHGLD�S WUDWLF � e) mediana.

30) Un meteoURORJ� GRUHúWH� V � úWLH� vQ� FH� P VXU � SUHYL]LXQLOH� VDOH� VXQW� IRQGDWH�� ÌQ� DFHVW� VHQV�� HO�

DQDOL]HD] �YDULDELOD�QXPLW �SUHYL]LXQH��$FHDVW �YDULDELO �LD�GRX �YDORUL

x =

0

1

,

,

daca previziunea a fost incorecta

daca previziunea este corecta

0HWHRURORJXO�UHVSHFWLY�D�XUP ULW�SUHYL]LXQLOH�HIHFWXDWH�vQ�FHOH����GH�]LOH�FRQVHFXWLYH�úL�D�FRQVWDWDW�F ����DX�IRVW�FRUHFWH�LDU����DX�IRVW�LQFRUHFWH��3H�ED]D�DFHVWRU�GDWH�HO�WHVWHD] �LSRWH]D� H0��SURSRU LD�SUHYL]LXQLORU�HIHFWXDWH�úL�FRUHFWH�HVWH�GH�����úL H1��SURSRU LD�HVWH�GLIHULW �GH�����úL cu testul χ2:

Page 77: STATISTICA - TESTE GRILA

a)

( )

( ) ( )

χ

χ

22

2 2

1 0 95232 25 18 25

25203 9 3 84

= =

=+ + +

= > =

∑frecventelor observate + frecventa teoretica

frecventa teoretica

, ,; ,

⇒ se respinge ipoteza H0;

b)

( )

( ) ( )

χ

χ

22

2 2

1 0 95232 25 18 25

253 92 3 84

= =

=− + −

= > =

∑frecventelor observate - frecventa teoretica

frecventa teoretica

, ,; ,

⇒ se respinge ipoteza H0;

c) VH�FDOFXOHD] �χ2�vQ�YDULDQWD�E��úL�VH�DOHJH�DWXQFL�LSRWH]D�+0; d) VH�FDOFXOHD] �χ2�vQ�YDULDQWD�D��úL�VH�DOHJH�DWXQci ipoteza H1; e)

( )χ

χ

22

2 2

1 0 95232 18

25 25269 6 3 84

=

=

= ++

= > =

∑∑frecventelor observate

frecventelor teoretice

, ,; ,

⇒ se respinge ipoteza H0. 31) 1RWHOH� RE LQXWH� GH� �� VWXGHQ L� GLQ� DFHHDúL� JUXS �� vQ� VHVLXQHD� GH� YDU �� OD� SDWUX� GLVFLSOLQH� VH�

SUH]LQW �DVWIHO�

1XPH�úL� DISCIPLINA prenume NR. 1 NR. 2 NR. 3 NR. 4

A.B. 9 6 7 8 C.D. 6 7 9 9 E.F. 7 8 8 6 G.H. 10 9 10 8 M.V. 5 7 4 5

3HQWUX�FDUDFWHUL]DUHD�GLVLPLODULW LL�VWXGHQ LORU�GXS �QRWHOH�RE LQXWH��VH�FDOFXOHD] �PDWULFHD�GLVWDQ HORU�DEVROXWH��$FHDVWD�HVWH�

a) AB CD EF GH MV b) AB CD EF GH MV AB 0 7 7 7 11 AB 0 7 7 7 0 CD 7 0 6 8 10 CD 7 0 6 0 8 EF 7 6 0 8 8 EF 7 6 0 8 10 GH 7 8 8 0 15 GH 7 0 8 0 15 MV 11 10 8 15 0 MV 0 8 10 15 0

Page 78: STATISTICA - TESTE GRILA

c) NR1 NR2 NR3 NR4 d) AB CD EF GH MV NR1 0 7 7 11 NR1 0 7 7 7 11 NR2 7 0 6 8 NR2 7 0 6 8 10 NR3 7 6 0 15 NR3 7 6 0 8 8 NR4 11 8 15 0 NR4 11 10 8 0 15

e) AB CD EF GH MV

AB 0 -7 -7 11 7 CD -7 0 -6 8 -10 EF -7 -6 0 8 8 GH 11 8 8 0 15 MV 7 -10 8 15 0

Page 79: STATISTICA - TESTE GRILA

TESTUL 9

1) ÌQ�VWXGLXO� UHSDUWL LHL�QRUPDOH�VH� IRORVHúWH�úL�QR LXQHD������-α) - punct percentilic [ ]α ∈ 0 1, al

UHSDUWL LHL�N(0,1). Acesta:

a. este valoarea Cα pentru care Φ( )Cα α= −1 ;

b. este cuantila de ordin 1-α; c. este cuantila de ordin α;

d. este cuantila de ordin 1

α;

e. este valoarea pentru care Φ( )Cα α= +1 .

2) 'LVSHUVLD�XQHL�VXPH�GH�YDULDELOH��QRWDW �σ x x xn1 2

2+ + +.. :

a) HVWH� HJDO � FX� VXPD� GLVSHUVLLORU� YDULDELOHORU� σ xi

n

i

2

1=∑ GDF � vQWUH� YDULDELOHOH� x1, x2, …, xn

H[LVW �R�GHSHQGHQ �OLQLDU � b) HVWH�HJDO �FX�VXPD�GLVSHUVLLORU�YDULDELOHORU�PDMRUDW �FX�GXEOXO�VXPHL�FRYDULDQ HORU�GLQWUH�

YDULDELOH�OXDWH�VXFFHVLY�GRX �FkWH�GRX � σ xi

n

i jj ii

n

iCov x x2

1 1

2= >=∑ ∑∑+ ( , ) ;

c) HVWH�HJDO �FX�VXPD�FRYDULDQ HORU�GLQWUH�YDULDELOH�OXDWH�VXFFHVLY�GRX �FkWH�GRX � d) nu se poate calcula; e) HVWH�OLSVLW �GH�VHQV�GHRDUHFH�vQ�SUDFWLF �QX�VH�SRW�vQWkOQL�DVWIHO�GH�FD]XUL�

3) 'DF �SH�ED]D�GDWHORU�XQHL� VHULL� VWDWLVWLFH�YDORDUHD�PHGLH�D�FDUDFWHULVWLFLL� V-a calculat ca medie

DUPRQLF ��DWXQFL�vQ�FDOFXOXO�GLVSHUVLHL��SHQWUX�FDUDFWHUL]DUHD�vPSU úWLHULL��VH�XWLOL]HD] �

a) PHGLD�DULWPHWLF � b) media�JHRPHWULF � c) PHGLD�DUPRQLF � d) PHGLD�FURQRORJLF � e) mediana; f) PHGLD�S WUDWLF � g) cuartila a treia.

4) ÌQ�UHSUH]HQW ULOH�JUDILFH�DOH�GDWHORU�VWDWLVWLFH�VH�XWLOL]HD] �

a) vQ�H[FOXVLYLWDWH�VFDUD�DULWPHWLF � b) vQ� IXQF LH� GH� RUGLQXO� GH� P ULPH� DO� GDWHORU� VH� XWLOL]HD] � GXS � FD]� VFDUD� DULWPHWLF ��

ORJDULWPLF ��VHPLORJDULWPLF ��GXEOX�ORJDULWPLF ��HWF�� c) vQ� IXQF LH� GH� RUGLQXO� GH� P ULPH� DO� GDWHORU� VFDOD� QRPLQDO �� RUGLQDO �� GH� LQWHUYDOH�� GH�

UDSRDUWH��FRQWLQX �VDX�GLVFUHW � d) RULFH�VFDU ��QXPDL�JUDILFXO�V �ILH�WUDVDW�vQWU-un sistem de axe rectangulare; e) RULFH�VFDU ��QXPDL�JUDILFXO�V �ILH�WUDVDW�vQWU-un sistem de axe polare.

Page 80: STATISTICA - TESTE GRILA

5) 5HSDUWL LD�PXQFLWRULORU� GLQWU-R�XQLWDWH� LQGXVWULDO � GXS � VDODULXO� ORU�PHGLX� OXQDU�QHW� VH�SUH]LQW �astfel:

Clase salariale (u.m.) Nr. persoane

[800; 1000] 26 [1000; 1100] 33 [1100; 1200] 64 [1200; 1300] 7 [1300; 1500] 10

Procentul muncitorilor cu salariile medii lunare mai mici sau egale cu 1200 u.m. este:

a) 64%; b) 45,8%; c) 87,9%; d) 12,1%; e) 23,5%.

6) 6FRSXO�XQHL�REVHUY UL�VWDWLVWLFH�

a) vQ�PRG�REOLJDWRULX�WUHEXLH�V �FRUHVSXQG �FX�VFRSXO�FHUFHW ULL�VWDWLVWLFH�HIHFWXDWH� b) VH�SUHFL]HD] �vQ�IXQF LH�GH�QHFHVLW LOH�VSHFLILFH�GH�LQIRUPD LL�SHQWUX�GRPHQLXO�vQ�FDUH�VH�

RUJDQL]HD] �FHUFHWDUHD�úL�FDUH�VH�vQFDGUHD] �vQ�VFRSXO�JHQHUDO�DO�DFHVWHLD� c) QX� WUHEXLH� SUHFL]DW� GHRDUHFH� QX� LQIOXHQ HD] � YROXPXO� úL� FDOLWDWHD� GDWHORU� QHFHVDUH�

GHPHUVXOXL�úWLLQ LILF� d) QX� WUHEXLH� SUHFL]DW� GHRDUHFH� QX� SUH]LQW � LPSRUWDQ � SHQWUX� UH]ROYDUHD� SUDFWLF � D� XQRU�

SUREOHPH�FXP�DU�IL��GHOLPLWDUHD�RELHFWXOXL�GH�REVHUYDUH��GHILQLUHD�XQLW LORU�GH�REVHUYDUH��stabilirea programului propriu-]LV�DO�REVHUY ULL�

e) WUHEXLH� FODU� SUHFL]DW� GHRDUHFH� vQ� IXQF LH� GH� DFHVWD� VH� UHDOL]HD] � QXPDL� LQVWUXLUHD�personalului care culege datele.

ÌQ� FRQFHS LD� GH� DVW ]L�� VWDWLVWLFD� IDFH� SDUWH� GLQ� FDGUXO� úWLLQ HORU� FDUH� VWXGLD] �� VXE� DVSHFW�cantitatiY��IHQRPHQHOH�úL�SURFHVHOH�vQWU-R�YL]LXQH�VLVWHPLF ��OD�QLYHO�PLFUR�úL�PDFURHFRQRPLF�� LQkQG�VHDPD�GH�GLQDPLVPXO�VWUXFWXULORU�H[LVWHQWH�úL�GH�IDFWRULL�FDUH�DF LRQHD] �YDULDELO�vQ�WLPS�úL�VSD LX�� ���ÌQ�FRQVHFLQ ��VFRSXO�XQXL�GHPHUV�VWDWLVWLF�HVWH�

a) excluVLY�GH�FXQRDúWHUH�D�IHQRPHQHORU�úL�SURFHVHORU�LQYHVWLJDWH� b) GH�FXQRDúWHUH�úL�IXQGDPHQWDUH�D�YDULDQWHORU�GHFL]LLORU�GH�DF LXQH� c) GH�FXQRDúWHUH��GH�GHVSULQGHUH�D�OHJLW LORU�VXE�FDUH�VH�PDQLIHVW �IHQRPHQHOH�úL�SURFHVHOH�

LQYHVWLJDWH�úL�GH�IXQGDPHQWDUH�D�DFWLYLW LL�PDQDJHULDOH� d) GH�FRQVHPQDUH�D�PDQLIHVW ULL�IHQRPHQHORU�LQYHVWLJDWH��OD�XQ�PRPHQW�GDW� e) VLPLODU�FX�FHO�DO�XQHL�DFWLYLW L�FRQWDELOH�

8) 3HQWUX�D�vQ HOHJH�FDUDFWHUXO�DFHVWRU�IHQRPHQH�WUHEXLH�SRUQLW�GH�OD�

a) natura raporturilor de cauzalitate a acestora; b) scopXO�FHUFHW ULL� c) VFRSXO�REVHUY ULL� d) prelucrarea datelor culese; e) identitatea formelor lor individuale de manifestare.

Page 81: STATISTICA - TESTE GRILA

9) 8QLW LOH�FRPSOH[H�GH�REVHUYDUH�

a) VXQW�UH]XOWDWH�DOH�RUJDQL] ULL�VRFLDOH�úL�HFRQRPLFH�D�SRSXOD LHL��FROHFWLYLW LL��VWDWLVWLFH� b) pot fi de exemplu: angajatul într-R� vQWUHSULQGHUH�� MXF WRUXO� vQWU-R� HFKLS � GH� IRWEDO��

persoana unei familii; c) VXQW�QXPDL�XQLW LOH�UDSRUWRDUH�FDUH��SRWULYLW�OHJLVOD LHL�vQ�YLJRDUH��LQIRUPHD] �VLVWHPDWLF�

DVXSUD�DFWLYLW LL�XQLW LORU�DIODWH�vQ�VWUXFWXUD�ORU�RJDQL]DWRULF � d) VXQW�HOHPHQWHOH�VLPSOH�FRQVWLWXWLYH�DOH�SRSXOD LHL�VWDWLVWLFH�FDUH�VXQW�GLVSXVH�V �U VSXQG �

OD�vQWUHE ULOH�GLQ�FKHVWLRQDU��GH�H[HPSOX��VWXGHQWXO��SHUVRDQD�FX�GUHSW�GH�YRW��HWF��� e) VXQW�GH�WLSXO��PXO LPHD�vQWUHSULQGHULORU�PLFL�úL�PLMORFLL��PXO LPHD�F V toriilor,etc.

10) 3UHFL]D L�úL�DUJXPHQWD L�GDF �DILUPD LD��³RULFH�QXP U�HVWH�R�GDW �VWDWLVWLF ´�HVWH�

a) DGHY UDW � b) IDOV � c) HVWH�DGHY UDW �GDF �QXP UXO�HVWH�QDWXUDO� d) HVWH�DGHY UDW ��GHRDUHFH�VWDWLVWLFD�VWXGLD] �IHQRPHQHOH�GH�PDV �GLQ�SXQFW�GH�YHGHUH�FDQWLWDWLY� e) QX� HVWH� DGHY UDW �� GHRDUHFH� VWDWLVWLFD� VWXGLD] � úL� YDULDELOH� DOH� F URU� YDULDQWH� VXQW�

nenumerice.

11) /D�H[DPHQXO�GH�%D]HOH�6WDWLVWLFLL�GLQ������������SULPLL����VWXGHQ L�GLQ�FDWDORJXO�JUXSHL������DX�RE LQXW�XUP WRDUHOH�QRWH�

Nr. crt 1 2 3 4 5 6 7 8 9 10 Nota 10 7 4 8 9 9 7 3 6 2

Datele prezentat în tabel sunt:

a) individuale; b) agregate; c) de stoc; d) de flux; e) grupate.

12) 0HGLD�DULWPHWLF �HVWH�DFHD�YDORDUHD�QXPHULF �D�YDULDELOHL�VWXGLDWH�FDUH�PLQLPL]HD] �

a) ( )x xii

n−

=∑

2

1

;

b) max x xi − ;

c) x x x xi ji j

i j

n− −

=≠

∑, 1

;

d) ( )x xii

n−

=∑

3

1

;

e)

( )( )x x x xi ji j

n

x

− −=

∑, 1

σ.

Page 82: STATISTICA - TESTE GRILA

13) 3HQWUX� GRX � VHULL� GH� GLVWULEX LH� GH� IUHFYHQ H�� LQGLFDWRUXO� ³DPSOLWXGLQHD� vPSU úWLHULL´� HVWH�FRPSDUDELO�GDF �

a) FHOH�GRX �VHULL�VH�UHIHU �OD�DFHHDúL�FDUDFWHULVWLF � b) FHOH�GRX �VHULL�VH�UHIHU �OD�DFHHDúL�FROHFWLYLWDWH� c) FHOH�GRX �VHULL�VH�UHIHU �OD�FDUDFWHULVWLFL�GLIHULWH��GDU�FX�DFHHDúL�XQLWDWH�GH�P VXU � d) FHOH�GRX �VHULL�DX�DFHODúL�JUDG�GH�DVLPHWULH� e) FHOH�GRX �VHULL�VH�UHIHU �OD�FROHFWLYLW L�GH�DFFHODúL�YROXP�

14) 3XQFWXO�$�VHPQLILF �

a) ( )P X xx x< = −

’Φσ

;

1,0

0,5

x − 3σ x − 2σ x − σ x x’ x + σ x + 2σ x + 3σ

-3 -2 -1 0 1 2 3

b) ( )P X xx x> = −

’Φσ

;

c) ( )P X xx x= = −

’Φσ

;

d) ( )P X xx x< > −

’Φσ

;

e) ( )P X xx x< < −

’Φσ

.

15) ����GH� HOHYL� GLQ� GRX �RUDúH� SDUWLFLS � OD� XQ� FRQFXUV� GH� FXOWXU � JHQHUDO ��&HL� ��� GH� HOHYL� GLQ�

SULPXO�RUDú�RE LQ�XQ�SXQFWDM�PHGLX�GH����SXQFWH��FX�XQ�FRHILFLHQW�GH�YDULD LH�GH������LDU�FHL�GLQ�DO�GRLOHD�RUDú�RE LQ�XQ�SXQFWDM�PHGLX�GH����SXQFWH�FX�R�DEDWHUH�PHGLH�S WUDWLF �GH�����SXQFWH��)DFWRUXO�GH�JUXSDUH���RUDúXO��FRQWULEXLH�OD�YDULD LD�SXQFWDMHORU�RE LQXWH�GH�HOHYL�vQ�SURSRU LH�GH�

a) 23,46%; b) 10,28%; c) 76,54%;

A

Page 83: STATISTICA - TESTE GRILA

d) 48,44%; e) 24,48%.

16) 3ULQFLSDOD� SURSULHWDWH� D� IHQRPHQHORU� GH� PDV � HVWH� YDULDELOLWDWHD� vQ� WLPS� úL� vQ� VSD LX� úL�

OHJHD� GH� DSDUL LH� D� DFHVWRUD� VH� PDQLIHVW � FD� WHQGLQ � úL� QX� vQ� ILHFDUH� FD]� vQ� SDUWH�� 'LQ�DFHDVW �FDX] ��IHQRPHQHOH�GH�PDV �VXQW�QXPLWH�úL�IHQRPHQH�QHGHWHUPLQLVWH�VDX�VWRFKDVWLFH��LDU�LQWHUSUHWDUHD�úL�DQDOL]D�ORU�WUHEXLH�V �FDG �VXE�LQFLGHQ D�QXPHUHORU�PDUL��3RWULYLW�DFHVWHL�legi:

a) YDULD LLOH�vQWkPSO WRDUH�GH�OD�WHQGLQ D�JHQHUDO �SURYRFDWH�GH�IDFWRULL�RELHFWLYL�úL�HVHQ LDOL�

VH�FRPSHQVHD] �UHFLSURF�GDF �H[LVW �XQ�QXP U�PDUH�GH�FD]XUL�LQGLYLGXDOH� b) QXPDL�vQWkPSO WRU�YDULD LLOH�GH�OD�WHQGLQ D�JHQHUDO �VH�FRPSHQVHD] � c) QX�HVWH�SRVLELO �WUHFHUHD�GH�OD�QXPHURDVHOH�GDWH�LQGLYLGXDOH�OD�LQGLFDWRUL�VLQWHWLFL�VSHFLILFL�

ansamblului investigat; d) YDULD LLOH�vQWkPSO WRDUH�GH�OD�WHQGLQ D�JHQHUDO �SURYRFDWH�GH�IDFWRULL�DOHDWRUL�GH�LQIOXHQ �

se compeQVHD] � UHFLSURF� GDF � H[LVW � XQ� QXP U�PDUH� GH� FD]XUL� LQGLYLGXDOH� GH� DFHHDúL�HVHQ ��OXDWH�vQ�VWXGLX�

e) WHQGLQ D�GH�PDQLIHVWDUH�WUHEXLH�V �VH�YHULILFH�OD�QLYHOXO�ILHF UHL�XQLW L�GH�REVHUYDUH� 17) 3URFHVXO�GH�FXQRDúWHUH�VWDWLVWLF �VH�vQFKHLH�FX�

a) observarea total �VDX�SDU LDO �D�IHQRPHQHORU�GH�PDV �GHOLPLWDWH� b) prelucrarea datelor înregistrate; c) interpretarea rezultatelor; d) prezentarea datelor în tabele, serii sau grafice; e) DQDOL]D� úL� LQWHUSUHWDUHD� UH]XOWDWHORU� úL� FX� IRUPXODUHD� FRQFOX]LLORU� VWDWLVWLFH� FDUH�

obligatoriu� WUHEXLH�V �FXSULQG �YDULDQWH�SUREDELOH�GH�DSDUL LH�DOH�DFHORUDúL� IHQRPHQH�în viitor.

18) 3HQWUX�VWDELOLUHD�JUHXW LL�VSHFLILFH�D�SURGXF LHL�UHEXWDWH�vQWU-un lot de volum N=3000 produse

s-DX�SUHOHYDW�vQWkPSO WRU�úL�QHUHSHWDW�����GH�SURGXVH��ÌQ�XUPD�HIHFWX ULL controlului acestora 9 produse au fost depistate rebuturi. Pentru o probabilitate de 0,975 (zα=1,96) procentul de rebut estimat pentru întregul lot este:

a) (0,015; 0,06);

b) (0,012; 0,048;

c) (0,15; 0,20);

d) (0,02; 0,05);

e) (0,18; 0,25).

19) 2�PHGLH�FDOFXODW �GLQWU-un úLU�GH�YDORUL�LQGLYLGXDOH�HVWH�UHSUH]HQWDWLY �GDF �

a) s-DX�XWLOL]DW�IUHFYHQ HOH�DEVROXWH�GH�DSDUL LH�D�YDORULORU�LQGLYLGXDOH� b) úLUXO�GH�YDORUL�LQGLYLGXDOH�HVWH�RPRJHQ� c) XQXO�GLQ�FRHILFLHQ LL�GH�DVLPHWULH�LD�YDORUL�vQ�LQWHUYDOXO�>-1, 1]; d) úLUXO�GH�YDORUL�HVWH�Vtructurat pe intervale de grupare egale; e) s-D�XWLOL]DW�PHGLD�DULWPHWLF �

Page 84: STATISTICA - TESTE GRILA

20) &DUH�HVWH�UHOD LD�FRUHFW �GH�FDOFXO�D�FRHILFLHQWXOXL�GH�FRUHOD LH�OLQLDU �VLPSO �

a) rxy x y

yxx y

=− ⋅

σ σ;

b) ( )( )

rx x y y

nyxx y

=− −∑σ σ

;

c) r byxx

y=

σσ

;

d)

( ) ( )r

n xy x y

n x x n y yyx =

∑∑∑∑∑ ∑∑2 2 2 2

;

e) ( )( )

ry Y

y yyx

i

i

= −−

∑∑

12

2.

21) 2� FRPSDQLH� FDUH� SURGXFH� XQ� QRX� WLS� GH� vQJU ú PkQW� DJULFRO� HVWH� LQWHUHVDW � GH� VWXGLHUHD�FRUHOD LHL�GLQWUH�SURGXF LD�GH�URúLL��<��úL�FDQWLWDWHD�GH�vQJU ú PkQW�DSOLFDW��;���2�VXSUDID �HVWH�GLYL]DW � vQ� RSW� SDUFHOH� GH�P ULPL�HJDOH� SH� FDUH� VXQW� DSOLFDWH� FDQWLW L� GLIHULWH� GH� vQJU ú PkQW��3URGXF LLOH� GH� URúLL� �NJ�� úL� FDQWLW LOH� GH� vQJU ú PkQW� DSOLFDW� �NJ��� vQUHJLVWUDWH� SHQWUX� ILHFDUH�SDUFHO �VXQW�

xi 1 1,5 2 2,5 3 3,5 4 4,5 yi 25 31 27 28 36 35 32 34

&RHILFLHQWXO�GH�FRUHOD LH�DUH�valoarea:

a) 0,37; b) 0,98; c) 0,73; d) -0,84; e) 1,00.

22) Într-XQ� úLU� GH� YDORUL� LQGLYLGXDOH� UHIHULWRDUH� OD� DFHHDúL� YDULDELO � úL� REVHUYDW � vQWU-R� SRSXOD LH�VWDWLVWLF �GHOLPLWDW �vQ�WLPS�úL�vQ�VSD LX��YDORDUHD�PRGDO �HVWH�

a) YDORDUHD�LQGLYLGXDO �SR]LWLY �FHD�PDL�PDUH� b) valoaUHD�LQGLYLGXDO �QHJDWLY �PD[LP �vQ�YDORDUH�DEVROXW � c) YDORDUHD�LQGLYLGXDO �SR]LWLY �VDX�QHJDWLY ��FX�FHD�PDL�PDUH�IUHFYHQ �GH�DSDUL LH� d) DFHD�YDORDUH�FDUH�vQUHJLVWUHD] �FHD�PDL�PDUH�DEDWHUH�DEVROXW �ID �GH�PHGLH� e) YDORDUHD�FDUH�PLQLPL]HD] �GLVSHUVLD�

23) PentrX�DQDOL]D�GHSHQGHQ HORU�VWDWLVWLFH�GLQWUH�YDULDELOH�PHWRGD�JUDILF �SHUPLWH�

a) LQWHUSUHWDUHD�LQWHQVLW LL�OHJ WXULORU�GLQWUH�YDULDELOH� b) FRQVWDWDUHD�H[LVWHQ HL�OHJ WXULL�VWDWLVWLFH� c) LGHQWLILFDUHD�H[LVWHQ HL��GLUHF LHL�úL�IRUPHL�OHJ WXULL�GLQWUH�GRX �YDULDELOH statistice; d) HVWLPDUHD�SDUDPHWULORU�IXQF LHL�GH�UHJUHVLH� e) HVWLPDUHD�UDSRUWXOXL�GH�FRUHOD LH�GDU�QX�úL�D�FRHILFLHQWXOXL�GH�FRUHOD LH�VDX�GH�DVRFLHUH�

Page 85: STATISTICA - TESTE GRILA

24) )LH�R�VHULH�VWDWLVWLF ��IRUPDW �GLQ�Q� ��S���YDORUL�LQGLYLGXDOH�[1, x2, …, xn�úL�������51, R2, …, Rn rangurile ordonate ale celor n valori. Mediana (Me) este:

a) Men

xii

n=

=∑1

1

;

b) F Me( ) = 1

2;

c) Me Rp= +1 ;

d) Me xn= +

1

2;

e) Me

xn

xn

=

+ +

2

1

2

2.

25) Într-R�VHULH�GH�UHSDUWL LH�GH�LQWHUYDOH�LQWHUYDOXO�PHGLDQ�HVWH�

a) acela care vPSDUWH�vQ�GRX �S U L�HJDOH�QXP UXO�GH�LQWHUYDOH�DOH�VHULHL�

b) FRUHVSXQ] WRU�SULPHL�IUHFYHQ H�FXPXODWH�FDUH�GHS úHúWH�

nii

r

=∑

1

2;

c) FRUHVSXQ] WRU�SULPHL�IUHFYHQ H�FXPXODWH�FDUH�GHS úHúWH�

nii

r+

=∑ 1

21 ;

d) FRUHVSXQ] WRU�LQWHUYDOXOXL�FX�IUHFYHQ D�FHD�PDL�PDUH� e) FRUHVSXQ] WRU�LQWHUYDOXOXL�vQ�FDUH�HVWH�SODVDW �PHGLD�

26) 'DF �vQWU-R�VHULH�GH�UHSDUWL LH�GH�IUHFYHQ H�x

ni

i i r

=1,

, n nii

r

=∑ =

1

��VH�FDOFXOHD] �IUHFYHQ HOH�

FXPXODWH�FUHVF WRU� ( )Fai i r=1,�úL�IUHFYHQ HOH�FXPXODWH�GHVFUHVF WRU� ( )Fd i i r=1, , atunci între ele

H[LVW �UHOD LD�

a) nFdFa ii =+ ;

b) nFdFa ii += ;

c) nFdFa ii =+ + )1( ;

d) 100=+ ii FdFa ;

e) 100)1( =+ +ii FdFa .

27) )UHFYHQ D�DEVROXW �FXPXODW �FUHVF WRU�D�XOWLPHL�JUXSH�HVWH�vQWRWGHXQD�HJDO �FX�

a) QXP UXO�GH�XQLW L�GLQ�FROHFWLYLWDWH� b) QXP UXO�GH�XQLW L�GLQ�XOWLPD�JUXS � c) 100%; d) IUHFYHQ D�DEVROXW �FXPXODW �GHVFUHVF WRU�D�XOWLPHL�JUXSH� e) IUHFYHQ D�DEVROXW �D�XOWLPHL�JUXSH�SOXV�YROXPXO�FROHFWLYLW LL�

Page 86: STATISTICA - TESTE GRILA

28) În general, în cadrul VRFLHW LL�� GDU� úL� vQ� QDWXU �� IHQRPHQHOH� SRW� V � DSDU � FD� UH]XOWDW� DO� XQHL�

VLQJXUH�FDX]H�VDX�FD�UH]XOWDW�DO�PDL�PXOWRU�FDX]H�FDUH�VH�PDQLIHVW �L]RODW�VDX�vQ�LQWHUGHSHQGHQ �vQWUH� HOH�� ÌQ� SULPXO� FD]�� VXQW� IHQRPHQH� XQLYRF� GHWHUPLQDWH� úL� GH� UHJXO � HOH� VH� SUH]LQW � FD�IHQRPHQH�VLPSOH��LGHQWLFH�vQWUH�HOH��GHQXPLWH�úL�IHQRPHQH�WLSLFH��ÌQ�FHO�GH-al doilea caz, apar ca IHQRPHQH� PXOWLFDX]DOH� DO� F URU� SURFHV� GH� IRUPDUH� SRDWH� V � SUH]LQWH� JUDGH� GLIHULWH� GH�FRPSOH[LWDWH�� FX� UHOD LL� PXOWLSOH� GH� LQWHUGHSHQGHQ �� IRUPkQG� � vPSUHXQ � XQ� DQVDPEOX� D� F UXL�GLPHQVLXQH� úL� VWUXFWXU � SRW� IL� GHOLPLWDWH� vQ� WLPS�� vQ� VSD LX� úL� RUJDQL]DWRULF�� 6WDWLVWLFD� VWXGLD] �fenomenele din:

a) primul caz; b) cazul al doilea; c) ambele cazuri; d) DOW �FDWHJRULH�GHFkW�FHOH�SUHFL]DWH� e) cazul al doilea, dar numai cele cuantificabile.

29) 0HGLD�DULWPHWLF �D�VXPHL�GLQWUH�GRX �YDULDELOH�HVWH�HJDO �FX�VXPD�PHGLLORU�FHORU�GRX �YDULDELOH��FkQG�

a) FHOH�GRX �YDULDELOH�VH�DIO �vQWU-R�UHOD LH�GH�LQWHUGHSHQGHQ � b) FHO�GRX �YDULDELOH�VH�DIO �vQWU-R�UHOD LH�GH�LQYHUV �SURSRU LRQDOLWDWH� c) FHOH�GRX �YDULDELOH�VH�UHIHU �OD�DFHHDúL�FROHFWLYLWDWH� d) FHOH�GRX �YDULDELOH�VXQW�LQGHSHQGHQWH� e) FHOH�GRX �YDULDELOH�VXQW�GLUHFW�SURSRU LRQDOH�

30) 6WXGLD L�XUP WRDUHOH�DILUPD LL������)HQRPHQHOH�GH�PDV ��vQ�JHQHUDO��DSDU�FD�R�PXO LPH�GH�IRUPH�

individuale diferiWH�� DSDUHQW� I U � QLFL� R� OHJ WXU � GH� OD� R� IRUP � OD� DOWD�� GDU� FDUH�� DQDOL]DWH�FRPSDUDWLY��VH�FRQVWDW �F �DX�DFHHDúL�HVHQ �����$FHDVWD�VH�H[SOLF �vQ�SULQFLSDO�SULQ�IDSWXO�F �HOH�VXQW�JHQHUDWH�GH�R�VHULH�GH�FDX]H�FRPXQH�FDUH�VH�PDQLIHVW �GH�UHJXO �vQ�FRQGL LL diferite; 3) La IHQRPHQHOH� GH� PDV � GLQ� VRFLHWDWH�� UHOD LLOH� GH� PXOWLFDX]DOLWDWH� GLUHFW � VDX� LQGLUHFW � FDUH� OH�GHWHUPLQ �IDF�LPSRVLELO �FXQRDúWHUHD�OHJLORU�FDUH�OH�SURGXF�úL�JXYHUQHD] ��GDF �VH�LDX�vQ�VWXGLX�izolat doar câteva din formele lor de manifestare, ignorând ansamblul din care fac parte; 4) În SUDFWLF �IRUPHOH�LQGLYLGXDOH�GH�PDQLIHVWDUH�GLIHU �GH�OD�R�XQLWDWH�OD�DOWD�vQ�IXQF LH�GH�PRGXO�FXP�VH�DVRFLD] �úL�VH�FRPELQ �IDFWRULL�GH�LQIOXHQ �GH�QDWXU �GLIHULW ��O VkQG�LPSUHVLD�F �ILHFDUH�IRUP �de manifHVWDUH� GLQ� FDGUXO� DQVDPEOXOXL� I U � V � H[LVWH� R� FDX]DOLWDWH� FHUW �� ���$QDOL]DWH�� IRUPHOH�LQGLYLGXDOH�GH�PDQLIHVWDUH�DOH�IHQRPHQHORU�GH�PDV �SDU�DVHP Q WRDUH�vQWUH�HOH��ILLQG�JHQHUDWH�GH�FDX]H�HVHQ LDOH�FRPXQH��VXSXQkQGX-VH�DFHOHLDúL�OHJL�GH�DSDUL LH�úL�GH]Yoltare.

&DUH�GLQ�DILUPD LLOH�GH�PDL�VXV�VXQW�IDOVH�

a) ��������úL��� b) ��������úL��� c) ��������úL��� d) WRDWH��FX�H[FHS LD���� e) nici una.

Page 87: STATISTICA - TESTE GRILA

TESTUL 10

1) 3HQWUX�YHULILFDUHD�QRUPDOLW LL�GLVWULEX LHL�HPSLULFH��vQWU-R�FROHFWLYLWDWH�GH�Q�XQLW L��VLVWHPDWL]DWH�

pe r intHUYDOH� GH� JUXSDUH�� GDF � VH� XWLOL]HD] � WHVWXO� χ2�� YDORDUHD� FDOFXODW � HVWH� FRPSDUDW � FX�valoarea χ2�WDEHODU�FRUHVSXQ] WRDUH�XQXL�QXP U�GH�JUDGH�GH�OLEHUWDWH�HJDO�FX�

a) n-r; b) n-1; c) r-1; d) r-3; e) n-3.

2) 'LVSHUVLD�XQHL�UHSDUWL L�ELQRPLDOH�FX�S�- probabilitatea succesului, q - probabilitatea insuccesului

úL�Q��QXP UXO�GH�REVHUYD LL��HVWH�

a) np; b) nq;

c) npq ; d) npq(q-p); e) npq.

3) &RQVLGHU P� XUP WRDUHOH� SHUHFKL� GH� REVHUYD LL� SHQWUX� YDULDELOHOH� ;� úL� <�� vQWUH� FDUH� H[LVW � R�

GHSHQGHQ �GH�IRUPD�\� �I�[��

xi 1 4 3 2 5 6 0 yi 1 3 3 1 4 7 2

6 �VH�DUDWH�FDUH�GLQ�XUP WRDUHOH�DILUPD LL�HVWH�DGHY UDW �

a) HFXD LD�GH�UHJUHVLH�OLQLDU �HVWH� xy 821,0536,0ˆ −= ;

b) SHQWUX� XQ� SUDJ� GH� VHPQLILFD LH� α=0,05, coeficientul de regresie nu este semnificativ statistic;

c) intervalul de încredere pentru coeficientul de regresie este (0,243, 1,399); d) HFXD LD�GH�UHJUHVLH�OLQLDU �HVWH�

xy 821,0536,0ˆ += ; e) FRHILFLHQWXO�GH�FRUHOD LH�HVWH�U -0,92.

4) 3HQWUX�R�VHULH�GH�UHSDUWL LH�GH�IUHFYHQ H��FX�WHQGLQ �GH�QRUPDOLWDWH��DEDWHUHD�PHGLH�OLQLDU �

a) HVWH�DSUR[LPDWLY�����GLQ�DEDWHUHD�LQWHUTXDUWLOLF � b) HVWH�PDL�PLF �VDX�HJDO �FX����� c) HVWH�DSUR[LPDWLY�����GLQ�YDORDUHD�DEDWHULL�PHGLL�S WUDWLFH� d) HVWH�HJDO �FX�]HUR� e) FXSULQGH�����GLQ�XQLW LOH�VWDWLVWLFH�GLQ�FHQWUXO�GLVWULEX LHL�

Page 88: STATISTICA - TESTE GRILA

5) Pentru verificarea norPDOLW LL� UHSDUWL LLORU� HPSLULFH� XWLOL]kQG� WHVWXO� χ2, valoarea χ calculat2 se

FRPSDU �FX�YDORDUHD� χ tabelar2 �FRUHVSXQ] WRU�XQXL�QXP U�GH�JUDGH�GH�OLEHUWDWH�HJDO�FX�

a) QXP UXO�XQLW LORU�VWDWLVWLFH�GLQ�FROHFWLYLWDWH�PLQXV�XQX� b) QXP UXO�XQLW LORU�VWDWLVWLFH�GLQ�FROHFWLYLWDWH�PLQXV�GRL� c) QXP UXO�LQWHUYDOHORU�GH�YDULD LH�PLQXV�XQX� d) QXP UXO�LQWHUYDOHORU�GH�YDULD LH�PLQXV�QXP UXO�GH�SDUDPHWUL�DL�OHJLL�GH�UHSDUWL LH�χ2 ; e) QXP UXO� LQWHUYDOHORU� GH� YDULD LH�PLQXV� QXP UXO� GH� SDUDPHWUL� DL� OHJLL� GH� UHSDUWL LH�χ2 ,

minus unu. 6) &DUH�GLQ�XUP WRDUHOH�DILUPD LL�HVWH�DGHY UDW �

a) PHGLD�JHRPHWULF �VH�FDOFXOHD] �FD�R�PHGLH�DULWPHWLF �D�ORJDULWPLORU�YDORULORU�LQGLYLGXDOH� b) SURGXVXO�DEDWHULORU�WHUPHQLORU�VHULHL�GH�OD�PHGLD�ORU�JHRPHWULF �HVWH��� c) suma abaterilor WHUPHQLORU�VHULHL�GH�OD�PHGLD�ORU�JHRPHWULF �HVWH��� d) SURGXVXO�DEDWHULORU�WHUPHQLORU�VHULHL�GH�OD�PHGLD�ORU�JHRPHWULF �HVWH��� e) PHGLD�JHRPHWULF �HVWH�DFHD�YDORDUH�FDUH��vQORFXLQG�WHUPHQLL�VHULHL��QX�PRGLILF �SURGXVXO�

S WUDWHORU�ORU� 7) Într-o colectivitate staWLVWLF ��IHQRPHQXO�GH�FRQFHQWUDUH�vQVHDPQ �

a) R�YDULD LH�VF ]XW �D�YDORULORU�FDUDFWHULVWLFLL�vQ�MXUXO�PHGLHL� b) R�GLVWULEX LH�vQ�IRUP �GH�³-´� c) R�DVLPHWULH�VF ]XW �D�GLVWULEX LHL� d) R�GLVWULEX LH�vQ�IRUP �GH�³8´� e) cumularea valorilor caracteristicii în cadrul uneL�JUXSH�FODVH�DOH�FROHFWLYLW LL�

8) 'DF � vQWUH� FXDUWLOHOH� FDOFXODWH�SHQWUX�R�VHULH�GH� UHSDUWL LH� H[LVW � UHOD LD� QQ Q

21 3

2=

+ atunci

UHSDUWL LD�HVWH�

a) DVLPHWULF �OD�GUHDSWD� b) DVLPHWULF �OD�VWkQJD� c) QRUPDO � d) KLSHUEROLF � e) ELGLPHQVLRQDO � f) ELPRGDO �

9) PriQ��FH�WHVW�VH�YHULILF �FRUHVSRQGHQ D�GLQWUH�UHSDUWL LLOH�WHRUHWLFH�úL�FHOH�HPSLULFH"

a) χ2 ; b) F (R.A.Fisher); c) t (Student); d) Kolmogorov-Smirnov; e) Wald.

10) )LH� VHULD� VWDWLVWLF � { }x x xn1 2, , . . . , � RE LQXW � SULQ� REVHUYDUHD� XQHL� YDULDELOH� QXPHULFH� ;� úL�

pentru care s-au calculat media x �úL�GLVSHUVLD��σx2 . Controlându-se calitatea datelor culese, se

FRQVWDW �F �ILHFDUH�GLQ�DFHVWHD�DX�IRVW�PDMRUDWH�OD�vQUHJLVWUDUH�FX�����GH�XQLW L��6HULD�FRUHFW �DU�

Page 89: STATISTICA - TESTE GRILA

fi fost: x x xn1 2

100 100 100, , . . . ,

. Calculându-se din nou dispersia pentru valorile corecte se

FRQVWDW �F �DFHDVWD�HVWH�

a) HJDO �FX�GLVSHUVLD�LQL LDO "

b) PDL�PLF �GHFkW�σx2 de 10.000 ori?

c) PDL�PLF �GHFkW�σx2 cu

1

100?

d) mai mare decât σx2 cu

1

100?

e) mai mare decât σx2 de 100 de ori?

11) 3HQWUX�GRX �YDULDELOH�VWDWLVWLFH�GHSHQGHQWH�[�úL�\�FX�\ I�[���V-DX�FXOHV�GDWH�GH�OD����XQLW L�úL�V-au calculat indicatorii:

y y x x x yii

ii

ii

ii

i ii

∑ ∑ ∑ ∑ ∑= = = = =1133 92703 3658 0957118 2967342 2; ; , ; , ; ,

ÌQ� LSRWH]D�XQHL� GHSHQGHQ H� OLQLDUH�HFXD LD� GH� UHJUHVLH� FDUH�PRGHOHD] � OHJ WXUD� GLQWUH� FHOH�GRX �YDULDELOH�HVWH�

a) xy 35,52255,55ˆ += ; b) xy 55,5535,522ˆ +−= ; c) xy 55,5535,522ˆ −= ; d) 55,5535,522ˆ +−= xy ; e) xy 35,52255,55ˆ +−= ;

12) Se precizeaz �XUP WRDUHOH�SRSXOD LL�VWDWLVWLFH� ���SRSXOD LD�%XFXUHúWLXOXL�OD���RFWRPEULH������ ���SRSXOD LD�GLQ�5RPkQLD�GLQ�PHGLXO�XUEDQ�OD����LXOLH������ ���PXO LPHD�IDFWXULORU�HODERUDWH�GH�6�&��³,&6´�65/�vQ�WULP��,������ 4) PXO LPHD�F V WRULLORU�vQFKHLDWH�vQ�5RPkQLD�vn anul 1997; 5) VWRFXULOH�GH�P UIXUL�DOH�vQWUHSULQGHULORU�PLFL�úL�PLMORFLL�OD�VIkUúLWXO�DQXOXL������

3RSXOD LL�VWDWLVWLFH�GLQDPLFH�VXQW�

a) ��úL���

b) ��úL���

c) ��úL���

d) ��úL���

e) ��úL���

13) ÌQ�FD]XO�XQHL�REVHUY UL�VWDWLVWLFH�DO�F UHL�VFRS�HVWH�³IRWRJUDILHUHD�]LOHL�GH�Oucru a unui muncitor”:

a) WLPSXO�REVHUY ULL�FRLQFLGH�FX�WLPSXO�OD�FDUH�VH�vQUHJLVWUHD] �GDWHOH� b) WLPSXO�REVHUY ULL�QX�FRLQFLGH�FX�WLPSXO�OD�FDUH�VH�vQUHJLVWUHD] �GDWHOH� c) WLPSXO�REVHUY ULL�VH�UHIHU �OD�GXUDWD�V SW PkQLL�GH�OXFUX�D�PXQFLWRUXOXL� d) precizarea timpXOXL�REVHUY ULL�HVWH�OLSVLW �GH�VHQV� e) WLPSXO�REVHUY ULL�HVWH�PRPHQWXO�FULWLF��³RUD�]HUR´�D�]LOHL�vQ�FDUH�PXQFLWRUXO�VH�SUH]LQW �OD�OXFUX�

Page 90: STATISTICA - TESTE GRILA

14) Coeficientul de concentrare al lui Corrado-*LQL�VH�FDOFXOHD] �FD�

a) ∑=

=n

iixG

1

2 ;

b) ∑∑=

=

=n

in

ii

i

x

xG

1

1

;

c) 1

2

1

1

=

=

∑∑

=n

in

ii

i

x

xnG ;

d)

2

1

1

∑∑=

=

=n

in

ii

i

x

xG ;

e) n

ix

x

G

n

in

i

i∑∑=

==

1

2

1 .

15) 0HGLD�DULWPHWLF �D�XQHL�YDULDELOH�DOHDWRDUH�;��UHSUH]LQW �

a) momentul simplu de ordinul întâi;

b) momentul centrat de ordinul întâi;

c) momentul centrat de ordinul al doilea;

d) momentul simplu de ordinul al doilea;

e) PRPHQWXO�VLPSOX�GH�RUGLQXO�DO�GRLOHD�PLQXV�PRPHQWXO�VLPSOX�GH�RUGLQXO�vQWkL�OD�S WUDW�

16) /D�WHVWDUHD�QRUPDOLW LL�UHSDUWL LLORU�HPSLULFH�XWLOL]kQG�WHVWXO�χ2���GDF � χ χcalc tab2 2< , atunci:

a) VH� DFFHSW � LSRWH]D� F � vQWUH� GLVWULEX LD� HPSLULF � úL� FHD� QRUPDO � �WHRUHWLF �� QX� H[LVW �

FRQFRUGDQ � b) VH� DFFHSW � LSRWH]D� F � vQWUH� GLVWULEX LD� HPSLULF � úL� FHD� QRUPDO � �WHRUHWLF �� H[LVW �

FRQFRUGDQ � c) VH� UHVSLQJH� LSRWH]D� FRQIRUP� F UHLD� vQWUH� GLVWULEX LD� HPSLULF � úL� FHD� WHRUHWLF � H[LVW �

concordDQ � d) VH�DFFHSW �LSRWH]D�FRQIRUP�F UHLD�GLVWULEX LD�HPSLULF �GLIHU �VHPQLILFDWLY�GH�FHD�QRUPDO �

�WHRUHWLF �� e) QX�H[LVW �PRWLYH�VXILFLHQWH�SHQWUX�D�DFFHSWD�LSRWH]D�QRUPDOLW LL�GLVWULEX LHL�HPSLULFH�

Page 91: STATISTICA - TESTE GRILA

17) $PSOLWXGLQHD�UHODWLY �D�YDULD LHL�VH�FDOFXOHD] �FD�

a) x xmax min−

100;

b) x x

xmax min

min

−100 ;

c) x x

xmax min

max

−100 ;

d) x x

xmax min−

100 ;

e) x x

xmax −

100 .

18) 5HSDUWL LD�ELQRPLDO ��WLQGH�F WUH�UHSDUWL LD�QRUPDO �

a) GDF �QLFL�S��SUREDELOLWDWHD�VXFFHVXOXL��úL�QLFL�T��SUREDELOLWDWHD�LQVXFFHVXOXi) nu sunt nule; b) GDF �S T ���� c) GDF � XQD� GLQWUH� SUREDELOLW L� GHYLQH� IRDUWH� PLF � úL� Q� �QXP UXO� GH� REVHUYD LL�� FUHúWH�

VXILFLHQW�SHQWUX�D�S VWUD�QS�ILQLW� d) GDF �R�SUREDELOLWDWH��S�VDX�T��GHYLQH�QXO � e) GDF �QLFL�S�úL�QLFL�T�QX�VXQW�PLFL��LDU�Q�DUH�YDORUL�PDUL�

19) ÌQ�PRGHOXO�GH�DQDOL] �GLVSHUVLRQDO �XQLIDFWRULDO ��GLVSHUVLD�FRUHFWDW �GLQ�LQWHULRUXO�JUXSHORU�VH�

RE LQH� UDSRUWkQG� VXPD�S WUDWHORU� DEDWHULORU� GLQ� LQWHULRUXO� FHORU� U� JUXSH� OD�QXP UXO� JUDGHORU� GH�OLEHUWDWH��O���$FHVW�QXP U�

a) l=n; b) l=n-1; c) l=r-1; d) l=n-2; e) l=n-r.

20) 3HQWUX� XQ� VWXGLX� VRFLRORJLF� FX� WHPD� ³,PSOLFD LL� DOH� IHQRPHQXOXL� GH� úRPDM� vQ� 5RPkQLD´� V-a

IRUPDW� XQ� HúDQWLRQ� GH� ����� GH� SHUVRDQH� LQFOXVH� vQ� ³VIHUD� IRU HL� GH� PXQF ´�� ÌQ� FKHVWLRQDUXO�special elaborat s-DX� FXSULQV� úL� vQWUHE UL� UHIHULWRDUH� OD� VWDUHD� FLYLO � úL� categoria socio-SURIHVLRQDO ��&HOH�GRX �YDULDELOH�VXQW�GH�DFHHDúL�QDWXU �FX�YDORUL�VLWXDWH�SH�R�VFDO �

a) FRQWLQX � b) GLVFUHW � c) RUGLQDO � d) QRPLQDO � e) de intervale.

21) Într-R� SRSXOD LH� VWDWLVWLF � VH� XUP UHVF� YDULDELOHOH� QXPHULFH� [�� \� úL� ]�� vQWUH� FDUH� H[LVW � UHOD LD:

\ [�]��0HGLD�DULWPHWLF �D�YDULDELOHL�[�HVWH�HJDO �FX�SURGXVXO�PHGLLORU�YDULDELOHORU�\�úL�]�DWXQFL�când:

a) \�úL�]�VH�DIO �vQWU-R�DQXPLW �GHSHQGHQ �

Page 92: STATISTICA - TESTE GRILA

b) \�úL�]�VXQW�LQGHSHQGHQWH�vQWUH�HOH� c) \�úL�]�VXQW�YDULDELOH�QRUPDOL]DWH�GDU�GHSHQGHQWH� d) \�úL�]�VXQW�OLQLDU�Gependente; e) \�úL�]�DX�FRYDULDQ D�GLIHULW �GH�]HUR�

22) 'HVSUH�VWRFXO�GH�P UIXUL�H[LVWHQW�OD�R�VRFLHWDWH�FRPHUFLDO �VH�FXQRVF�XUP WRDUHOH�GDWH�RE LQXWH�în urma inventarierii:

Data inventarierii 1.01.1997 1.02.1997 15.03.1997 10.05.1997 1.07.1997

Stocul existent (mil. lei) 50 58 68 70 75 6WRFXO�PHGLX�GH�P UIXUL�DO�VRFLHW LL�FRPHUFLDOH�GLQ�SHULRDGD�����������- 1.07.197 a fost de:

a) 66 mil. lei; b) 60 mil. lei; c) 64,2 mil. lei; d) 50 mil. lei; e) 75 mil. lei.

23) 2�PDúLQ �XWLOL]DW �SHQWUX�D�GR]D�FDQWLWDWHD�GH�FXORDUH�vQ�YRSVHD��GR]HD] �vQ�PHGLH�m ml pe cutie GH�YRSVHD��&DQWLWDWHD�GH�FXORDUH�GR]DW �HVWH�FXQRVFXW �D�DYHD�R�GLVWULEX LH�QRUPDO �FX�GLVSHUVLD�HJDO �FX��������'DF �PDL�PXOW�GH���PO�GH�FXORDUH�HVWH�DPHVWHFDW �vQ�RE LQHUHD�XQHL�QXDQ H�GH�albastru, vopseaua este respins ��9DORDUHD�OXL�m��DVWIHO�vQFkW�V �QX�ILH�UHVSLQVH�PDL�PXOW�GH����din cutii este:

a) 5,072; b) 5,6272; c) 5,536; d) 5,068; e) 5,6288.

24) 3HQWUX� FRQVWUXLUHD� LQGLFLORU� GH� JUXS� VH� XWLOL]HD] � PDL� PXOWH� VLVWHPH� GH� SRQGHUDUH�� ,QIOXHQ D�sistemului de ponderare utilizat poate fi SXV �vQ�HYLGHQ �XWLOL]kQG�

a) H[FOXVLY� FRHILFLHQWXO� GH� FRUHOD LH� DO� LQGLFLORU� LQGLYLGXDOL� DL� IDFWRUXOXL� FDQWLWDWLY� úL� DL�factorului calitativ ( r

i ix f );

b) DQDOL]kQG�FRHILFLHQ LL�GH�YDULD LH�DL�FHORU�GRX �FDWHJRULL�GH�LQGLFL�LQGLYLGXDOL�� fx iiVV ; );

c) produsul )(0/1

)(0/1

01 : fxfx

iiiIIrVV

fixfx =⋅⋅ ;

d) UHOD LD� fxfix iii

fxfx VVrII ⋅⋅+= 1: )()( 01 ;

e) UHOD LD� fxfix iii

fxfx VVrII ⋅⋅+=⋅ 1)()( 01 .

25) &DUH�HVWH�PXO LPHD�YDORULORU�FRHILFLHQWXOXL�GH�FRUHOD LH�vQ�FDGUXO�OHJ WXULORU�GLUHFWH�

a) [ -1, 1 ]; b) [ -1, 0 ]; c) ( 0, 1 ]; d) PXO LPHD�QXPHUelor reale; e) [ -3, 3 ].

26) 3HQWUX�R�FROHFWLYLWDWH�VWUXFWXUDW �vQ�U�JUXSH�GXS �YDORULOH�FDUDFWHULVWLFLL�;��IDFWRU�GH�JUXSDUH��úL�vQ�P�JUXSH�GXS �YDORULOH�YDULDELOHL�DQDOL]DWH�<���UHJXOD�GH�DGXQDUH�D�GLVSHUVLLORU�VH�SRDWH�DSOLFD��XWLOL]D�úL�GDF �DYHP�OD�GLVSR]L LH�IUHFYHQ HOH�UHODWLYH�vQ�ORFXO�IUHFYHQ HORU�DEVROXWH��FX�FRQGL LD�

Page 93: STATISTICA - TESTE GRILA

ca:

a) f jj

m

.=∑ =

1

1 �úL� f ii

r

.=∑ =

11;

b) f ijj

m

i

r=

==∑∑ 1

11

;

c) f ii

r

.=∑ =

11;

d) f ijj

m

=∑ =

11 �úL� f i

i

r

.=∑ =

1

1;

e) f ijj

m

=∑ =

1

1 .

27) Coeficientul lui Pearson βµµ

24

22

= �VH�XWLOL]HD] �SHQWUX�DQDOL]D�VWDWLVWLF �D�

a) asimetriei; b) YDULD LHL� c) boltiri; d) WHQGLQ HL�FHQWUDOH� e) LQGLFDWRULORU�PHGLL�GH�SR]L LH�

28) ÌQ� WHVWDUHD� LSRWH]HL� VWDWLVWLFH�SULYLWRDUH� OD�SDUDPHWUXO�³PHGLD�SRSXOD LHL´�� UHJLXQHD�FULWLF �HVWH�GDW �GH�� t t n< − −α ; 1 când:

a) datele provin dintr-XQ�HúDQWLRQ�GH�YROXP�UHGXV�úL�VH�HIHFWXHD] �WHVW�XQLODWHUDO�VWkQJD� b) datele provin dintr-XQ�HúDQWLRQ�GH�YROXP�UHGXV�úL�VH�HIHFWXHD] �WHVW�XQLODWHUDO�GUHDSWD� c) datele provin dintr-XQ�HúDQWLRQ�GH�YROXP�QRUPDO��VH�FXQRDúWH�GLVSHUVLD�SRSXOD LHL�úL�V-a

efectuat test unilateral stânga; d) datele provin dintr-XQ�HúDQWLRQ�GH�YROXP�UHGXV�úL�V-a efectuat test bilateral; e) datele provin dintr-XQ�HúDQWLRQ�GH�YROXP�QRUPDO�úL�V-a efectuat test bilateral.

29) Într-R� VHULH� GH� GLWULEX LH� QRUPDO � GXS �R� DQXPLW � YDULDELO � QXPHULF �� vQWUH� YDORDUHD�PHGLDQ ��PRGDO �úL�PHGLH�HVWH�DGHY UDW �UHOD LD�

a) x Mo Me< < ;

b) Me x Mo< < ;

c) x Mo Me= = ;

d) x Me Mo< < ;

e) Mo Me x< < .

Unde x �PHGLD�DULWPHWLF ��Me = mediana; Mo� �YDORDUHD�PRGDO 30) 3HQWUX�R�UHSDUWL LH�GH�IUHFYHQ H�FX�WHQGLQ �GH�QRUPDOLWDWH��V �VH�SUHFL]H]H�FDUH�GLQ�XUP WRDUHOH�

DILUPD LL�SULYLWRDUH�OD�PHGLD�VD�QX�HVWH�DGHY UDW � a) UHSUH]LQW �SXQFWXO�IRFDO�GH�SH�VFDO ��vQ�MXUXO�F UXLD�YDORULOH�VH�EDODQVHD] �SHUIHFW�

Page 94: STATISTICA - TESTE GRILA

b) PLQLPL]HD] �IXQF LD�GH�GLVWDQ ��GH�WLSXO� ( )a xii

n−

=∑ 2

1

;

c) HVWH�SX LQ�VHQVLELO �OD�IOXFWXD LLOH�GH�VHOHF LH� d) vQ�SURFHVXO�LQIHUHQ HL�VWDWLVWLFH��HVWH�GH�RELFHL�SUHIHUDW �DOWRU�LQGLFDWRUL�DL�WHQGLQ HL�FHQWUDOH� e) HVWH�PDL�SX LQ�DIHFWDW �GH�YDORULOH�H[WUHPH��GHFkW�PHGLDQD�úL�PRGXO�

31) 6H�FXQRVF�XUP WRDUHOH�GDWH�SULYLQG��QXP UXO�GH�IDFWRUL���vQWRFPLWH�GH�6�&���$QRQLPXV��65/�vQ�OXQD�noiembrie 1997:

3RSXOD LD�VWDWLVWLF �VWXGLDW �HVWH�VWUXFWXUDW �úL�SUH]HQWDW �vQ�

a) Tabelul I; b) Tabelul II; c)Tabelul III; d) Tabelul IV; e) Tabelul V.

Data Nr. facturi Data Nr. facturi Data Nr. facturi 1 6 11 10 21 14 2 10 12 14 22 12 3 12 13 6 23 11 4 10 14 18 24 10 5 8 15 13 25 8 6 9 16 9 26 4 7 10 17 14 27 12 8 11 18 12 28 9 9 12 19 17 29 12 10 9 20 12 30 16

I II III

Grupe de ]LOH�GXS �QU��

de facturi

Nr. zile

Grupe de zile GXS �QU��GH�

facturi

Nr. zile

Intervale de timp

Nr. facturi

0 - 5 1 0 -5 1 0 - 6 55 6 - 11 13 6 - 10 16 7 - 14 90

11 - 15 13 11 - 15 10 15 - 22 103 16 - 20 3 16 - 20 3 23 - 30 82

IV V

Intervale ale QXP UXOXL�]LOQLF�GH�

facturi

Nr. de zile Intervale ale QXP UXOXL�GH�

facturi zilnice

Nr. de zile

( 0 - 5 ] 1 [ 0 - 5 ) 1 ( 5 - 10 ] 13 [ 5 - 10 ) 9 (10 - 15 ] 13 [10 - 15 ) 17 ( 15 - 20 ] 3 [ 15 - 20 ) 3

Page 95: STATISTICA - TESTE GRILA

TESTUL 11

1) 1RW P�FX�σ REV2 �úL�FX�σ FREV

2 �GLVSHUVLLOH�PHGLHL�GH�VHOHF LH�vQ�FD]XULOH�IRUP ULL�HúDQWLRDQHORU�

vQ�YDULDQWHOH�FX�UHYHQLUH�úL�I U �UHYHQLUH��&RPSDUkQG�FHOH�GRX �GLVSHUVLL�V �VH�DSUHFLH]H�FDUH�GLQ�variantele de mai jos sunt corecte:

a) 22

FREVREV σσ < ;

b) 22FREVREV σσ > ;

c) 22REVFREV σσ = ;

d) 12

2

−−>

N

nN

REV

FREV

σσ

;

e) 12

2

−−=

N

nN

REV

FREV

σσ

.

2) 6H�FRQVLGHU �R�SRSXOD LH�VWDWLVWLF �GH�YROXP�1 cu N n k= ⋅ ; unde n -�YROXPXO�HúDQWLRQXOXL�úL�N�-

XQ� QXP U� QDWXUDO� QHQXO�� /D� XQLW LOH� GH� REVHUYDUH� V-D� XUP ULW� YDULDELOD� ;�� DOH� F UHL� YDORUL�individuale sunt x ii = (cu i=1,2,…,N).

'LVSHUVLD�PHGLHL�GH�VHOHF LH�vQ�FD]XO�IRUP ULL�HúDQWLRQXOXL�vQ�YDULDQWD�I U �UHYHQLUH�HVWH�

a) N + 1

2;

b) ( )N N + 1

12;

c) ( )kN− 12

;

d) ( )( )k N− +1 1

12;

e) ( )k −1

12.

3) 6H�FRQVLGHU �R�SRSXOD LH�VWDWLVWLF �GH�YROXP�1�FX� N n k= ⋅ ; unde n -�YROXPXO�HúDQWLRQXOXL�úL�N�-

XQ� QXP U� QDWXUDO� QHQXO�� /D� XQLW LOH� GH� REVHUYDUH� V-D� XUP ULW� YDULDELOD� ;�� DOH� F UHL� YDORUL�individuale sunt x ii = (cu i=1,2,…,N��� �3UHVXSXQHP�F �VH�H[WUDJH�OD�vQWkPSODUH�XQ�QXP U�³a”

vQWUH� �� úL� k ( ( )a k∈ 1, ��� (IHFWX P� R� H[WUDJHUH� PHFDQLF � D� HúDQWLRQXOXL� FHHD� FH� vQVHDPQ � F �

HúDQWLRQXO�HVWH�IRUPDW�GLQ�XQLW LOH�a a k a n k, , .. , ( )+ + − 1 . 'LVSHUVLD�PHGLHL�GH�VHOHF LH�HVWH�

a) ( )( )k N− +1 1

12;

b) k 2 1

12

−;

Page 96: STATISTICA - TESTE GRILA

c) ( )k N2 1

12

−;

d) ( )k N− 1

12;

e) ( )N N + 1

12.

6 �FRQVLGHU P�FD]XO�XQXL�VRQGDM�FX�UHYHQLUH�úL�SUREDELOLW LOH�LQHJDOH��$FHDVWD�vQVHDPQ �F �

în fiecare din cele n� SUHOHY UL� XQLW LOH�Ui ( i N= 1, �� VH� UHJ VHVF� vQ� HúDQWLRQ� FX�SUREDELOLW ile Ai

( i N= 1, ��� /D� XQLW LOH� GH� REVHUYDUH� V-D� XUP ULW� YDULDELOD� ;�� DOH� F UHL� YDORUL� VXQW� xi ( i N= 1, ). �3UHFL] UL�SHQWUX�SUREOHPHOH����úL����

4) Suma T X ii

N=

=∑

1

HVWH�HVWLPDW �

a) nedeplasat de �Tn

x

Ai

ii

n=

=∑1

1 deoarece [ ] TTM =ˆ , unde cu [ ]M ⋅ s-a notat media;

b) deplasat de �Tn

x

Ai

ii

n=

=∑1

1

deoarece [ ]M T T� − ≠ 0 ;

c) nedeplasat de �Tn

x

Ai

ii

n=

=∑1

1 deoarece T T= � ;

d) deplasat de �Tn

x

Ai

ii

n=

=∑1

1

deoarece [ ]M T T2 2 0� − ≠ ;

e) nedeplasat de �Tn

x

Ai

ii

n=

=∑1

1 deoarece [ ]M T T2 2 0� − = .

5) 1RW P� FX� ( )D x A Ax

ATi i i

i

ii

N/ = −

=∑

2

1dispersia valorilor xi /Ai cu i N= 1, . Dispersia

estimatorului �T este:

a) ( )D Tn

Ax

AT

n

x

ATi

i

ii

Ni

ii

� = −

≠ −

=

∑ ∑1 12

1

22 ;

b) ( )D Tn

Ax

AT

n

x

ATi

i

ii

Ni

ii

� = −

= −

=

∑ ∑1 12

1

22 ;

c) ( )D Tn

A Ax

A

x

Aii j

n

x

ATi j

i

i

j

jj

i

ii

� = −

=

<

−∑∑ ∑1 22

2 22 ;

Page 97: STATISTICA - TESTE GRILA

d) ( )D Tn

x

ATi

ii

� = +∑22

22 ;

e) ( )D Tn

x

AT

n

x

ATi

ii

Ni

ii

N� = −

= −

= =

∑ ∑1 12

1

22

1

.

6) $QDOL]kQG�FRQGL LLOH�IRUPXODWH�OD����úL����VH�FRQVWDW �F �HVWH�DGHY UDW �UHOD LD�

a) ( )Dx

A

n

ND Ti

i

= � ;

b) ( )Dx

A

n N

ND Ti

i

= −

− 1� ;

c) ( )Dx

AnD Ti

i

= � ;

d) ( )Dx

AD Ti

i

= � ;

e) ( )Dx

A nD Ti

i

= 1

� .

7) Un estimator nedeplasat pentru ( )D T� este:

a) ( )� �

( )�D T

n n

x

ATi

ii

n=

−−

=∑1

1

2

1;

b) ( )� � �D Tn

x

ATi

ii

n=

−−

=∑1

1

2

1;

c) ( )� �

( )�D T

n n

x

ATi

ii

N=

−−

=∑1

1

2

1;

d) SUH]HQWDW�vQ�YDULDQWD�D��úL�vQ�SOXV� ( )� �

( )D T

n n

x

A

x

Ai

i

j

jj

n

ii j

n=

−−

∑∑

<

1

12

2

;

e) SUH]HQWDW�vQ�YDULDQWD�F��úL�vQ�SOXV� ( )� �D Tx

A

x

Ai

i

j

jj

N

ii j

N= −

∑∑

<

2

.

8) &RPSDUkQG� GLVSHUVLD� HVWLPDWRUXOXL� GLQ� FD]XO� VHOHF LHL� FX� SUREDELOLW L� LQHJDOH� 'I cu cel cu SUREDELOLW L�HJDOH�'E�FRQVWDW P�F �UHOD LD�DGHY UDW �GLQ�XUP WRDUHOH�YDULDQWH�HVWH :

a) DI > DE�vQ�RULFH�VLWXD LH�

Page 98: STATISTICA - TESTE GRILA

b) DI < DE i i

⇔ >∑ ∑Nxx

Aii

i

22

;

c) DI < DE A >1

Ni⇔ �GDF � xi2 HVWH�PDUH��DGLF �xi este corelat pozitiv cu Ai);

d) DI < DE A <1

Ni⇔ �GDF � xi2 HVWH�PLF��DGLF �xi este corelat pozitiv cu Ai);

e) DI = DE. 6 � FRQVLGHU P� FD]XO� vQ� FDUH� ILHFDUH� XQLWDWH� VHOHFWDW � vQ� HúDQWLRQ� PRGLILF � FRQGL LLOH�

XUP WRDUHORU� H[WUDJHUL� DOH� XQLW LORU� vQ� HúDQWLRQ��'HFL� Ai1HVWH� GDF � SUREDELOLWDWHD� GH� H[WUDJHUH� D�

primei unit L� vQ� HúDQWLRQ� WUHEXLH� V �FXQRDúWHP�DWXQFL� Ai j( )2 SUREDELOLWDWHD�GH� LHúLUH� vQ� HúDQWLRQ�D�

XQLW LORU�8i�vQ�D�GRXD�H[WUDJHUH�GXS �FH�vQ�SULPD�H[WUDJHUH�D�DS UXW�XQLWDWHD�8j, etc. De exemplu,

GDF �8j�HVWH�VHOHF LRQDW�OD�SULPD�H[WUDJHUH�DWXQFL ( )AA

A

A

Ai j

i

j

i

j( )2

1

1

1

11= =

−≠∑ α

α

. Problema aceasta,

GHVWXO�GH�FRPSOLFDW ��D�IRVW�VWXGLDW �WHKQLF�úL�SUDFWLF�vQ������GH�+RURYLW]�úL�7KRPSVRQ��$VWIHO��DX�IL[DW�GRX �JUXSH�GH�QXPHUH��Si - probabilitatea ca Uj�V �ILJXUH]H�vQ�HúDQWLRQ�úL�Sij - probabilitatea ca Uj� úL� 8j� V � ILJXUH]H� VLPXOWDQ� vQ� HúDQWLRQ�� $FHVWH� SUREDELOLW L� VXQW� QXPHUH� VXEXQLWDUH� úL� vQ� SOXV�UHVSHFW �FRQGL LLOH�XUP WRDUH�

p nii

=∑ úL� pij n n

jii j

= −

∑∑ ( )1 �� ÌQ� DFHVWH� FRQGL LL�� HVWLPDWRUXO� XQXL� 7RWDO� T xii

N=

=∑

1

este

�Tx

pHTi

ii

N=

=∑

1��QXPLW�úL�HVWLPDWRUXO� OXL�+RURYLW]� - Thompson. �3UHFL] UL�SHQWUX�SUREOHPHOH���� úL�

10)). 9) ÌQ�FRQGL LLOH�SUH]HQWDWH�SUHFL]D L�YDORDUHD�GH�DGHY U�D�DILUPD LLORU�XUP WRDUH�

a) �THT este un estimator nedeplasat;

b) �THT este un estimator deplasat cu 1

2THT ;

c) [ ]M T THT HT� = ;

d) [ ]M T T pHT HT i� − = ;

e) [ ]M T T pHT HT ij� − = .

Page 99: STATISTICA - TESTE GRILA

10)�ÌQ�FRQGL LLOH�SUH]HQWDWH�GLVSHUVLD�HVWLPDWRUXOXL� �THT este:

a) [ ]D Tp p

pX

p p p

p pX XHT

i i

ii

N

iij i j

i jjii j

i j�

( )=

−−

=≠

∑ ∑∑12

1

2 ;

b) [ ]D Tp p

pX

p p p

p pX XHT

i i

ii

N

iij i j

i jjii j

i j�

( )=

−+

=≠

∑ ∑∑12

1

2 ;

c) [ ] ( )D T p p px

p

x

pHT i j ijji

i j

i

i

j

j

� = − −

∑∑

1

2

2

;

d) [ ]D Tp p

pX

p p p

p pX XHT

i i

ii

N

iij i j

i jjii j

i j�

( ):=

− −

=≠

∑ ∑∑12

1

2 ;

e) [ ]D Tp p p

p

x

p

x

pHTi j ij

ijj

n

ii j

ni

i

j

j

� =−

∑∑

1

2

2

.

11)�1RW P� FX� σ S2 � úL� FX� σ STRAT

2 � GLVSHUVLD�PHGLLORU� GH� VHOHF LH� SHQWUX� FD]XO� VHOHF LHL� VLPSOH� úL�

UHVSHFWLY�SHQWUX�FD]XO�VHOHF LHL�VWUDWLILFDWH��&RPSDUkQG�FHL�GRL�LQGLFDWRUL��FRQVWDW P�YDORDUHD�GH�DGHY U�D�DILUPD LLORU�XUP WRDUH�

a) σ σSTRAT S2 2< , deoarece media dispersiilor straturilor este mai mare decât dispersia

JHQHUDO �

b) σ σSTRAT S2 2< , deoarece media dispersiilor straWXULORU� vQ� RULFH� VLWXD LH� HVWH�PDL�PLF �

GHFkW�GLVSHUVLD�JHQHUDO ��FX�FRQGL LD�FD�GLVSHUVLD�GLQWUH�VWUDWXUL�V �ILH�QHQXO �

c) σ σSTRAT S2 2= � �� GHRDUHFH� PHGLD� GLVSHUVLLORU� VWUDWXULORU� HVWH� HJDO � FX� GLVSHUVLD� GLQWUH�

straturi;

d) σ σSTRAT S2 2− V �ILH�PDL�PLF �GHFkW�GLVSHUVLD�GLQWUH�VWUDWXUL�

e) FRPSDUDUHD�FHORU�GRX �GLVSHUVLL�HVWH�OLSVLW �GH�VHQV�

12)�6H� FRQVLGHU � F � σ STRAT2 � HVWH� GLVSHUVLD� PHGLHL� GH� VHOHF LH� vQ� FD]XO� VHOHF LHL� VWUDWLILFDWH� SH�

straturile “h” (cu mh ,1= ). SH�QRWHD] �FX�nh volumul stratului h ⇒ ==∑n nhh

m

1

��ÌQ�DFHDVW �

VLWXD LH��GLVSHUVLD�HVWH�PD[LP ��h ���GDF �

a) n n n nh m1 2= = = = =. . . . . . ;

b) n n n nh m1 2≠ ≠ ≠ ≠ ≠... ... ;

Page 100: STATISTICA - TESTE GRILA

c) nN

Nh

h

hh

m=

=∑

1

pentru ( )∀ =h m1, ;

d) n n1 2≠ �úL��n n n nh m3 4= = = = =... ... ;

e) N N N Nh m1 2= = = = =... ... .

Page 101: STATISTICA - TESTE GRILA

TESTUL 12*)

1) Estimatorul unui parametru θ VH�QRWHD] �FX� �θ ��$FHVW�HVWLPDWRU�HVWH�QHGHSODVDW�GDF �

a) GLIHUHQ D� GLQWUH� PHGLD� VD� úL� YDORDUHD� SDUDPHWUXOXL� HVWH� GLIHULW � GH� ]HUR�� GDU� DFHDVW �GLIHUHQ �QX�GHS úHúWH�����GLQ�YDORDUHD�SDUDPHWUXOXL�

b) GLVSHUVLD� VD� HVWH� PLQLP � � ( )D θ → 0FkQG� YROXPXO� HúDQWLRQXOXL� WLQGH� F WUH� YROXPXO�

SURGXF LHL�n N→ ); c) GLVSHUVLD�VD�HVWH�PLQLP �SHQWUX�RULFH�YROXP�IL[DW�DO�HúDQWLRQXOXL�

d) mHGLD�VD�HVWH�HJDO �FX�YDORDUHD�SDUDPHWUXOXL�� ( )M θ θ→ );

e) GLVSHUVLD�VD�HVWH�PD[LP �

2) 6 � VH� SUHFL]H]H� FDUH� GLQ� VHULLOH� GH� UHSDUWL LH�� FDUDFWHUL]DWH� SULQ� XUP WRDUHOH� VHWXUL� GH� YDORUL��SUH]LQW �R�DVLPHWULH�SR]LWLY �

a) u.m 40=x ; Me = 40 u.m.; Mo = 40 u.m.;

b) u.m 2500=x ; Me = 3000 u.m.; Mo = 3300 u.m.;

c) x = 151 25, u.m ; Me = 138,75 u.m.; Mo = 112,58 u.m.;

d) u.m 180=x ���0H� �����X�P����0R� �����X�P��úL�����X�P��

e) x Me Mo= = = 0

3) Scala de interval:

a) DUH�WRDWH�FDUDFWHULVWLFLOH�VFDOHORU�RUGLQDOH�úL�GH�UDSRUW� b) DUH�WRDWH�FDUDFWHULVWLFLOH�VFDOHL�RUGLQDOH�úL��vQ�SOXV��GLVWDQ D�GLQWUH�GRX �QXPHUH�DOH�VFDOHL�

DUH�R�VHPQLILFD LH�FRQFUHW � c) HVWH�R�VFDO �QXPHULF �úL��vQ�SOXV��UDSRUWXO�GLQWUH�GRX �SXQFWH�DOH�scalei este independent

GH�XQLWDWHD�GH�P VXU � d) SUH]LQW �PXOWH�GLQ�FDUDFWHULVWLFLOH�VFDOHL�RUGLQDOH� e) PDL�HVWH�GHQXPLW �úL�VFDO �GH�UDSRUW�VDX�VFDO �GLVFUHW �

4) 3HQWUX� FRQVWUXLUHD� LQGLFLORU� GH� JUXS� VH� XWLOL]HD] � PDL� PXOWH� VLVWHPH� GH� SRQGHUDUH�� ,QIOXHQ D�sistePXOXL�GH�SRQGHUDUH�XWLOL]DW�SRDWH�IL�SXV�vQ�HYLGHQ �

a) XWLOL]kQG�H[FOXVLY�FRHILFLHQWXO�GH�FRUHOD LH�DO�LQGLFLORU�LQGLYLGXDOL�DL�IDFWRULORU�[�úL�I� b) DQDOL]kQG�FRHILFLHQ LL�GH�YDULD LH�DL�FHORU�GRX �FDWHJRULL�GH�LQGLFL�LQGLYLGXDOL��V

ix ; Vi f );

c) utilizând valorile raportului I I V V rx f x f

i i ix f xi f1 0 1 0

1 0/( )

/( ): = , unde r

i xi f este coeficientul

GH�FRUHOD LH�

d) XWLOL]kQG�UHOD LD� I I r V Vx f x f

i i ixi f x f1 0 1 0

1 0 1/( )

/( ): = + ;

e) XWLOL]kQG�UHOD LD� I I r V Vx f x f

i i ixi f x f1 0 1 0

1 0 1/( )

/( )+ = + .

*)�6XELHFW� OD� H[DPHQXO�GH� OLFHQ � OD�GLVFLSOLQD�³7HRULD� VWDWLVWLFLL´� OD� IDFXOWDWHD�GH�&LEHUQDWLF ��6WDWLVWLF � úL�,QIRUPDWLF �(FRQRPLF �-�VSHFLDOL]DUHD�6WDWLVWLF ��6HVLXQHD�0DL������

Page 102: STATISTICA - TESTE GRILA

5) 6H�FRQVLGHU �XQ�WDEHO�GH�FRQWLQJHQ ��FRUHOD LH��vQ�IRUPD�VD�JHQHUDO �

( )[ ]{ }x y n j J k Kj k jk, ; ,∈ ∈ �� 'DF � SH� ED]D� WDEHOXOXL� FRQVLGHUDW� FDOFXO P� YDORULOH� FHQWUDWH� úL�

reduse Ux x

jj

x=

−σ

�úL�Vy y

kk

y=

−σ

( cu x úL� y mediile variabLOHORU�;�úL�<��LDU�σ x úL�σ y abaterile

VWDQGDUG�DOH�YDULDELOHORU�;�úL�<���DWXQFL�FRYDULDQ D�GLQWUH�YDULDELOHOH�;�úL�<���QRWDW �FX�&RY�;�<���este:

a) Cov X Y Cov U Vx y( , ) ( , )≠ σ σ ;

b) Cov X YCov U V

x y( , )

( , )=σ σ

;

c) Cov X Y Cov U Vx y( , ) ( , )= σ σ ;

d) Cov X Y Cov U V x y( , ) ( , )− = σ σ ;

e) Cov X Y Cov U VU V( , ) ( , )= σ σ . 6) 5HIHULWRU�OD�DFWLYLWDWHD�HFRQRPLF �D�XQHL�VRFLHW L�FRPHUFLDOH�VH�FXQRVF�XUP WRDUHOH�GDWH�

9DORDUHD�SURGXF LHL� �PLO��OHL�SUH XUL�FXUHQWH�

Unitatea

Perioada ED]

Perioada FXUHQW

Modificarea valorii SH�VHDPD�PRGLILF ULL SUH XULORU (mil. lei)

A 1200 1850 350 B 875 1600 275

0RGLILFDUHD�UHODWLY �D�YDORULL�SURGXF LHL�OD�QLYHOXO�vQWUHJLL�VRFLHW L��FDX]DW �GH�PRGLILFDUHD�YROXPXOXL�IL]LF�DO�SURGXF LHL�vQWUH�FHOH�GRX �SHULRDGH�D�IRVW�HJDO �FX�

a) -12,5%; b) +100,0%; c) +36,1%; d) +136,1%; e) -112,5%.

7) ÌQ�FD]XO�XQHL�REVHUY UL�VWDWLVWLFH�DO�F UXL�VFRS�HVWH�³IRWRJUDILHUHD´�]LOHL�GH�OXFUX�D�XQXL�OXFU WRU�

a) WLPSXO�REVHUY ULL�FRLQFLGH�FX�WLPSXO�OD�FDUH�VH�vQUHJLVWUHD] �GDWHOH� b) WLPSXO�REVHUY ULL�QX�FRLQFLGH�FX�WLPSXO�OD�FDUH�VH�vQUHJLVWUHD] �GDWHOH� c) WLPSXO�REVHUY ULL�VH�UHIHU �OD�GXUDWD�V SW PkQLL�GH�OXFUX�D�OXFU WRUXOXL� d) SUHFL]DUHD�WLPSXOXL�REVHUY ULL�QX�DUH�VHQV� e) WLPSXO�REVHUY ULL�HVWH�PRPHQWXO�FULWLF�³RUD�]HUR´�D�]LOHL�vQ�FDUH�OXFU WRUXO�VH�SUH]LQW �OD�

lucru. 8) $QDOL]D L�XUP WRDUHOH�SRSXOD LL�VWDWLVWLFH�����SRSXOD LD�%XFXUHúWLXOXL�OD���LXOLH����������SRSXOD LD�

GLQ�5RPkQLD�GLQ�PHGLXO�XUEDQ�OD����LXOLH����������PXO LPHD�IDFWXULORU�HODERUDWH�GH�6�&��³,&6´�65/�vQ�WULP��,����������PXO LPHD�F V WRULLORU�vQFKHLDWH�vQ�5RPkQLD�vQ�anul 1997; 5) stocurile de P UIXUL�DO�vQWUHSULQGHULORU�PLFL�úL�PLMORFLL�OD�VIkUúLWXO�DQXOXL������

Page 103: STATISTICA - TESTE GRILA

3RSXOD LL�VWDWLVWLFH�GLQDPLFH�VXQW�

a) ��úL��� b) ��úL��� c) ��úL��� d) ��úL��� e) ��úL���

9) 6H� úWLH� F � ( ) ( )σ σy ii

y x i iir

y yn

y Y2 2 2 21 1= − = −∑ ∑; .� úL� ( )σ Y i

inY y2 21= −∑ � unde

�Y b b xi i= +0 1 ��'DF �U�HVWH�FRHILFLHQWXO�GH�FRUHOD LH�GLQWUH�YDULDELOHOH�<�úL�;��DWXQFL�

a) ( )σ σy x y r.2 2 21= − �úL�σ σ σy y x Y

2 2 2= +. ;

b) ( )σ σy x y r.2 2 21= − �úL�σ σ σy y x Y

2 2 2< +. ;

c) ( )σ σy x y r.2 2 21> − �úL�σ σ σy y x Y

2 2 2= +. ;

d) ( )σ σy x y r.2 2 21> − �úL�σ σ σy y x Y

2 2 2< +. ;

e) ( )σ σy x y r.2 2 21< − �úL�σ σ σy y x Y

2 2 2> +. .

10) 2�YDULDELO � FRPSOH[ �<� HVWH� H[SULPDW � vQ� IXQF LH� GH� IDFWRULL� [�� ]�� X�� Y�� J�� K��Z�� S�� DOH� F URU�

LQIOXHQ H�WUHEXLH�L]RODWH��5HOD LD�RELHFWLY �GLQWUH�<�úL�IDFWRULL�V L�ILLQG�PXOWLSOLFDWLY ��SHUPLWH�R�descompunere în trepte de forma:

cu y x z u v z u v g p u v g w h= ⋅ = ⋅ ⋅ = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅

ÌQWUH� LQGLFHOH� YDULDELOHL� <� úL� LQGLFLL� YDULDELOHORU� IDFWRULDOH�� GDF � VH� XWLOL]HD] � WHKQLFD�VXEVWLWXLULL�vQO Q XLWH��QX�H[LVW �UHOD LD�

a) I I Iy y x y z= ⋅( ) ( ) ;

b) I I I Iy y z y u y v= ⋅ ⋅( ) ( ) ( ) ;

c) I I I I I Iy y u y v y g y w y h= ⋅ ⋅ ⋅ ⋅( ) ( ) ( ) ( ) ( ) ;

d) I I I I Iy y x y g y w y h= ⋅ ⋅ ⋅( ) ( ) ( ) ( ) ;

e) I I I I I Iy y u y v y g y w y h− ⋅ ⋅ ⋅ ⋅ ≠( ) ( ) ( ) ( ) ( ) 0 .

Y = x ��������������]

p g v u

w h

Page 104: STATISTICA - TESTE GRILA

11) (YROX LD�3URGXVXOXL�,QWHUQ�%UXW�SH�ORFXLWRU�vQ�SHULRDGD�����-�����VH�SUH]LQW �DVWIHO�

Anii 1994 1995 1996 1997 ��ID �GH�DQXO�SUHFHGHQW 14,0 +7,3 +4,4 -6,3

0HGLD�DQXDO �D�HYROX LHL�SURFHQWXDOH�HVWH�GH�

a) -0,09%; b) 102,0%; c) 201,3%; d) +2,21%; e) +4,35%.

12) 1RW P� FX� σ R2 � úL� FX� σ F

2 � GLVSHUVLLOH� PHGLLORU� GH� VHOHF LH� SHQWUX� SURFHGHHOH� GH� IRUPDUH� D�

HúDQWLRDQHORU� vQ� YDULDQWHOH� FX� UHYHQLUH� úL� I U � UHYHQLUH�� &RPSDUkQG� FHL� GRL� LQGLFDWRUL�� UHOD LD�FRUHFW �HVWH�

a) σ σR F2 2> ;

b) σ σF R2 2> ;

c) σ σR F2 2= ;

d) σ σF R2 21

2= ;

e) σ σF R2 2= �YROXPXO�HúDQWLRQXOXL�

13) Inegalitatea dintre aEDWHULOH� VWDQGDUG� DOH� XQHL� YDULDELOH� ;� QRUPDO� UHSDUWL]DWH� vQ� SRSXOD LLOH�

VWDWLVWLFH� ��� ��� ��� GH� DFHODúL� YROXP� úL� DFHHHDúL� PHGLH� x , σ σ σ1 2 3> > � HVWH� YL]XDOL]DW � vQ�varianta:

a) b) c) d)

3

2

1

3

1

2

1

2

3

2

3

1

Page 105: STATISTICA - TESTE GRILA

e)

14) 6H�FXQRDúWH�IDSWXO�F �6�&��³,&6´�65/�D�UHDOL]DW�vQ�OXQD�,$1�¶���R�FLIU �GH�DIDFHUL�GH����POG��lei, iar în perioada IAN ’97 - APR ’98 a cunoscut o modificare�PHGLH�OXQDU �GH������POG��OHL��ÌQ�ipoteza în care în perioada MAI ’98 -�,81�¶���vQUHJLVWUHD] �DFHHDúL�HYROX LH�FD�DFHHD�GLQ�,$1�’97 -�$35�¶���YDORULOH�HVWLPDWH�DOH�FLIUHL�GH�DIDFHUL�vQ�OXQLOH�PDL��LXQLH�úL�LXOLH�VXQW�

a) �����POG��OHL�������POG��OHL�úL����� mld. lei; b) ���POG��OHL�������POG��OHL�úL������POG��OHL� c) ��POG��OHL�������POG��OHL�úL����POG��OHL� d) ���POG��OHL�������POG��OHL�úL������POG��OHL� e) ���POG��OHL�������POG��OHL�úL������POG��OHL�

15) 'DF � vQWUH� GRX � YDULDELOH� <� úL� ;� QX� H[LVW � QLFL� R� OHJ WXU � �YDULDELlele sunt independente) FRHILFLHQWXO�GH�FRUHOD LH�HVWH�HJDO�FX�]HUR��5HFLSURFD�DFHVWHL�DILUPD LL�

a) HVWH�IDOV � b) HVWH�DGHY UDW � c) HVWH�DGHY UDW �GRDU�GDF �GLVSHUVLLOH�FHORU�GRX �YDULDELOH�VXQW�HJDOH� d) HVWH�DGHY UDW �GRDU�GDF �FHOH�GRX �GLVWULEX LL�IRUPDOH�GXS �;�úL�<�VXQW�QRUPDOH� e) HVWH� DGHY UDW � GRDU� GDF � GDWHOH� FHORU� GRX � YDULDELOH� VXQW� VLVWHPDWL]DWH� vQWU-un tabel de

FRQWLQJHQ ��FRUHOD LH�� 16) La un punct comercial din vânzarea unui produs s-a realizat în luna APR ’98 o încasare de 8

mil. lei. Ca urmare a major ULL�SUH XOXL� ID �GH� OXQD�$35�¶��� vQFDV ULOH�GLQ� OXQD�$35�¶���DX�FXQRVFXW�R�FUHúWHUH�GH���������OHL��&DUH�DU�IL�IRVW�vQFDV ULOH�OXQLL�$35�¶���GDF �SUH XO�QX�V-ar fi modificat?

a) 7,7 mil. lei; b) 7,3 mil. lei; c) 5 mil. lei; d) 6 mil. lei; e) 7 mil. lei.

17) ÌQ�HYROX LD�VD�vQGHOXQJDW �VWDWLVWLFD�V-a dezvoltat continuu atât sub aspectul obiectului de studiu

GDU�PDL� DOHV�DO� SHUIHF LRQ ULL� úL� GLYHUVLILF ULL�PHWRGHORU�GH�DERUGDUH�D� DFHVWXL� RELHFW�� ÌQ� WRDWH�PRPHQWHOH�GH]YROW ULL�VDOH�VWDWLVWLFD�VH�RFXS �GH�

a) fenomene care se proGXF�OD�R�DQXPLW �XQLWDWH�GH�REVHUYDUH� b) IHQRPHQH�FDUH�VH�UHSURGXF�vQ�PRG�LGHQWLF�OD�XQLW LOH�GH�REVHUYDUH� c) fenomene care se produc într-XQ� QXP U�PDUH� GH� FD]XUL� úL� DOH� F URU� IRUPH� LQGLYLGXDOH�

PDQLIHVW �DQXPLWH�UHJXODULW L� d) fenomene exclusiv economice; e) fenoPHQH�FDUH�DX�OD�RULJLQHD�SURGXFHULL�ORU�XQ�VLQJXU�IDFWRU�GH�LQIOXHQ �

2

1

3

Page 106: STATISTICA - TESTE GRILA

18) $QDOL]D L� XUP WRDUHOH� QR LXQL�� ��� $XWRQRPLH�� ��� FRQILGHQ LDOLWDWH�� ��� WUDQVSDUHQ �� ���VSHFLDOL]DUH�� � ��� SURSRU LRQDOLWDWH�� � ��� GHRQWRORJLH� SURIHVLRQDO �� ��� LQGHSHQGHQ � SROLWLF �� ���elDERUDUHD�GHFL]LLORU������DUJXPHQWDUHD�DF LXQLORU�GXS �GHFODQúDUHD�ORU�������SUHOXFUDUHD�GDWHORU���11) observare.

$FWLYLWDWHD�VWDWLVWLFLL�SXEOLFH�WUHEXLH�V �VH�GHVI úRDUH�UHVSHFWkQG�XUP WRDUHOH�SULQFLSLL�

a) �����������������úL��� b) �����������������úL��� c) 3, ��������������úL��� d) �����������������úL���� e) ������������������úL����

19) 6WDELOL L� YDULDQWD� GH� DGHY U� D� DILUPD LHL� XUP WRDUH�� 5HFHQV PkQWXO� FD� PHWRG � GH� REVHUYDUH�

VWDWLVWLF �

a) QX�SUHVXSXQH�FXOHJHUHD�GDWHORU�GH�OD�WRDWH�XQLW LOH�SRSXOD LHL�VWDWLVWLFH�ELQH�GHOLPLWDW � b) are exclusiv un caracter demografic; c) VH�vQFDGUHD] �vQ�VIHUD�REVHUY ULORU�FX�FDUDFWHU�SHUPDQHQW� d) VH�RUJDQL]HD] �FX�R�DQXPLW �SHULRGLFLWDWH� e) VH� RUJDQL]HD] � RUL� GH� FkWH� RUL� 6WDWLVWLFD� 218� GHFODQúHD] � DF LXQHD� GH� HIHFWXDUH� D�

UHFHQV PLQWHORU�vQ� ULOH�membre. 20) *UDILFHOH�VWDWLVWLFH�WUDVDWH�vQ�FRRUGRQDWH�SRODUH�VH�XWLOL]HD] �vQ�PRG�FXUHQW�SHQWUX�YL]XDOL]DUHD�

a) RULF UHL�VHULL�GH�GDWH�VWDWLVWLFH� b) VHULLORU�GH�UHSDUWL LH� c) WUHQGXOXL��WHQGLQ HL��GLQ�HYROX LD�vQ�WLPS�D�XQXL�IHQRPHQ� d) HYROX LD�vQ�WLPS�D�XQXL�IHQRPHQ�DIHFWDW �GH�RVFLOD LL�VH]RQLHUH� e) WHQGLQ HL�OHJ WXULL�GLQWUH�YDULDELOH�úL�SHQWUX�DOHJHUHD�PRGHOHORU�GH�UHJUHVLH�

21) 6H� FXQRDúWH� IDSWXO� F � vQWU-R� UDPXU � GH� DFWLYLWDWH� YDULDELOD� ³VDODULXO� PHGLX� EUXW´� �<�� HVWH�

GHSHQGHQW �SULQWUH�DOWHOH�GH�³JUDGXO�PHGLX�DO� vQGHSOLQLULL�QRUPHORU´��;���úL�³JUDGXO�PHGLX�GH�vQ]HVWUDUH� WHKQLF �D�PXQFLL´� �;����&RQWULEX LD�FHORU�GRL� IDFWRUL�;��úL�;�� OD�YDULD LD�VDODULXOXL�PHGLX�EUXW��\��HVWH�HVWLPDW �SULQ�

a) R r ry x x y x y x/ / /1 2 1 2

2 2 2= + ;

b) Rr r r r r

ry x x

y x y x y x y x x x

x x/

/ / / /

1 2

1 2 1 2 1 2

1 2

2 2

2

2

1=

+ −

−;

c) R r r r r ry x x y x y x y x y x x x/ / / / /1 2 1 2 1 2 1 22 2 2= + − ;

d) rx x1 20= ;

e) Rr r

ry x x

y x y x

x x/

/ /

1 2

1 2

1 2

2 2

21=

+

−.

127 ��r -�FRHILFLHQWXO�GH�FRUHOD LH�OLQLDU �

Page 107: STATISTICA - TESTE GRILA

22) Prin AUDIT-ul financiar efectuat în luna ianuarie 1998 la S.C. “ICS” SRL s-D�FRQVWDWDW�F � vQ�IDFWXULOH�HODERUDWH� vQ������H[LVW �DQXPLWH�HURUL�vQ�FDOFXOXO�79$-ului�FDUH�DX�DYXW�GUHSW�VXUV ��QHFXQRDúWHUHD� PHWRGRORJLHL� GH� FDOFXO� D� 79$-XOXL� OD� XQHOH� SURGXVH�� DSUR[LP UL� HURQDWH��GHIHF LXQL�DOH�PLMORFXOXL�WHKQLF�GH�FDOFXO��HWF�

3RSXOD LD�VWDWLVWLF �VWXGLDW �HVWH�

a) ansamblul facturilor elaborate de S.C. “ICS” SRL; b) ansambOXO�SURGXVHORU�úL�VHUYLFLLORU�UHDOL]DWH�GH�6�&��³,&6´�65/�SkQ �OD����;,,������ c) DQVDPEOXO� SURGXVHORU� úL� VHUYLFLLORU� UHDOL]DWH� GH� 6�&�� ³,&6´� 65/� GHVI FXWH� SH� SLD � úL�

IDFWXUDWH�SkQ �OD����;,,������ d) DQVDPEOXO�SURGXVHORU�úL�VHUYLFLLORU�UHDOL]DWH�SHQWUX�D�IL�GHVI FXWH�SH�SLD �GH�6�&��³,&6´�

65/��IDFWXUDWH�SkQ �OD����;,,������úL�OD�FDUH�VH�SHUFHSH�79$� e) DQVDPEOXO�IDFWXULORU�HODERUDWH�GH�6�&��³,&6´�65/�SkQ �OD����;,,������SHQWUX�SURGXVHOH�

úL�VHUYLFLLOH�UHDOL]DWH�úL�GHVI FXWH�SH�SLD �úL�OD�FDUH�VH�SHUFHSH�79$� 23) G.U�<XOH� ������� SUHFL]HD] � F � LQGLFDWRULL� UHSDUWL LLORU� VWDWLVWLFH� WUHEXLH� V � vQGHSOLQHDVF �

XUP WRDUHOH�FRQGL LL�����V �ILH�GHILQL L�vQ�PRG�RELHFWLY����V �GHSLQG �GH�WRDWH�GDWHOH�GLQ�VHUL����V �DLE �VHPQLILFD LL�FRQFUHWH����V �ILH�VLPSOX�GH�FDOFXODW����V �ILH�SX LQ�VHQVLELOL�OD�IOXFWXD LLOH�GH�VHOHF LH�����V �VH�SUHWH]H�XúRU�OD�FDOFXOH�DOJHEULFH�

$FHVWH�FRQGL LL��vQ�WRWDOLWDWH�

a) sunt respectate de medie; b) sunt respectate de dispersie; c) VXQW�UHVSHFWDWH�GH�FRYDULDQ � d) VXQW�UHVSHFWDWH�GH�YDORDUHD�PRGDO � e) nu sunt rHVSHFWDWH�GH�QLFL�XQ�LQGLFDWRU�DO�WHQGLQ HL�FHQWUDOH�VDX�DO�YDULD LHL�

24) /X P�vQ�FRQVLGHUDUH�XQ�WDEHO�GH�FRQWLQJHQ ��FRUHOD LH�� ( )[ ]{ }KkJjnyx jkkj ∈∈ ,,, úL�GLVWULEX LLOH�

OXL�<�FRQGL LRQDWH�GH�;�� ( ){ }Kk , ,, ∈fixatjny jkk ��3HQWUX�DFHVWHD�GLQ�XUP �VH�FXQRVF�PHGLLOH�úL�

dispersiile:

( ) ∑=k

jkkj

j nyn

xy.

1úL� ( ) ( )[ ]σ y j

jk j jk

k

xn

y y x n2 21= −∑.

unde ∑=k

jkj nn . � HVWH� HIHFWLYXO� �IUHFYHQ D�� PDUJLQDO� �� DVRFLDW � YDULDQWHL� [M� D� YDULDELOHL� ;�� ÌQ�

IXQF LH� GH� HOHPHQWHOH� SUH]HQWDWH� vQ� LSRWH] � GLVSHUVLD� YDULDELOHL� <� �σ y2 �� VH� SUH]LQW � FRUHFW� vQ�

varianta:

a) ( ) ( )[ ]σ σy jj

y j jj

jnn x

nn y x y2 2 21 1= + −∑ ∑. . ;

b) ( )[ ]σ y jj

jnn y x y2 21< −∑ . ;

c) ( )σ σy jj

y jnn x2 21< ∑ . ;

d) ( ) ( )[ ]σ σy jj

y j jj

jnn x

nn y x y2 2 21 1= − −∑ ∑. . ;

Page 108: STATISTICA - TESTE GRILA

e) ( ) ( )[ ]σ σy jj

y j jj

jnn x

nn y x y2 2 21 1> + −∑ ∑. . .

FX�FRYDULDQ D�GLQWUH�<�úL�FHLODO L�IDFWRUL�GH�LQIOXHQ �FX�H[FHS LD�IDFWRUXOXL�;� 25) 3HQWUX� GRX � YDULDELOH� VWDWLVWLFH� D� F URU� WHQGLQ � D� GHSHQGHQ HL� VWDWLVWLFH� D� IRVW�PRGHODW � SULQ�

HFXD LD� GH� UHJUHVLH� � ,y xi i= −25 0 7 � úL� VH� PDL� FXQRVF� GLVSHUVLLOH�� σ x2 2603 04= , úL�

σ y2 1896 6= , ��&RHILFLHQWXO�GH�FRUHOD LH�DUH�YDOoarea:

a) 0,82; b) 0,96; c) -0,96; d) -0,59; e) -0,82.

26) 'DF � vQWUH� FXDUWLOHOH� FDOFXODWH� SHQWUX� R� VHULH� GH� UHSDUWL LH� H[LVW � UHOD LD� ( )Q Q Q2 1 3 2= + /

DWXQFL�UHSDUWL LD�HVWH�

a) DVLPHWULF �VSUH�YDORULOH�PDUL� b) DVLPHWULF �VSUH�YDORULOH�PLFL� c) QRUPDO � d) KLSHUEROLF � e) bidimHQVLRQDO �

27) 9HULILFDUHD�FRQFRUGDQ HL�GLQWUH�UHSDUWL LD�HPSLULF �RE LQXW �vQWU-R�FHUFHWDUH�FRQFUHW �úL�UHSDUWL LD�

WHRUHWLF � SUHVXSXV � VH� HIHFWXHD] � FX� DMXWRUXO� PDL� PXOWRU� WHVWH�� ([SUHVLD�( )n np

npi i

ii

k −

=∑

2

1

UHSUH]LQW �VWDWLVWLFD�WHVWXOXL�

a) Shapiro-Wilk; b) Lilliefors;

c) Hi-S WUDW�� χ 2 );

d) Kolmogorov - Smirnov; e) Gnedenko.

28) 2�JUXS �GH����GH�VWXGHQ L�VXV LQH�OD�GRX �GLVFLSOLQH�FkWH�XQ�WHVW�SHQWUX�YHULILFDUHD�FXQRúWLQ HORU��

7HVWHOH�DX�SXQFWDMH�GLIHULWH��LDU�SH�ED]D�ORU�VH�FXQRDúWH�F �

- la testul A: 900025

1

2 =∑=i

iAx 45025

1

=∑=i

iAx

- la testul B: 42525

1

2 =∑=i

iBx 10025

1

=∑=i

iBx

*UXSD�GH�VWXGHQ L�HVWH�PDL�RPRJHQ �GLQ�SXQFWXO�GH�YHGHUH�DO�FXQRúWLQ HORU�DFXPXODWH� a) la disciplina A; b) la disciplina B; c) la ambele disciplLQH�H[LVW �DFHODúL�JUDG�GH�RPRJHQLWDWH�

Page 109: STATISTICA - TESTE GRILA

d) QX�VXQW�VXILFLHQWH�GDWH�SHQWUX�D�IL�VWXGLDW �RPRJHQLWDWHD� e) QX� VH� SRW� FRPSDUD� RPRJHQLW LOH� FXQRúWLQ HORU� OD� FHOH� GRX � GLVFLSOLQH�� GHRDUHFH�

punctajele testelor au fost diferite.

29) (YROX LD�QXP UXOXL�GH�ERYLQH�úL�YROXPXO�SURGXF LHL�GH�FDUQH�DX�HYROXDW�DVWIHO�

Anii 1990 1991 1992 1993 1994 1995 1996 1997 Nr. bovine (mii) 5381 4355 3683 3597 3481 3496 3435 3431

Prod. carne (mii tone) 2232 2023 1895 1935 1852 1846 1868 1871

'HSHQGHQ D�GLQWUH�FHOH�GRX �YDULDELOH�VH�P VRDU �FX�DMXWRUXO�FRHILFLHQWXOXL�6SHDUPDQ��DOH�F UXL�YDORUL�VXQW�

a) 0,738; b) 0,901; c) -0,675; d) 0,991; e) 0,307.

30) Media ( x �� XQXL� HúDQWLRQ� GH� PDUH� YROXP� �Q�� SRDWH� IL� FRQVLGHUDW � F � XUPHD] � R� GLVWULEX LH�

QRUPDO �GH�PHGLH� x 0 úL�DEDWHUH�PHGLH�S WUDWLF ��HURDUH�PHGLH��σn

în cazul unui sondaj simplu

cu revenire. Pentru o probabilitate 1− α intervalul de estimare (de încredere) a parametrului

x 0 este x x zn

− ≤0 ασ

��3HQWUX�FD�SUHFL]LD�HVWLPD LHL�V �ILH�PDL�PLF �FX�k% din valoarea lui

x 0 �YROXPXO�HúDQWLRQXOXL�� ( )k ∈ 0 1; ) este:

a) nz

k x≤ ⋅α σ2

2

2

02

;

b) ( )nz

kCV≥ α

2

22 �XQGH�&9�HVWH�FRHILFLHQWXO�GH�YDULD LH�

c) nk x

= σ 2

20

;

d) nz k

x= α σ2 2 2

0;

e) Q!���XQLW L�vQ�RULFH�VLWXD LH�

Page 110: STATISTICA - TESTE GRILA

TESTUL 13

���5HFHQV PkQWXO�SRSXOD LHL�HVWH� D��R�REVHUYDUH�WRWDO �XQLF � E��R�REVHUYDUH�WRWDO ��LQWHJUDO ��SHULRGLF � F��R�REVHUYDUH�FXUHQW �SHULRGLF � d) o observare curHQW �GH�R�VLQJXU �GDW � H��R�REVHUYDUH�SHULRGLF �SDU LDO � 2) (URULOH�GH�UHSUH]HQWDWLYLWDWH�VXQW�VSHFLILFH�FHUFHW ULORU� a) prin sistemul rapoartelor statistice; b) prin sondaj; F��SULQ�UHFHQV PkQW� G��SULQ�REVHUYDUHD�S U LL�SULQFLSDOH� e) prin monografii. 3) 3URSULHWDWHD�GHWHUPLQDQW �D�YDULDELOHL�[�vQ�ED]D�F UHLD�VH�GHWHUPLQ �PHGLD�DULWPHWLF �HVWH�

)x ,... ,x ,x( f = )x ,... ,x ,x( f a) 2n

22

21

222

;

)x ,... ,x ,x( f = )x ,... ,x ,x( f b) n21 ;

)x ,... ,x ,x( f = )x ,... ,x ,x( f c) nn

221 ;

)x ,... ,x ,x( f = )x ,... ,x ,x( f d) n21mn

m2

m1 ;

)x ,... ,x ,x( f = )x ,... ,x ,x( f e) n21n21 . 4) 6H�FXQRVF�GDWH�FRQYHQ LRQale referitoare la valorile unei caracteristici:

Grupe )UHFYHQ H

9,0 - 9,5 3

9,5 - 10,0 1

10,0 - 10,5 42

10,5 - 11,0 23

11,0 - 11,5 9

11,5 - 12,0 1

12,0 - 12,5 1

Total n = 80

&XQRVFkQG� F � PHGLD� DULWPHWLF � D� FDUDFWHULVWLFLL� [� HVWH� � � ������ XQLW L�� FRHILFLHQWXO� GH�RPRJHQLWDWH��YDULD LH��HVWH�GH�

a) 4,62 %;

Page 111: STATISTICA - TESTE GRILA

b) 13,32 %; c) 22,19 %;

d) 23,32 %; e) 14,62 %.

5) 6WDELOLUHD�LQGLFHOXL�SUH XULORU��EXQXULORU��GH�FRQVXP�VH�IDFH�GXS �UHOD LD�

a) p q

p q

01

11

∑∑

;

b) )q + q( p

)q + q( p

010

011

∑∑

;

c) q p

q p

q p

q p

10

11

00

01

∑∑

⋅∑∑

;

d) p q

p q i

00

00p

∑∑

;

e) p q

i

1

p q

11p

11

.

6) )DFWRUXO�GH�FRUHF LH�LQWURGXV�vQ�FDOFXOXO�HURULL��DEDWHULL��PHGLHL�GH�VRQGDM��vQ�YDULDQWD�SUHOHY ULL�QHUHSHWDWH�D�XQLW LORU��HVWH�HJDO�FX�

a)

2

;

b) 1 - (n / N) ;

c)

1

N - 1 ;

d)

1

N ;

e)

1

n/

1

N

.

7) &XQRVFkQG�UHSDUWL LD�YDULDELOHL�[�

Grupe )UHFYHQ H 1,1 - 1,3 6 1,3 - 1,5 9 1,5 - 1,7 4 1,7 - 1,9 1

Total ni =∑ 20

valoarea quantilei doi (Q2��HVWH�HJDO �FX� a) 1,375; b) 1,51; c) 1,40;

Page 112: STATISTICA - TESTE GRILA

d) 1,45; e) 1,55.

8) 6H�FXQRVF�XUP WRDUHOH�GDWH��FRQYHQ LRQDOH��DVXSUD�UHSDUWL LHL�XQHL�FDUDFWHULVWLFL�

Grupe )UHFYHQ H 11,0 - 13,0 12 13,0 - 15,0 18 15,0 - 17,0 8 17,0 - 19,0 2

Total n = 40 'DWH� ILLQG��YDORDUHD�PRGDO �0R��[mo) = 13,75; valoarea medie = 14,0, coeficientul de asimetrie (Pearson) are valoarea:

a) 0,377; b) 0,677; c) 1,377; d) 0,963; e) 0,09.

9) ÌQ� OHJ WXU � FX� H[HUFL LXO� DQWHULRU�� VH� FHUH� V � VH� GHWHUPLQH� GLVSHUVLD� FDUDFWHULVWLFLL� DOWHUQDWLYH��ELQDUH����QXP U�XQLW L�FX�YDORUL�PDL�PDUL�FD�����

'LVSHUVLD�DFHVWHL�FDUDFWHULVWLFL�HVWH�HJDO �FX� a) 0,1875; b) 0,2875; c) 0,0912; d) 1,1725; e) 0,5000. 10) Se cunosc�GDWH��FRQYHQ LRQDOH��DVXSUD�YROXPXOXL�YkQ] ULORU�vQ�OXQD�PDUWLH������OD�6�&���*,*,�

,03(;�V�U�O����SHQWUX�WUHL�SURGXVH�GLQ�QRPHQFODWRU��FkW�úL�PRGLILFDUHD�SUH XULORU�

Produsul Valoarea vânz rilor în SHULRDGD�FXUHQW ��PLL�OHL�

Modificarea procenWXDO �D�SUH XULORU����

1 13.860 + 5,0 2 51.300 - 10,0 3 57.200 + 10,0

TOTAL Σ= 122.360 X 0RGLILFDUHD�DEVROXW �D�YROXPXOXL�YkQ] ULORU��FDX]DW �GH�PRGLILFDUHD�SUH XULORU� OD�FHOH� WUHL�SURGXVH��D�IRVW�HJDO �FX� a) 0 (zero) mii lei; b) - 80,0 mii lei; c) + 160,0 mii lei; d) + 180,0 mii lei; e) - 102,0 mii lei. 11) &XQRVFkQG� UH]XOWDWHOH� FHUFHW ULL� FDUDFWHULVWLFLL� ;� GLQWU-XQ� VRQGDM� Q� � ��� XQLW L�� SUHOHYDWH�

DOHDWRU�úL�QHUHSHWDW�GLQWU-R�SRSXOD LH�1� �����XQLW L�úL�DQXPH = 17,45 u.m., respectiv S2 = 0,61 u.m., pentru o probabilitate P = 95 % (Za� �������LQWHUYDOXO�GH�vQFUHGHUH�SHQWUX�PHGLD�SRSXOD LHL�JHQHUDOH�HVWH�HJDO�FX��YDORUL�URWXQMLWH�FX�GRX �]HFLPDOH��

Page 113: STATISTICA - TESTE GRILA

a) (17,01 ; 17,93); b) (16,25 ; 19,73); c) (10,63 ; 22,75); d) (14,29 ; 21,33); e) (17,29 ; 17,61). 12) 6H� FXQRVF� XUP WRDUHOH� GDWH� � �FRQYHQ LRQDOH�� UHIHULWRDUH� OD� YDORDUHD� YkQ] ULORU� SHQWUX� GRX �

SURGXVH��vQ�SHULRDGD�GH�ED] ��UHVSHFWLY�LQGLFLL�SUH XULORU�úL�PRGLILFDUHD�SURFHQWXDO �D�YROXPXOXL�fizic.

Produsul Valoarea vânz ULORU�vQ�SHULRDGD�GH�ED] ��POG��OHL�

,QGLFHOH�SUH XULORU (%)

0RGLILFDUHD�SURFHQWXDO �D�volumului fizic

(%)

1 10 130 0

2 12 100 0

Total S = 22 X X

0RGLILFDUHD� UHODWLY � D� YROXPXOXL� YDORULF� DO� YkQ] ULORU� OD� QLYHOXO� DQVDPEOXOXL� FHORU� GRX �produse este eJDO �FX� a) + 100 %; b) + 13,64 %; c) 0 %; d) - 25,0 %;

e) + 117,5 %.

13) ÌQ� FDGUXO� DQDOL]HL� GLVSHUVLRQDOH� ELIDFWRULDOH� XWLOL]DW � SHQWUX� D� WHVWD� VHPQLILFD LD� IDFWRULORU� GH�

LQIOXHQ �� GDF � � YDORULOH� � IDFWRUXOXL� $� �i = 1,r ), respectiv B ( j = 1,p ��� DWXQFL� QXP UXO�gradelor de libertate al dispersiei reziduale este:

a) rp - 1; b) r(r - 1); c) (r - 1)(p - 1); d) r(p - 1)p; e) r2(p - 1).

14) În cadrul analizei dispersionale unifactoriale, i = 1,r �QXP UXO�JUXSHORU��j = 1,ni -�QXP UXO�

XQLW LORU� vQ� JUXS �� VXPD�S WUDWHORU� DEDWHULORU� SHQWUX�FDOFXOXO� GLVSHUVLHL� UH]LGXDOH� �vQ� LQWHULRUXO�JUXSHL��VH�VWDELOHúWH�FX�UHOD LD�

a)

n

y

- y i

ijj

2

i

2ij

ij

∑∑;

b)

c) n

y

- n

y

ij

ji

2

i

ijj

2

i

∑∑∑

∑;

Page 114: STATISTICA - TESTE GRILA

d) y -

n

y 2ij

iji

ijji

2

∑∑∑∑

;

e) n

y

- y ij

ji

2

2ij

ij

∑∑

∑;

n

y

- n

y

- y i

ijj

2

i

ijji

2

2ij

ij

∑∑∑

∑.

15) ÌQWUH�GRX �YDULDELOH�OHJDWH��XQD�UH]XOWDWLY �\�úL�DOWD�IDFWRULDO �[��SHQWUX�Q� �����SHUHFKL�YDORUL�GH�

REVHUYD LH�� VH� FXQRVF� DJUHJDWHOH� GH� FDOFXO�� 1

100

i x = 2105∑; 1

100

i2 x = 49.665∑

;

1

100

i y = 4160∑; 1

100

i i x y = 96.640∑.

ÌQ�LSRWH]D�XQHL�OHJ WXUL�OLQLDUH�\x� �D���E[��HFXD LD�HVWH� a) yx = 0,963 + 12,735 x; b) yx = 1,259 + 0,799 x; c) yx = 22,933 + 12,811 x; d) yx = 5,937 + 1,694 x; e) yx = 7,339 + 2,437 x. 16) %XQXULOH� GH� IRORVLQ � vQGHOXQJDW � úL� FX� GXUDW �PHGLH� GH� IRORVLQ � LQFOXVH� vQ� DYX LD� QD LRQDO �

DFXPXODW �FXSULQG� a) Bunurile destinate s �VDWLVIDF �SH�R�GXUDW �GH�PD[LP�XQ�DQ��GLIHULWH�FHULQ H�PDWHULDOH�úL�

VSLULWXDOH�DOH�SRSXOD LHL��FD�GH�H[HPSOX��DXWRWXULVPH��WHOHYL]RDUH��DSDUDWH�GH�UDGLR��IULgidere, PRELO �HWF��

b) Bunurile destinate s � VDWLVIDF � SH� R� GXUDW � GH� SHVWH� XQ� DQ�� GLIHULWH� FHULQ H�PDWHULDOH� úL�VSLULWXDOH� DOH� SRSXOD LHL�� FD� GH� H[HPSOX�� IRQGXO� IXQFLDU�� FO GLULOH� GH� ORFXLW�� DXWRWXULVPHOH��televizoarele, aparatele de radio, frigiderele, mobila etc.;

c) Bunurile destinate s �VDWLVIDF �SH�R�GXUDW �PDL�PDUH�GH�XQ�DQ��GLIHULWH�FHULQ H�PDWHULDOH�úL�VSLULWXDOH� DOH� SRSXOD LHL�� FD� GH� H[HPSOX�� FO GLULOH� GH� ORFXLW�� DXWRWXULVPHOH�� WHOHYL]RDUHOH��aparatele de radio, frigiderele, mobila etc.;

d) Bunurile destinate s �VDWLVIDF �SH�R�GXUDW �GH�PD[LP�XQ�DQ��GLIHULWH�FHULQ H�PDWHULDOH�úL�spirituale, ca de exemplu: autoturisme, mijloace financiar-valutare, televizoare, aparate de UDGLR��IULJLGHUH��PRELO �HWF��

e) Bunurile materiale destinate s satisfac � SH� R� GXUDW � GH� SHVWH� XQ� DQ�� GLIHULWH� FHULQ H�PDWHULDOH� úL� VSLULWXDOH� DOH� SRSXOD LHL�� FD� GH� H[HPSOX�� FO GLULOH� GH� ORFXLW�� DXWRWXULVPHOH��PLMORDFHOH�ILQDQFLDU�YDOXWDUH��WHOHYL]RDUH��DSDUDWH�GH�UDGLR��IULJLGHUH��PRELO �HWF�

Page 115: STATISTICA - TESTE GRILA

17) (ILFLHQ D�IRQGXULORU�IL[H�QRL�VH�GHWHUPLQ �FX�UHOD LD�

a) FN

i i

i - 1e =

PIB

FN

∆ / −1

;

b) FN

i

i - 1e =

PIB

FN

∆ /0

;

c) FN

ie =

PIB

FN ;

d) FN

ie =

PIB

Ff;

e) FN

i i

ie =

PIB

Ff

∆ / −1

. unde: eFN -�HILFLHQ D�IRQGXULORU�IL[H�QRL� PIB - produsul intern brut;

i = 0,n - LQGH[XO�SHULRDGHORU�GH�UHIHULQ � Ffi - fondurile fixe în anul i; FNi - fondurile fixe noi; D -�PRGLILFDUHD�DEVROXW �D�LQGLFDWRULORU� 18) 5HVXUVHOH�GH�PXQF �OD�XQ�PRPHQW�GDW�VH�GHWHUPLQ � D�� 5HVXUVH� GLVSRQLELOH� � �7RWDO� SRSXOD LH�� -� �3RSXOD LD� vQ� YkUVW � GH� PXQF � GDU� vQ�

LQFDSDFLWDWH�����3RSXOD LD�vQ�DIDUD�YkUVWHL�GH�PXQF �GDU�FDUH�OXFUHD] �� E��5HVXUVH�GLVSRQLELOH� ��7RWDO�SRSXOD LH�DSW �GH�PXQF �����3RSXOD LD� vQ�YkUVW �GH�PXQF �

dar în incapacitate) -��3RSXOD LD�vQ�DIDUD�YkUVWHL�GH�PXQF �GDU�FDUH�OXFUHD] ); F��5HVXUVH�GLVSRQLELOH� ��7RWDO�SRSXOD LH�DSW �GH�PXQF ��-��3RSXOD LD�vQ�YkUVW �GH�PXQF �GDU�

DIODW �vQ�LQFDSDFLWDWH�GH�PXQF �����3RSXOD LD�vQ�DIDUD�YkUVWHL�GH�PXQF �GDU�FDUH�OXFUHD] �� G��5HVXUVH�GLVSRQLELOH� � �7RWDO�SRSXOD LH���� �3RSXOD LD� vQ�DIDUD�YkUVWHL�GH�PXQF �GDU�FDUH�

OXFUHD] �����3RSXOD LD�DIODW �vQ�LQFDSDFLWDWH�GH�PXQF �� H�� 5HVXUVH� GLVSRQLELOH� � �7RWDO� SRSXOD LH� DSW � GH� PXQF �� -� �(OHYL�� VWXGHQ L�� PLOLWDUL� vQ�

WHUPHQ��úRPHUL��FDVQLFH�����3RSXOD LD�DIODW �vQ�LQFDSDFLWDWH�GH�PXQF ��

19) Durata mediH�D�]LOHL�GH�OXFUX�VH�FDOFXOHD] ��DZ ):

a) DZ =

durata lunii de lucru

durata zilei de lucru ;

b) DZ =

totalul orelor - om lucrate

totalul om - zilelor lucrate ;

c) DZ =

totalul om - zilelor lucrate

durata lunii de lucru ;

d) DZ =

totalul om - zilelor lucrate

totalul om - orelor lucrate ;

Page 116: STATISTICA - TESTE GRILA

e) DZ =

totalul om - zilelor lucrate

numarul mediu al salariatilor . 20) 6H�FXQRVF�XUP WRDUHOH�GDWH�

- mld. lei - Indicatori 1993 1994 Modificarea (‘94/’93) %

���&RQVXPXO�ILQDO�DO�JRVSRG ULLORU 12.670 31.442 + 2,6

���&RQVXPXO�DGPLQLVWUD LHL 2.566 7.011 + 3,1

���)RUPDUHD�EUXW �D�FDSLWDOXOXL�IL[ 3.584 10.096 + 20,7

4) Modificarea stocurilor 2.212 2.253 - 57,0

5) Exportul net - 996 - 1.028 - 72,0

5DWD�LQIOD LHL�vQ�LQWHUYDOXO������-������D�IRVW�HJDO �FX��FDOFXOH�FX�YDORUL�URWXQMLWH�� a) 73 %; b) 173 %; c) 313 %; d) 141 %; e) 256 %.

21) 'DF �VH�QRWHD] � L - durata medie a lunii de lucru; S -�GXUDWD�PHGLH�D�V SW PkQLL�GH�OXFUX� Z - durata medie a zilei de lucru; TH - volumul om-orelor lucrate; TZ - volumul om-zilelor lucrate; WH, WZ -�SURGXFWLYLWDWHD�RUDU �úL�]LOQLF � $WXQFL��SLHUGHUHD�GH�SURGXF LH�FD�XUPDUH�D�QHIRORVLULL�LQWHJUDOH�D�]LOHL�GH�OXFUX�VH�GHWHUPLQ �

WH normata) durata - LD( = Q a) ∆ ;

b) Q = ( DZ - durata normata) TH WH∆ • ; c) Q = ( DL - DS ) TH WZ∆ • ;

d) Q = ( DZ - DS ) TH WH∆ • ;

e) Q = ( DZ - 8) DS WZ∆ • .

22) Dac �VH�QRWHD] �

wi - productivitatea muncii pe subdiviziuni organizatorice (i = 1,n ) iw -�LQGLFLL�LQGLYLGXDOL�DL�SURGXFWLYLW LL�PXQFLL T -�QXP UXO�PHGLX�DO�VDODULD LORU g(T) -�VWUXFWXUD�VDODULD LORU�SH�VXEGLYL]LXQL�RUJDQL]DWRULFH 0,1 -�SHULRDGHOH�FRPSDUDWH��ED] ��HIHFWLY � $WXQFL�HVWH�YDODELO �UHOD LD�

a) w T

T =

w g

w g0 1

1

1 1(T)

0 0(T)

∑∑

∑;

Page 117: STATISTICA - TESTE GRILA

b) w T

T : w T

T =

w g

w g0 1

1

0 0

0

0 1(T)

1 1(T)

∑∑

∑∑

∑;

c) w T

T : w T

T = w T

w T = w T

1

i w T

1 1

1

0 1

1

1 1

0 1

1 1

w 1 1

∑∑

∑∑

∑∑

∑;

d) w T

T : w T

T = w T

w T0 0

0

1 1

1

1 1

0 0

∑∑

∑∑

∑∑ ;

e) w g

w g = w T

T : w T

T1 0

(T)

0 0(T)

1 1

1

0 1

1

∑∑

∑∑

∑.

23) &RQWXO�VLQWHWLF�GH�EXQXUL��FRQWXO����DUH�vQ�FRPSRQHQ �XUP WRULL�LQGLFDWRUL� a)

R U

î�9DORDUHD�SURGXF LHL�LQWHUQH��SURGXF LH�EUXW � - firme - stat -�JRVSRG ULL��PHQDMH�

× Consum intermediar - firme - stat -�JRVSRG ULL��PHQDMH�

× Import de bunuri -�79$�QHGHGXFWLELO

× Consum final - privat - guvernamental

× Impozite pe import î�,QYHVWL LL�EUXWH - firme - guvern

× Export de bunuri Total resurse 7RWDO�XWLOL] UL

b)

R U × Valoarea ad ugat �QHW × Consum intermediar

- firme - stat -�JRVSRG ULL

× Import de bunuri -�79$�QHGHGXFWLELO

× Consum final - privat - guvernamental

× Impozite pe import î�,QYHVWL LL�EUXWH - firme - guvern

× Export de bunuri Total resurse 7RWDO�XWLOL] UL

Page 118: STATISTICA - TESTE GRILA

c)

R U î�9DORDUHD�SURGXF LHL�LQWHUQH��SURGXF LH�EUXW � - firme - guvern (stat) -�PHQDMH��JRVSRG ULL�

× Amortizarea capitalului fix - firme - guvern (stat) -�JRVSRG ULL

× Import de bunuri -�79$�QHGHGXFWLELO

× Consum final - privat - guvernamental

× Impozite pe import î�,QYHVWL LL�EUXWH - firme - guvern

Total resurse 7RWDO�XWLOL] UL d)

R U

î�9DORDUHD�SURGXF LHL�LQWHUQH��SURGXF LH�EUXW ) - firme - guvern (stat) -�PHQDMH��JRVSRG ULL�

× Consum intermediar - firme - guvern (stat) -�JRVSRG ULL

× Export de bunuri -�79$�QHGHGXFWLELO

× Consum final - privat - guvernamental

× Impozite pe export î�,QYHVWL LL�EUXWH - firme - stat (guvern)

× Import de bunuri

Total resurse 7RWDO�XWLOL] UL

e)

R U

î�9DORDUHD�SURGXF LHL�LQWHUQH��SURGXF LH�EUXW � - firme - guvern (stat) -�PHQDMH��JRVSRG ULL�

× Consum intermediar - firme - guvern (stat) -�JRVSRG ULL��PHQDMH�

× Export de bunuri - TVA nedeductLELO

× Consum final - privat - guvernamental

× Amortismente - firme - guvern

Total resurse 7RWDO�XWLOL] UL

Page 119: STATISTICA - TESTE GRILA

24) 'DF �

ramurilor productiei vectorul reprezinta

X

.

.

.

.

X

X = X

n

2

1

finale productiei vectorul -

Y

.

.

.

.

Y

Y = Y

n

2

1

directelorcheltuieliilorcoeficientmatricea

aaa

aaa

aaa

A

nnnnn

n

n

...

............

...

...

1

22221

11211

=

I - matricea unitate; T - transpus Corect �HVWH�UHOD LD� a) Y = (I - A)-1 X; b) Y = (I - A) X; c) X = (1 - A) Y; d) X = [AT]-1 X + Y; e) Y = (1 - A) XT. 25) 5DWD�DQXDO �D�LQIOD LHL�UHSUH]LQW � D�� &UHúWHUHD� SUH XULORU� GH� FRQVXP�� P VXUDW � SULQ� LQGLFHOH� SUH XULORU� GH� FRQVXP�� vQ� OXQD�

decembrie a anului curent ID �GH�OXQD�GHFHPEULH�D�DQXOXL�SUHFHGHQW� b) &UHúWHUHD�SUH XULORU�GH�FRQVXP��P VXUDW �SULQ�LQGLFHOH�SUH XULORU�GH�FRQVXP��vQ�OXQD�GHFHPEULH�

D�DQXOXL�FXUHQW�ID �GH�OXQD�RFWRPEULH�������OXQD�SUHPHUJ WRDUH��OLEHUDOL] ULL��SUH XULORU� F�� &UHúWHUHD� SURFHQWXDO � D� SUH XULORU� GH� FRQVXP�� P VXUDW � SULQ� LQGLFHOH� SUH XULORU� GH�

FRQVXP��vQ�DQXO�FXUHQW�ID �GH�DQXO�GH�ED] � G�� 0HGLD� FUHúWHULORU� OXQDUH� DOH� SUH XULORU�� P VXUDW � SULQ� LQGLFHOH� SUH XULORU� GH� FRQVXP��

FDOFXODW � FD� PHGLH� JHRPHWULF � D� LQGLFLORU� OXQDUL� DL� SUH XULORU� GH� FRQVXP� FX� ED] � PRELO ��ODQ ��GLQ�DQXO�GH�FDOFXO�

H��6F GHUHD�SURFHQWXDO �D�SUH XULORU�GH�FRQVXP��P VXUDW �SULQ�LQGLFHOH�SUH XULORU�GH�FRQVXP��vQ�DQXO�FXUHQW�ID �GH�DQXO�GH�ED] �

Page 120: STATISTICA - TESTE GRILA

26) 6H�FXQRVF�XUP WRDUHOH�GDWH�UHIHULWRDUH�OD�UHVXUVHOH�3,%�SHQWUX�DQXl 1997 (miliarde lei): - industrie: 88.944,7 -�DJULFXOWXU ��VLOYLFXOWXU ��H[��IRUHVWLHU ���������� -�FRQVWUXF LL���������� - servicii: 84.689,3 -�DMXVWDUH�SHQWUX�SURGXF LD�VHUYLFLLORU�EDQFDUH��- 4.415,0 -�LPSR]LWH�úL�VXEYHQ LL�SH�SURGXV��������,6 -�YDORDUH�DG XJDW �EUXW ����������� Produsul intern brut pentru anul 1997 este egal cu: a) 479.484,8; b) 249.750,2; c) 254,165,2; d) 229.734,6; e) 459.469,2. 27) 'DF �vQ�DQXO�������FkúWLJXO�VDODULDO�PHGLX�QRPLQDO�QHW�D�IRVW���������FRPSDUDWLY cu anul 1996,

LDU�SUH XULOH�GH�FRQVXP�DX�HYROXDW�DVWIHO����� -�P UIXUL�DOLPHQWDUH������� -�P UIXUL�QHDOLPHQWDUH������� - servicii: 276,5 în structura pe cele trei categorii: -�P UIXUL�DOLPHQWDUH�������� -�P UIXUL�QHDOLPHQWDUH�������� - servicii: 11,8 % 'LQDPLFD�VDODULXOXL�PHGLX�UHDO�D�IRVW�vQ�DQXO������FRPSDUDWLY�FX������HJDO �FX� a) 112,5; b) 88,9; c) 53,9; d) 250,1; e) 77,6. 28) 8WLOL]DUHD�EXQXULORU�úL�VHUYLFLLORU�vQ�HFRQRPLD�QD LRQDO �VH�VWDELOHúWH�FRQIRUP�UHOD LHL� a) Consumul priYDW� �� FRQVXPXO� JXYHUQDPHQWDO� � FRQVXPXO� WRWDO� �� IRUPDUHD� EUXW � D�

FDSLWDOXOXL�IL[���PRGLILFDUHD�VWRFXULORU� �XWLOL]DUHD�ILQDO �D�EXQXULORU�úL�VHUYLFLLORU� E�� &RQVXPXO� SULYDW� �� FRQVXPXO� JXYHUQDPHQWDO� � FRQVXPXO� ILQDO� �� LQYHVWL LLOH� EUXWH� vQ�

capitalul fix + PRGLILFDUHD� VWRFXULORU� � XWLOL]DUHD� ILQDO � vQ� LQWHULRUXO� ULL� �� H[SRUWXO� GH�EXQXUL�úL�VHUYLFLL� �XWLOL]DUHD�ILQDO �D�EXQXULORU�-�LPSRUWXO�GH�EXQXUL�úL�VHUYLFLL� �XWLOL]DUHD�bunurilor ce compun PIB;

F��&RQVXPXO�SULYDW���FRQVXPXO�JXYHUQDPHQWDO���LQYHVWL LLle nete + modificarea stocurilor + importul - exportul = utilizarea bunurilor;

G��&RQVXPXO�VWDWXOXL��JXYHUQDPHQWDO����LQYHVWL LLOH�EUXWH�GH�FDSLWDO�-�H[SRUWXO�GH�EXQXUL�úL�servicii -�LPSRUWXO�GH�EXQXUL�úL�VHUYLFLL�-�XWLOL]DUHD�ILQDO �D�EXQXULORU� �XWLOL]DUHD�EXQXULORU�úL�serviciilor ce compun PIB;

H��&RQVXPXO�SULYDW���FRQVXPXO�VWDWXOXL��JXYHUQDPHQWDO����LQYHVWL LLOH�QHWH�GH�FDSLWDO�IL[���PRGLILFDUHD�VWRFXULORU���H[SRUWXO�QHW� �XWLOL]DUHD�EXQXULORU�úL�VHUYLFLLORU�FH�FRPSXQ�3,%�

Page 121: STATISTICA - TESTE GRILA

29) 6H�FXQRVF�XUP WRDUHOH�GDWH� - Produsul Intern Brut (PIB) în anul 1996: 108396 mld. lei pr. curente - PIB 1997: 249750 mld. lei pr. curente - PIB 1998 (previziune): 411.135 mld. lei pr. curente - Modificarea PIB: 1997/1996 : - 6,6 % 1998/1997 : 0 % 5DWD�LQIOD LHL�vQ�LQWervalul 1996 - 1998 va fi de: a) 64,50 %; b) 125,75 %; c) 115,12 %; d) 305,99 %; e) 225,75 %. 30) &DUH�GLQ�HOHPHQWHOH�GH�PDL�MRV�FH�LQWU �vQ�FRQVXPXO�GLUHFW�DO�SRSXOD LHL�VH�LQFOXGH�vQ�FDOFXOXO�

LQGLFHOXL�SUH XULORU�GH�FRQVXP� a) cheltuieli aferenWH� SO LL� PXQFLL� SHQWUX� SURGXF LD� JRVSRG ULHL� �DUDW�� VHP QDW�� SU úLW��

îngrijirea culturilor, cositul fânului, tratamentul medical al animalelor etc.); E��FKHOWXLHOL�FDUH�VH�UHIHU �OD�SO LOH�HIHFWXDWH�OD�FUHGLWH��UDWH�GH�DVLJXUDUH��DPHQ]L��MRFXUL�GH�

noroc, impozite etc.; F��FKHOWXLHOL�SHQWUX�SURFXUDUHD�SURGXVHORU�YkQGXWH�SH�SLD D� U QHDVF � G�� FKHOWXLHOL� FX� FDUDFWHU� GH� LQYHVWL LL� úL� DFXPXODUH� �FXPS UDUHD� GH� ORFXLQ H�� PDWHULDOH� GH�

FRQVWUXF LL�IRORVLWH�SHQWUX�FRQVWUXLUHD�GH�ORFXLQ H�QRL�VDX�HIHFWXDUHD�GH�UHSDUD LL�OD�ORFXLQ HOH�vechi etc.);

H�� FRQVXPXO� GLQ� UHVXUVH� SURSULL� UHSUH]HQWkQG� FRQWUDYDORDUHD� FDQWLW LORU� GH� SURGXVH�FRQVXPDWH�GH�SRSXOD LH��DOWHOH�GHFkW�GLQ�FXPS U WXUL��VWRF��SURGXF LH�SURSULH��FDGRXUL�HWF���

Page 122: STATISTICA - TESTE GRILA

TESTUL 14

���3HQWUX�GLVWULEX LD� DQJDMD LORU�XQHL�FRPSDQLL�GXS �QLYHOXO�GH�SUHJ WLUH�SURIHVLRQDO �QX�VH�SRDWH�calcula:

a) structura; E��WRWDOXO�DQJDMD LORU� c) valoarea medie; G��YDORDUHD�PRGDO � H���IUHFYHQ HOH�QXOH��GDF �H[LVW �

���5DWD�úRPDMXOXL�QX�VH�SRDWH�FDOFXOD�UDSRUWkQG��

a) popula LD�QHRFXSDW �OD�SRSXOD LD�FXUHQW�DFWLY � E��QXP UXO�GH�úRPHUL�OD�SRSXOD LD�DFWLY � F��SRSXOD LD�QHRFXSDW �OD�SRSXOD LD�DFWLY � G��QXP UXO�GH�úRPHUL�OD�SRSXOD LD�WRWDO � H��QXP UXO�GH�úRPHUL�OD�IRU D�GH�PXQF �

3) Pe termen lung poate fi doar atenuat, dar QX�HYLWDW�úRPDMXO�

a) ciclic; b) structural; c) tehnologic; d) nici una din formele de mai sus; H��SRW�IL�HYLWDWH�WRDWH�IRUPHOH�GH�úRPDM�

���7LWOXULOH�UHSUH]HQWDWLYH�DOH�S U LORU�VRFLDOH�GHILQHVF�vQ�&RQWDELOLWDWHD�1D LRQDO ��

D��REOLJD LXQLOH� b) bonurile de tezaur; c) orice hârtie de valoare; G��DF LXQLOH� H��DFHDVW �GHILQL LH�QX�DSDUH�LQ�&RQWDELOLWDWHD�1D LRQDO �

��� ,QWHUYDOXO� GH� vQFUHGHUH� SHQWUX� HVWLPDUHD� PHGLHL� SRSXOD LHL� JHQHUDOH� SRUQLQG� GH� OD� YDORDUHD�FDOFXODW �SHQWUX�HúDQWLRQ��VH�PDL�QXPHúWH�úL���

a) evantaiul valorilor estimate; b) parametru de încredere; c) interval previzionat; G��FODV �HYDOXDW � H��QX�H[LVW �VLQRQLP�SHQWUX�QR LXQHD�GH�LQWHUYDO�GH�vQFUHGHUH�

���,QGLFDWRUXO�WHQGLQ HL�FHQWUDOH�FH�VLQWHWL]HD] �YDORULOH�vQUHJLVWUDWH�DOH�XQHL�FDUDFteristici cantitative este:

a) cuartila a 3-a; b) coeficientul de asimetrie; c) media; d) mediana; H��QX�H[LVW �XQ�DVWIHO�GH�LQGLFDWRU�

Page 123: STATISTICA - TESTE GRILA

��� &RQWXO� VWDWLVWLF� vQ� FDUH� VH� vQUHJLVWUHD] � � WUDQ]DF LLOH� GH� EXQXUL� úL� VHUYLFLL�� vPSUHXQ � FX�transferurile publice sau private dintr-R�SHULRDG ��vQWUH�R� DU �úL�H[WHULRU�UHSrH]LQW ��

D��EDODQ D�FRPHUFLDO �� E��EDODQ D�GH�SO L� F��EDODQ D�RSHUD LXQLORU�FXUHQWH� G��EDODQ D�OHJ WXULORU�GLQWUH�UDPXUL� e) tabelul input-output.

8) Sinonimul pentru ecart statistic este:

a) difHUHQ �VHPQLILFDWLY � b) abatere; c) echilibru; d) clopotul lui Gauss; H��HFXD LH�VWDWLVWLF �

���&DUWRJUDPD�VH�IRORVHúWH�SHQWUX�D�UHSUH]HQWD�JUDILF��

D��XQLW L�VWDWLVWLFH�FX�GRX �GLPHQVLXQL��vQWRWGHDXQD�GXS �R�FDUDFWHULVWLF � b) XQLW L�VWDWLVWLFH�FX�GRX �GLPHQVLXQL��vQWRWGHDXQD�GXS �PDL�PXOWH�FDUDFWHULVWLFL� c) XQLW L�VWDWLVWLFH�FX�GRX �GLPHQVLXQL��QLFLRGDW �GXS �PDL�PXOWH�FDUDFWHULVWLFL� G��XQLW L�VWDWLVWLFH�FX�GRX �GLPHQVLXQL��GXS �XQD�VDX�PDL�PXOWH�FDUDFWHULVWLFL� e) cartograma nu este un grafic utilizat�GH�VWDWLVWLF �

����0XO LPHD�XQLW LORU�VWDWLVWLFH�H[WUDVH�DOHDWRULX�GLQWU-R�FROHFWLYLWDWH�VWDWLVWLF �HVWH�GHQXPLW �úL�

D��SURE � E��HúDQWLRQDUH� F��VFKHP �SUREDELOLVWLF � G��SDV�GH�QXP UDUH� H��ED] �GH�VRQGDM�

����3HQWUX�D�RE LQH�FHUHUHD�LQWHUQ �EUXW �VH�DGXQ �OD�FHUHUHD�LQWHUQ �QHW �

D��LPSR]LWHOH�LQGLUHFWH�I U �VXEYHQ LL� E��YHQLWXO�QD LRQDO� F��LPSR]LWHOH�LQGLUHFWH�FX�VXEYHQ LL� d) amortizarea; e) cei doi indicatori sunt egali.

����'DF �GLQ�311�H[SULPDW�vQ�SUH XULOH�SLH HL�VH�VFDG�LPSR]LWHOH�LQGLUHFWH�I U �VXEYHQ LL�VH�RE LQH��

D��YHQLWXO�QD LRQDO� b) PNN; c) PIB; G��311�H[SULPDW�vQ�SUH XULOH�IDFWRULORU� e) PNB.

Page 124: STATISTICA - TESTE GRILA

���� ,QGLFDWRUXO�FH�FDUDFWHUL]HD] �DFWLYLWDWHD� XQHL� HFRQRPLL�QD LRQDOH� SULQ� vQVXPDUHD� RSHUD LXQLORU�HIHFWXDWH�GH�DJHQ LL�HFRQRPLFL�VH�PDL�QXPHúWH��

a) aglomerat macroeconomic; E��VXP �PDFURHFRQRPLF � c) agregat macroeconomic; d) agent macroeconomic; e) acord macroeconomic.

����$F LXQHD�GH�FRUHFWDUH�D�YDORULORU�vQUHJLVWUDWH�DOH�XQXL�IHQRPHQ�HFRQRPLFR-social la curba sa de WHQGLQ �GHILQHúWH�RSHUD LXQHD�GH��

a) eliminare a valorilor aberante; b) ajustare; c) grupare; G��HúDQWLRQDUH� H��FRUHF LH�D�HURULORU�VLVWHPDWLFH�

15) Prin formula ( ) ( )f y y x xij j

j

n

i

m

i⋅ − ⋅ −==

∑∑11 ���VH�GHILQHúWH�

D��QXP U WRUXO�UDSRUWXOXL�GH�FRUHOD LH� b) numitorul coeficientului GH�FRUHOD LH�OLQLDU � F��QXP U WRUXO�FRHILFLHQWXOXL�GH�FRUHOD LH�OLQLDU � G��QXPLWRUXO�UDSRUWXOXL�GH�FRUHOD LH� H��FRHILFLHQWXO�GH�FRUHOD LH�OLQLDU ��

����&RPSOHWD L�VSD LXO�OLEHU�GLQ�DILUPD LD� ³&RYDULDQ D� UHSUH]LQW � JHQHUDOL]DUHD� QR LXQLL� GH�«««��� DSOLFDELO � XQXL� VHW� GH� SHUHFKL� GH� GDWH�(atribute statistice)”, alegând dintre variantele:

a) variabilitate; E��YDULDQ � F��YDULD LH� G��YDULDQW � H��YDULDELO �

����&RHILFLHQWXO�GH�HODVWLFLWDWH�VH�FDOFXOHD] �DVWIHO�

a) ritmul de modificare a variabilei factoriale raportat la ritmul de modificare a variabilei rezultative;

E��ULWPXO�GH�PRGLILFDUH�D�YDULDELOHL� IDFWRULDOH� vQPXO LW�FX�ULWPXO�GH�PRGLILFDUH�D�YDULDELOHL�rezultative;

c) ritmul de modificare a variabilei rezultative raportat la ritmul de modificare a variabilei factoriale;

G��ULWPXO�GH�PRGLILFDUH�D�YDULDELOHL�UH]XOWDWLYH�vQPXO LW�FX�ULWPXO�GH�PRGLILFDUH�D�YDULDELOHL�factoriale;

H��PRGLILFDUHD�DEVROXW �D�YDULDELOHL�UH]XOWDWLYH�UDSRUWDW�OD�PRGLILFDUHD�DEVROXW �D�YDULDELOHL�factoriale.

Page 125: STATISTICA - TESTE GRILA

18) Extrapolarea UHSUH]LQW �RSHUD LXQHD�VWDWLVWLF �GH�

a) prelungire a valorilor unei serii cronologice dincolo de perioada pe care s-au efectuat REVHUYD LLOH��FRQIRUP�XQHL�OHJL�GH�WHQGLQ �

b) interpolare; c) estimare a unei valori dintr-o serie de date continue, cunoscâQG�YDORULOH�GLQ�GUHDSWD�úL�GLQ�

stânga sa; d) determinare a unui interval de încredere; H��GHWHUPLQDUH�D�WHQGLQ HL�GH�HYROX LH�D�XQXL�IHQRPHQ�

����&XQRVFkQG�GHILQL LLOH�QR LXQLORU�GH�PHGLH�DULWPHWLF � úL� DUPRQLF �� GDF �DFHVWHD� VXQW� FDOFXODWH�SHQWUX�DFHODúL�VHW�GH�GDWH��SUHFL]D L�FH�DILUPD LH�HVWH�DGHY UDW �

D��R�FUHúWHUH�D�YDORULL�PHGLHL�DULWPHWLFH�YD�GHWHUPLQD�R�FUHúWHUH�D�YDORULL�PHGLHL�DUPRQLFH� E��YDULD LD�PHGLHL�DULWPHWLFH�GHWHUPLQ �YDULD LD�vQ�VHQV�FRQWUDU�D�PHGLHL�DUPRQLFH� F�� FUHúWHUHD� PHGLHL� DUPRQLFH� YD� DWUDJH� GXS � VLQH�� vQ� PRG� DXWRPDW�� FUHúWHUHD� PHGLHL�

aritmetice; G��VF GHUHD�YDORULORU�FDUDFWHULVWLFLL�VWDWLVWLFH�vQUHJLVWUDWH�YD�DWUDJH�GXS �VLQH�VF GHUHD�PHGLHL�

DUPRQLFH�úL�DULWPHWLFH� H��PHGLD�DULWPHWLF �HVWH�LQGHSHQGHQW �GH�FHD�DUPRQLF ��úL�DPkQGRX �VXQW�LQGHSHQGHQWH�GH�

HYROX LD�YDORULORU�vQUHJLVWUDWH�DOH�FDUDFWHULVWLFLL� ����9DORULOH�DMXVWDWH�DOH�XQHL�VHULL�GH�WLPS�SRW�IL��ID �GH�FHOH�vQUHJLVWUDWH�

a) <; b) >; c) =; d) <, =, >; e) nu se pot compara.

���� 'DF �� SHQWUX� R� VHULH� FURQRORJLF �� VXPD� YDORULORU� DMXVWDWH� HVWH� DSUR[LPDWLY� HJDO � FX� VXPD�valorilor înregistrate, atunci:

D��PHWRGD�GH�DMXVWDUH�DOHDV �QX�HVWH�SRWULYLW �� E��PHWRGD�GH�DMXVWDUH�DOHDV �HVWH�RSWLP � c) metoda de aMXVWDUH�DOHDV �HVWH�XQLF � G��PHWRGD�GH�DMXVWDUH�DOHDV �HVWH�FRUHFW �� H��PHWRGD�GH�DMXVWDUH�DOHDV �HVWH�H[DFW �

����5DSRUWXO�GLQWUH�R�YDORDUH�vQUHJLVWUDW ��úL�FHD�WHRUHWLF ��DIODW �SH�FXUED�GH�UHJUHVLH�SRDWH�IL�

a) supraunitar; b) subunitar; c) unitar; d) negativ; e) pozitiv.

$OHJH L�FRPELQD LD�SRWULYLW ��GLQWUH�FHOH�QRWDte cu majuscule: A = a,b,d; B = b,d,e; C = a,b,c; D = a,b; E = a

Page 126: STATISTICA - TESTE GRILA

����'DF � vQ�XUPD�JUXS ULL�XQXL�VHW�GH�GDWH�SH� LQWHUYDOH�GH�YDULD LH�HJDOH��VH�RE LQ�IUHFYHQ H�QXOH��DWXQFL�VH�UHFRPDQG �

D��V �VH�UHJUXSH]H�GDWHOH�GXS �R�DOW �FDUDFWHULVWLF � b) se utilizea] �vQ�FRQWLQXDUH�DFHHDúL�GLVWULEX LH�QH LQkQG�FRQW��GH�IUHFYHQ HOH�QXOH� F��VH�XWLOL]HD] �vQ�FRQWLQXDUH�GLVWULEX LD�GDF �HVWH�GRDU�R�VLQJXU �IUHFYHQ �QXO � G��VH�UHJUXSHD] �GDWHOH��P ULQG�QXP UXO�GH�LQWHUYDOH�GH�YDULD LH� H��VH�UHJUXSHD] �GDWHOH�P ULQG�GLmensiunea intervalului.

����8Q�ULWP�GH�PRGLILFDUH�D�XQXL�IHQRPHQ��ULWP�FH�DUH�YDORDUHD�SR]LWLY ��LPSOLF ��vQ�PRG�QHFHVDU� D��YDORDUHD�VXSUDXQLWDU ��D�LQGLFHOXL�GH�GLQDPLF � E��YDORDUHD�QHJDWLY �D�PRGLILF ULL�DEVROXWH� F��YDORDUHD�QHJDWLY �D�VSRUXOXL�FX�ED] �IL[ � G��GHVFUHúWHUHD�IHQRPHQXOXL� e) stagnarea fenomenului .

����3HQWUX�VHULD�GH�GDWH�UHSUH]HQWkQG�GLVWULEX LD�IDPLOLLORU�GXS �QLYHOXO�GH�YHQLW�

Venit Foarte VF ]XW

6F ]XW Mediu Ridicat Foarte ridicat

Nr. familii 10 20 40 20 10 coeficientul de asimetrie propus de Pearson este:

a) zero; b) unitar; c) egal cu -1; d) nu se poate calcula; H��HJDO�FX�FRHILFLHQWXO�GH�YDULD LH�

���� 'DF � GRX � VHULL� GH� GLVWULEX LH� SDUDOHOH� SUH]LQW � R� WHQGLQ � FXUELOLQLH� SURQXQ DW �� DWXQFL�P VXUDUHD�LQWHQVLW LL�OHJ WXULL�GLQWUH�FHOH�GRX �YDULDELOH�VH�DSUHFLD] �vQ�IXQF LH�GH�YDORDUHD�

D��FRHILFLHQWXOXL�GH�FRUHOD LH�OLQLDU � E��FRYDULDQ HL� F��UDSRUWXOXL�GH�FRUHOD LH� d) valorilor ajustate; H�� QX� VH� SRDWH� FDOFXOD� XQ� LQGLFDWRU� FH� LQGLF � LQWHQVLWDWHD� OHJ WXULL�� GDF � DFHDVWD� este

curbilinie. ����9DULD LD�XQHL�FDUDFWHULVWLFL�VWDWLVWLFH�WLQGH�OD�]HUR�GDF �FROHFWLYLWDWHD�DQDOL]DW �HVWH�

a) de volum normal; E��QRUPDO�GLVWULEXLW �GXS �R�FDUDFWHULVWLF � F��HWHURJHQ � G��RPRJHQ � H��DVLPHWULF �

28) 'DF �SHQWUX��VHULH�GH�GLVWULEX LH�GH�IUHFYHQ H�FRHILFLHQWXO�GH�YDULD LH�LQGLF �XQ�QLYHO�ULGLFDW�GH�

HWHURJHQLWDWH��DWXQFL� VH� UHFRPDQG � vPS U LUHD�FROHFWLYLW LL� vQ�JUXSH�GXS �XQ� IDFWRU�GH�JUXSDUH�semnificativ, ceea ce va duce la:

Page 127: STATISTICA - TESTE GRILA

D��FUHúWHUHD�JUDGXOXL�GH�RPRJHQLWDWH�vQ�LQWHULRUXO�JUXSHORU� b��FUHúWHUHD�JUDGXOXL�GH�HWHURJHQLWDWH�vQ�LQWHULRUXO�JUXSHORU� F��VF GHUHD�JUDGXOXL�GH�RPRJHQLWDWH�vQ�LQWHULRUXO�JUXSHORU� G��FUHúWHUHD�QLYHOXOXL�FRHILFLHQWXOXL�GH�YDULD LH�vQ�LQWHULRUXO�JUXSHORU� e) nivelul de omogenitate în interiorul grupei va fi întotdeauna egal cu cel calculat pentru

GLVWULEX LD�PDUJLQDO � ����3HQWUX�R�SLD �FXQRDúWHP�GDWHOH�

Bunuri 3UH XUL������(u.m.)

&DQWLW L������(u.c.)

3UH XUL������(u.m.)

&DQWLW L������(u.c.)

A 45 300 65 400 B 90 500 105 500 C 260 900 320 1100 D 115 300 150 600 E 118 800 128 700

Atunci:

D��ÌQ������FRVW �FX��������PDL�PXOW�GHFkW�vQ������SHQWUX�D�DFKL]L LRQD�DFHHDúL�FDQWLWDWH�GH�PDUI �

E��ÌQ������FRVWD�FX��������PDL�SX LQ�GHFkW�vQ������SHQWUX�D�DFKL]L LRQD�DFHHDúL�FDQWLWDWH�GH�PDUI �FD�vQ������

F��$FHHDúL�FDQWLWDWH�GH�EXQXUL��FXPS UDWH�vQ������OD�SUH XULOH�GLQ�������FRVW �FX��������PDL�VFXPS�GHFkW�HYDOXDWH�OD�SUH XULOH�GLQ������

G��'DF �FDQWLW LOH�FXPS UDWH�vQ������V-DU�IL�DFKL]L LRQDW�OD�SUH XULOH�GLQ�������DU�IL�FRVWDW�FX�20,41% mai scump;

e) sunt date insuficiente pentru a alege a,b,c, sau d. ����'DF �vQWU-R� DU ��VDODULXO�PHGLX�D�IRVW�vQ�DQXO�W0�GH���PLOLRQ�OHL�úL�,3&� �������,33� �������LDU�în anul t1��VDODULXO�PHGLX�D�DMXQV�OD�QLYHOXO�GH�����PLOLRDQH�OHL�úL�,3&� �������,33� �������ÌQ�DFHVWH�FRQGL LL��salariul real:

a) a crescut; E��D�VF ]XW� F��D�U PDV�QHVFKLPEDW� G��QX�VH�SRDWH�SUHFL]D�HYROX LD�VD� e) este egal cu cel nominal din anul t1.

����3 WUDWXO�DEDWHULL�WLS�P VRDU ��

a) amplitudinea dispersiei unui set de date în jurul mediei lor; b) omogenitatea unui set de date; F��DVLPHWULD�XQHL�GLVWULEX LL� G��WHQGLQ D�FHQWUDO �D�XQXL�VHW�GH�GDWH� H��JUDGXO�GH�FRQFHQWUDUH�D�IUHFYHQ HORU�

����2�UDW �GHVFUHVF WRDUH�D�LQIOD LHL�SRDWH�V �GXF �OD�

D��FUHúWHUHD�úRPDMXOXL� E��GHVFUHúWHUHD�úomajului; c) stagnarHD�úRPDMXOXL� G��úRPDMXO�HVWH�XQ�IHQRPHQ�LQGHSHQGHQW�GH�LQIOD LH�

Page 128: STATISTICA - TESTE GRILA

d) VXQW� LQVXILFLHQWH� LQIRUPD LL� SHQWUX� D� SXWHD� SUHFL]D� LQIOXHQ D� � IHQRPHQHORU� GH� FUHúWHUH�JHQHUDOL]DW �D�SUH XULORU�DVXSUD�úRPDMXOXL�

����3XWHUHD�GH�FXPS UDUH�D�PRQHGHL�QD LRQDOH�HVWH�LQYHUV�SURSRU LRQDO �FX�

D��QLYHOXO�SUH XULORU� b) nivelul veniturilor; c) nivelul PIB/locuitor; G��YROXPXO�EXQXULORU�úL�VHUYLFLLORU�RIHULWH�SH�SLD � H��HVWH�R�P ULPH�LQGHSHQGHQW �

����/D�R�EDQF �VH�DQDOL]HD] �GLVWULEX LD�GHELWRULORU�GXS �VLWXD LD�]LOHORU�GH�vQWkU]LHUH�D�UDPEXUV ULL�creditelor, astfel:

,QWHUYDOH�GH�YDULD LH�D�QXP UXOXL�GH�]LOH�GH�vQWkU]LHUH�D�SO LL�

Nr. debitori “mai mult decât OLPLWD�LQIHULRDU ´

10-20 120 20-30 85 30-40 37 40-50 16 50-60 7 60-70 2

9DORDUHD�PHGLDQ �FDOFXODW �XWLOL]kQG�IUHFYHQ H�UHODWLYH�HVWH

a) 25 zile; b) 35 zile; c) 27 zile; d) 23 zile; H��QX�VH�SRDWH�FDOFXOD�PHGLDQD�XWLOL]kQG�IUHFYHQ H�UHODWLYH�

35) Dintr-XQ�VRQGDM�DX�UH]XOWDW�GDWHOH�UHIHULWRDUH�OD�JUDGXO�GH�vQDYX LUH��DVWIHO�

1LYHO�GH�vQDYX LUH Procente ale populD LHL 6WUXFWXUD�DYX LHL $��1LYHO�IRDUWH�VF ]XW 50 10 %��1LYHO�VF ]XW 25 20 C. Nivel minim acceptabil de avere 10 10 '��1LYHO�PHGLX�GH�vQDYX LUH 10 15 (��1LYHO�ULGLFDW�GH�vQDYX LUH 3 25 F. Nivel extrem de ridicat ... ...

'HFLGH L�GDF �

D��DYX LD�HVWH�HJDO�GLVWULEXLW � b) curba lui Lorentz coincide cu linia de egalitate; c) DYX LD� HVWH� GLVWULEXLW � LQHFKLWDELO�� DYDQWDMD L� ILLQG� FHL� FX� QLYHO� vQDOW� úL� IRDUWH� vQDOW� GH�

vQDYX LUH� G��DYX LD�HVWH�GLVWULEXLW � LQHFKLWDELO��DYDQWDMD L� ILLQG�FHL�FX�QLYHO�VF ]XW�úL� IRDUWH�VF ]XW�GH�

vQDYX LUH� e) nu se poate discuta echitatea distribuirii veniturilor.

����ÌQ�IRUPXOD�HURULL�PD[LPH��YROXPXO�HúDQWLRQXOXL�VH�QRWHD] �FX�n�GDF �VRQGDMXO�UHDOL]DW�HVWH�

a) de serii; E��UHDOL]DW�SH�XQ�HúDQWLRQ�IRUPDW�GLQ�XQLW L�FRPSOH[H; F��UHDOL]DW�SH�XQ�HúDQWLRQ�IRUPDW�GLQ�XQLW L�VLPSOH�

Page 129: STATISTICA - TESTE GRILA

G��UHDOL]DW�SH�XQ�HúDQWLRQ�IRUPDW�GLQ�XQLW L�VLPSOH�VDX�FRPSOH[H��LQGLIHUHQW� e) cu n�VH�QRWHD] �GH�RELFHL�YROXPXO�SRSXOD LHL�JHQHUDOH�

����ÌQWUH�GHFLOD�D�WUHLD�úL�D�úDSWHD�VH�DIO �

a) 40% din termenii seriei; b) 60% din termenii seriei; c) 50% din termeni seriei; d) 30% din termenii seriei; e) 70% din termenii seriei.

38) Formula lui Sturges se poate aplica pentru determinarea:

D��DPSOLWXGLQLL�YDULD LHL�XQHL�FDUDFWHULVWLFL� b) valorii maxime dintr-un set de date; c) valorii minime dintr-un set de date; G��QXP UXOXL�GH�JUXSH�� H��QXP UXOXL�GH�FDUDFWHULVWLFL�

����'LVSHUVLD�HVWH�LQYHUV�SURSRU LRQDO �FX��

D��YROXPXO�HúDQWLRQXOXL� b) volumul caracteristicilor studiate; c) abaterea standard; d) coeficientul de asimetrie; H��HVWH�R�P ULPH�LQGHSHQGHQW �

���� 5DSRUWXO� GLQWUH� LQGLFHOH� DJUHJDW� DO� SUH XULORU� FDOFXODW� GXS � SURFHGHXO� /DVSH\UHV�� vQWU-o HFRQRPLH� LQIOD LRQLVW �� úL� LQGLFHOH� DJUHJDW� DO� SUH XULORU� FDOFXODW� GXS � SURFHGHXO� 3DDVFKH� HVWH�� GH�obicei:

a) supraunitar; b) subunitar; c) unitar; d) negativ; e) QX�VH�úWLH�H[DFW�

Page 130: STATISTICA - TESTE GRILA

TESTUL 15

���&RHILFLHQWXO�GH�YDULD LH�DUDW �

D��GH�FkWH�RUL�HVWH�PDL�PDUH�DEDWHUHD�VWDQGDUG��WLS���ID �GH�PHGLD�DULWPHWLF � E��FX�FkWH�SURFHQWH�HVWH�GHS úLW ��OLPLWD�GH�RPRJHQLWDWH�DGPLV � F��FX�FkW�HVWH�PDL�PDUH�DEDWHUHD�VWDQGDUG�ID �GH�PHGLD�DULWPHWLF � d) de câte ori se cuprinde abaterea standard în medie; H��FkWH�SURFHQWH�GLQ�DEDWHUHD�VWDQGDUG�UHSUH]LQW �PHGLD�DULWPHWLF �

����'DF �XQ�IHQRPHQ�HYROXHD] �GXS �IXQF LD���������W��VXPD�S WUDWHORU�DEDWHULORU�GLQWUH�R�SDUWH�GLQ�YDORULOH�vQUHJLVWUDWH���������������������������úL�FHOH�DMXVWDWH�FRQVLGHUkQG�YDORULOH�FRUHVSXQ] WRDUH�GLQ�vectorul timpului : 2,4,5,6,7:

a) 0,5; b) 130; c) 133; d) 100; H��DOW �YDULDQW ���������«

3) Cunoscând dRDU�KLVWRJUDPD�XQHL�GLVWULEX LL�GH�IUHFYHQ H�QX�SXWHP�UHSUH]HQWD�JUDILF�

a) structura; E��RJLYD�IUHFYHQ HORU�FXPXODWH� c) corelograma; G��SROLJRQXO�IUHFYHQ HORU� H��GLVWULEX LD�IUHFYHQ HORU�UHODWLYH�

���'XS �ULWP��LQIOD LD�QX�SRDWH�IL��

a) târâtoare; b) GHVFKLV � F��JDORSDQW � d) deflatoare; H��IRUPHOH�LQIOD LHL�QX�VH�FODVLILF �GXS �ULWPXO�GH�PRGLILFDUH�

5) Pentru o serie de momente nu se pot calcula:

D��VSRUXUL�FX�ED] �vQ�ODQ � E��VSRUXUL�FX�ED] �IL[ � c) indici; d) ritmuri; H��PHGLD�DULWPHWLF �D�WHUPHnilor seriei.

���&RPSOHWD L�VSD LXO�OLEHU�FX�XQD�GLQ�YDULDQWHOH�D�- e: �9DULDELOD� GLVFUHW � ;� XUPHD] � OHJHD� GH� UHSDUWL LH� «««� D� SDUDPHWULORU� n� úL� p , atunci când IUHFYHQ D�VD�HVWH�FRQIRUP�

( )f C p p n n pnx x n x

= ⋅ ⋅ − > ∈ < <−

1 1 0 1, , ,Ν ¨ D��QRUPDO � E��ELQRPLDO �

Page 131: STATISTICA - TESTE GRILA

c) Student; d) Gauss Laplace; H��QX�H[LVW �DFHDVW �IXQF LH�GH�UHSDUWL LH�

���6WDELOL L�FH�UHOD LH�HVH�DGHY UDW �

a) PIB = VA + TVA + taxe vamale - servicii bancare imputate nerepartizate; b) PIB = VA + TVA + taxe vamale; c) PIB = VA + TVA; d) PIB = VA; e) PIB = VA + TVA + taxe vamale + servicii bancare imputate nerepartizate.

���7HUPHQXO�VWDWLVWLF�GH��UDW ��HVWH�VLQRQLP�FX�FHO�GH��LQGLFH��

a) întotdeauna; E��QLFLRGDW � F��GRDU�GDF �UDWD�H[SULP �R�HYROX LH� G��GRDU�GDF �H[SULP �SRQGHUHD�XQHL�S U L�vQ�vQWUHJ� e) doar vQ�FD]XO�H[FHS LLORU�

���/D�UHFHQV PkQW�VH�FXOHJ�LQIRUPD LL�GH�QDWXU �

D��GHPRJUDILF ��HFRQRPLF ��VRFLDO � E��FXOWXUDO � F��GRDU�HFRQRPLF � G��GRDU�VRFLDO � H��GRDU�GHPRJUDILF �

����6LQRQLPXO�SHQWUX�DEDWHUHD�WLS�QX�VH�PDL�QXPHúWH�

a) abatere standard; E��DEDWHUH�PHGLH�S WUDWLF � c) ecart tip; G��YDULDQ � H��YDULDQW �

����&RPSRQHQWD�VH]RQLHU �D�XQHL�VHULL�GH�WLPS�DSDUH�FD�UH]XOWDW�DO�DF LXQLL�

D�� IOXFWXD LLORU� OHJDWH� GH� DQRWLPS� VDX� FH� VH� UHSURGXF� VLPLODU� vQ� WLPS�� vQ� FXUVXO� XQHL� ]LOH��V SW PkQL��OXQL��trimestre;

E��IOXFWXD LLORU�FLFOLFH� c) factorilor aleatori; G��WHQGLQ HL� e) componenta sezonieU �QX�H[LVW �

����&RPSRQHQWD�FLFOLF �DSDUH�FD�XUPDUH��D�DF LXQLL�

a) factorilor sezonieri; E��IDFWRULORU�FH�GHWHUPLQ �ID]HOH�GH�FRQWUDF LH�úL�UHOD[DUH�D�IHQRPHnelor; c) factorilor aleatori; G��WHQGLQ HL� H��QX�H[LVW �DFHDVW �FRPSRQHQW �

����&XQRVFkQG�RJLYD�IUHFYHQ HORU�FXPXODWH��QX�VH�SRDWH�UHSUH]HQWD�JUDILF��vQ�FRQWLQXDUH�

a) structura; b) histograma;

Page 132: STATISTICA - TESTE GRILA

c) poligonul frecYHQ HORU�DEVROXWH� G��SROLJRQXO�IUHFYHQ HOor relative; H��JUDILFXO�GH�HYROX LH�

����'DF � � UDSRUWXO� GLQWUH� LQGLFHOH� DJUHJDW� DO� SUH XULORU� úL� LQGLFHOH� DJUHJDW� DO�YROXPXOXL� IL]LF� HVWH�supraunitar, atunci, indicele valorii poate fi:

a) supraunitar; b) subunitar; c) unitar; d) a,b,c; e) negativ.

15)� 3HQWUX�P VXUDUHD� HYROX LHL� SUH XULORU�� OD� QLYHOXO� DJHQWXOXL� HFRQRPLF�� VH� UHFRPDQG �XWLOL]DUHD�sistemului de ponderare:

a) Laspeyres; b) Paasche; c) Fisher; d) Edgeworth; e) nici unul din cele precizate mai sus.

���� 3HQWUX� P VXUDUHD� HYROX LHL� SUH XULORU�� OD� QLYHO� PDFURHFRQRPLF�� vQ� 5RPkQLD� VH� XWLOL]HD] �sistemul de ponderare:

a) Laspeyres; b) Paasche; c) Fisher; d) Edgeworth; e) nici unul din cele precizate mai sus.

17) În anul t1�ULWPXO�FLIUHL�GH�DIDFHUL�D�XQHL�ILUPH�D�IRVW�GH�������ID �GH�W0. În anul XUP WRU��W2, cifra GH�DIDFHUL�D�FUHVFXW�FX�������ùWLLQG�F �VSRUXO�DEVROXW�DO�FLIUHL�GH�DIDFHUL�vQ�SHULRDGD�W2 - t0 a fost de 100 u.m., cifra de afaceri din anul t1 a fost de:

a) 60 u.m.; b) 120 u.m.; c) 20 u.m.; d) 27,27 u.m.; e) nu se poate calcula datorLW �LQIRUPD LHL�LQVXILFLHQWH�

18) 'DF �SH�R�SHULRDG �GH�FLQFL�DQL�� LQGLFHOH�PHGLX�GH�FUHúWHUH�D�SURGXF LHL�XQXL�DJHQW�HFRQRPLF�D�IRVW�GH������vQ�FRQGL LLOH�vQ�FDUH�SURGXF LD�HVWH�R�YDULDELO �vQVXPDELO ��úWLLQG�F �vQ�XOWLPXO�DQ�QLYHOXO�SURGXF LHL�D�IRVW�FX����GH�XQLW L�PDL�PDUH�GHFkW�vQ�SULPXO�DQ��YDORDUHD�LQL LDO �D�SURGXF LHL�D�IRVW�GH�

a) 44,21; b) 4,21; c) 2,24; d) 3; e) nu se poate calcula.

���� 'DF � FKHOWXLHOLOH� SHQWUX� FRQVXP� VXQW� ����� X�P�� úL� LQYHVWL LLOH� UHSUH]LQW � ����� GLQ� YHQLWXO�QD LRQDO�� LPSRUWXO� � UHSUH]LQW � � GLQ� YHQLW� úL� H[SRUWXO� � GLQ� LQYHVWL LL�� DWXQFL� VROGXO� EDODQ HL�comerciale este:

Page 133: STATISTICA - TESTE GRILA

a) 875 u.m.; b) -875 u.m.; c) 1250 u.m.; d) 375 u.m.; e) 500 u.m..

����$JUHJDWHOH�PDFURHFRQRPLFH�VH�FDOFXOHD] �

D��vQ�XQLW L�IL]LFH� E��vQ�XQLW L�YDORULFH; F��H[FOXVLY�vQ�SUH XULOH�IDFWRULORU� G��H[FOXVLY�vQ�SUH XULOH�SLH HL� H��vQ�SUH XULOH�IDFWRULORU�úL�vQ�SUH XULOH�SLH HL�

����$FWLYLWDWHD�GH�UHGLVWULEXLUH�D�YHQLWXULORU�DUH�ORF�GDF �

D��VH�SO WHVF�DMXWRDUHOH�VRFLDOH� E��VH�SO WHVF�VDODULLOH�DQJDMD LORU�statului; F��VH�SO WHVF�SHQVLLOH� G��VH�DFKLW �LPSR]LWHOH� e) a, c.

����6ROGXO�EDODQ HL�FRPHUFLDOH�VH�FDOFXOHD] �

D��FD�UDSRUW�LQWUH�YDORDUHD�H[SRUWXOXL�úL�YDORDUHD�LPSRUWXOXL� E��FD�GLIHUHQ �vQWUH�FDQWLWDWHD�H[SRUWDW �úL�FHD�LPSRUWDW � F��FD�GLIHUHQ �vQWUH�YDORDUHD�LPSRUWXOXL�úL�D�H[SRUWXOXL� G��FD�GLIHUHQ �vQWUH�YDORDUHD�H[SRUWXOXL�úL�D�LPSRUWXOXL� H��FD�GLIHUHQ �vQWUH�FDQWLWDWHD�LPSRUWDW �úL�FHD�H[SRUWDW �

����'DF �GLQDPLFD�FDQWLW LL�RIHULWH�SH�R�SLD �HVWH�GH������úL�D�SUH XOXL�HVWH�GH�������FRHficientul GH�HODVWLFLWDWH�D�FHUHULL�OD�HYROX LD�SUH XOXL��HVWH�

a) unitar; b) supraunitar; c) subunitar; d) 3; e) 0,33.

����8Q�DJUHJDW�PDFURHFRQRPLF�FH�FDUDFWHUL]HD] �QLYHOXO�GH�GH]YROWDUH�D�HFRQRPLHL�QD LRQDOH�HVWH�

a) IPC; b) IPP; c) PNN/locuitor; d) PIB real; H��YROXPXO�SURGXF LHL�WRWDOH�

25) Sunt egale cu zero:

D��HURDUHD�PD[LP ��GDF �GLVSHUVLD�HVWH�HJDO �FX��� E��UDSRUWXO�GH�QHGHWHUPLQD LH��GDF �YDULD LD�UH]LGXDO �HVWH�HJDO �FX�]HUR� F��PHGLD��GDF �VXPD�YDORULORU�FDUDFWHULVWLFLL�HVWH�HJDO �FX�]HUo;

Page 134: STATISTICA - TESTE GRILA

G��FRHILFLHQWXO�GH�DVLPHWULH��GDF �PHGLDQD�HVWH�HJDO �FX�YDORDUHD�PRGDO � e) coeficientul de reprezentativitate, dac media este un indicator reprezentativ.

���� 6WDELOL L� QXP UXO� FRHILFLHQ LORU� vQWRWGHDXQD� � VXSUDXQLWDUL� VWXGLD L� GH� 6WDWLVWLFD� 6RFLDO� - (FRQRPLF �

D��WR L�FRHILFLHQ LL�VXQW�VXSUDXQLWDUL� b) nici unul nu este întotdeauna supraunitar; F��WR L�FRHILFLHQ LL�VXQW�VXEXQLWDUL� G��PDMRULWDWHD�FHORU�VWXGLD L� e) indicii.

����&RHILFLHQWXO�GH�DVLPHWULH�SURSXV�GH�3HDUVRQ�VH�DIO �vQ�UHOD LH�GH�LQYHUV �SURSRU LRQDOLWDWH�FX��

a) abaterea standard; E��DEDWHUHD�VWDQGDUG�úL�YDORDUHD�PRGDO � F��GLVSHUVLD�úL�YDORDUHD�PRGDO � G��PHGLD�DULWPHWLF � H��YDORDUHD�PRGDO �

����&RHILFLHQWXO�GH�FRUHOD LH�OLQLDU �VH�DIO �vQ�UHOD LH�GH�GLUHFW �SURSRU LRQDOLWDWH�FX��

a��FRYDULDQ D� E��DEDWHUHD��VWDQGDUG�FDOFXODW �SHQWUX�YDULDELOD�IDFWRULDO � F��DEDWHUHD�VWDQGDUG�FDOFXODW �SHQWUX�YDULDELOD�UH]XOWDWLY � d) volumul datelor studiate; e) este un indicator independent.

���� 'DF � XQ� IHQRPHQ� HFRQRPLF� vQUHJLVWUHD] � VF GHUL� FX� R� UDW � FUHVF WRDUH�� DWXQFL� XOWLPXO� QLYHO�observat va fi, comparativ cu primul:

a) mai mare; b) mai mic; c) egal; d) nu se poate compara; H��LQIRUPD LD�SUH]HQWDW �HVWH�LQVXILFLHQW �

����³([WHULRUXO´�UHSUH]LQW �vQ�&RQWDELOLWDWHD�1D LRQDO �

D��DJHQ LL�HFRQRPLFL�QD LRQDOL�LPSOLFD L�vQ�WUDQ]DF LL�FX�VWU LQ WDWHD� E��DJHQ L�HFRQRPLFL�GLQ�FHOHODOWH�HFRQRPLL�QD LRQDOH� F��DJHQ LL�HFRQRPLFL�FH�GHVI úRDU �DFWLYLW L�GH�FRPHU �H[WHULRU� d) a,b,c; e) b,c.

����,QWHUYDOXO�GH�vQFUHGHUH�SHQWUX�PHGLD�DULWPHWLF �HVWH�FX�DWât mai mic cu cât:

D��YROXPXO�HúDQWLRQXOXL�HVWH�PDL�PLF� E��SUREDELOLWDWHD�FX�FDUH�VH�JDUDQWHD] �UH]XOWDWHOH�HVWH�PDL�PLF � F��UD LD�GH�VRQGDM�HVWH�PDL�PDUH� G��YROXPXO�HúDQWLRQXOXL�VFDGH� H��SUREDELOLWDWHD�GH�JDUDQWDUH�D�UH]XOWDWHORU�HVWH�FRQVWDQW �

Page 135: STATISTICA - TESTE GRILA

32)�,QIOD LD�HVWH�FDX]DW �GH�GHILFLWXO�EXJHWDU�GDF �

D��FUHúWHUHD�FKHOWXLHOLORU�VWDWXOXL�GHS úHúWH�FUHúWHUHD�YHQLWXULORU� E��FKHOWXLHOLOH�VWDWXOXL�GHS úHVF�YHQLWXULOH� F��FUHúWH�GDWRULD�LQWHUQ �D�VWDWXOXL� G��VH�HPLWH�PRQHG �I U �DFRSHULUH�vQ�EXQXUL�úL�VHUYLcii; H��VH�HFKLOLEUHD] �EDODQ D�GH�SO L�

����2SHUD LXQLOH�HFRQRPLFH�GH�FRQVXP�VXQW�UHDOL]DWH�GH�F WUH�

D��GRDU�GH�F WUH��DJHQ LL�HFRQRPLFL�FH�HIHFWXHD] �RSHUD LXQL�DVXSUD�EXQXULORU�úL�VHUYLFLLORU� E��WR L�DJHQ LL�HFRQRPLFL� F��WR L�DJHQ LL�HFRQRPLFL��H[FOXVLY�PHQDMHOH�úL�DGPLQLVWUD LLOH�SXEOLFH� G��DGPLQLVWUD LLOH�SULYDWH� H��VRFLHW LOH�ILQDQFLDUH�QHILQDQFLDUH�

����ÌQ�&RQWDELOLWDWHD�1D LRQDO �RSHUD LXQLOH�GH�UHGLVWULEXLUH�D�YHQLWXULORU�VXQW�HIHFWXDWH�GH�F WUH��

D��DGPLQLVWUD LLOH�SXEOLFH� b) administrD LLOH�SULYDWH� F��VRFLHW LOH�GH�DVLJXUDUH� G��VRFLHW LOH�EDQFDUH� H��VRFLHW LOH�FRPHUFLDOH�QHILQDQFLDUH�

����/XQJLPHD�RSWLP �D�XQHL�YDORUL�HVWLPDWH�SH�ED]D�GDWHORU�GLQ�HúDQWLRQ�HVWH�

D��GLIHULW �GH�FHD�FDOFXODW �SHQWUX�SROXOD LD�WRWDO � E��DSURSLDW �GH�FHD�FDOFXODW �SHQWUX�SROXOD LD�WRWDO � F��HJDO �FX�FHD�FDOFXODW �SHQWUX�SROXOD LD�WRWDO � G��QX�VH�SRDWH�GHWHUPLQD�R�YDORDUH�RSWLP � e) variantele a - d sunt false, corect este......…

����0HWRGD�LQGLFLORU�QX�SRDWH�IL�XWLOL]DW �SHQWUX�DQDOL]D�

a) compaUD LLORU�vQ�SURILO�WHULWRULDO� E��GHVFRPSXQHULL�XQXL�IHQRPHQ�FRPSOH[�SH�IDFWRUL�GH�LQIOXHQ � F��GHWHUPLQ ULL�JUDGXOXL�GH�LQIOXHQ �D�XQXL�IDFWRU�DVXSUD�DOWXL�IDFWRU� G��HYROX LHL�XQXL�IHQRPHQ� e) analiza estimatorilor unui fenomen complex.

37) 9DULD LD�WRWDO �D�XQHL�FDUDFWHULVWLFL�VWXGLDWH�SHQWUX�XQ�HúDQWLRQ�HVWH�LQYHUV�LQIOXHQ DW �GH�

D��YROXPXO�HúDQWLRQXOXL�� E��YDULD LD�UH]LGXDO � F��YDULD LD�VLVWHPDWLF � G��YDULD LD�H[SOLFDW � H��FRHILFLHQWXO�GH�YDULD LH�

38) 'DF �VH�JUXSHD] �XQ�VHW�GH�GDWH�SH�LQWHUYDOH�HJDOH�GH�YDULD LH��SHQWUX�D�RE LQH��R�GLVWULEX LH�D�

IUHFYHQ HORU� PDL� DSURSLDW � GH� IRUPD� GLVWULEX LHL� QRUPDOH�� QXP UXO� GH� JUXSH� úL� GLPHQVLXQHD�ILHF UXL�LQWHUYDO�

Page 136: STATISTICA - TESTE GRILA

D��YRU��FUHúWH� b) vor scade; F��U PkQ�FRQVWDQWH� G��HYROXHD] �vQ�VHQV�FRQWUDU� e) nu se poate preFL]D�HYROX LD�ORU�

39) Cuartila întâi este:

D��PHGLD�DULWPHWLF �GLQWUH�FXDUWLOD�D�GRXD�úL�D�WUHLD� E��GLIHUHQ D�GLQWUH�FXDUWLOD�D�GRXD�úL�D�WUHLD� F��UDSRUWXO�GLQWUH�FXDUWLOD�D�GRXD�úL�D�WUHLD� G��R�YDORDUH�VLWXDW �OD�����GLQ�WHUPHQLL�VHULHL� H��HJDO �FX�YDORDUHD�PLQLP �D�FDUDFWHULVWLFLL�

����ÌQWUH�GHFLOD�D�]HFHD�úL�[min�VH�DIO �

a) 90% din termenii seriei analizate; b) 10% din termenii seriei; c) 100% din termenii seriei; G��MXP WDWH�GLQ�WHUPHQLL�VHULHL� H��GHFLOD�D�]HFHD�QX�H[LVW �

Page 137: STATISTICA - TESTE GRILA

TESTUL 16 1) DesprH�SURGXF LD�PDUI �D�ILOLDOHORU�XQHL�VRFLHW L�FRPHUFLDOH�VH�FXQRVF�XUP WRDUHOH�GDWH�

Filiala Structura valorii

SURGXF LHL�PDUI �vQ�perioada T0 (%)

0RGLILFDUHD�DEVROXW �D�YDORULL�SURGXF LHL�PDUI �FD�XUPDUH�D�PRGLILF ULL�SUH XULORU�

în T1�ID �GH�70 (mld.lei)

0RGLILFDUHD�UHODWLY �D�SUH XULORU�vQ�71�ID �GH�

T0 (%) A B C

25 35 …

10 18 6

+20 +25 + 8

6H�FXQRDúWH�GHDVHPHQHD�F �YDORDUHD�SURGXF LHL�PDUI �OD�ILOLDOD�&�vQ�70 a fost 80 mld. lei. Pentru a FDUDFWHUL]D� vQ� GLQDPLF � SURGXF LD� PDUI � D� VRFLHW LL� FRPHUFLDOe s-a determinat indicele valorii, YROXPXOXL� IL]LF� úL� DO� SUH XULORU� SUHFXP� úL� FRHILFLHQWXO� GH� FRUHOD LH� �U�� GLQWUH� LQGLFLL� LQGLYLGXDOL� DL�YROXPXOXL�IL]LF�úL�DL�SUH XULORU��9DORULOH�DFHVWRUD��vQ�RUGLQHD�SUHFL]DW �PDL�VXV�VXQW�

a) ������������������������úL�U �);

b) ������������������������úL�U!���

c) ������������������������úL�U!���

d) ������������������������úL�U����

e) ������������������������úL�U����

2) 8Q� VRQGDM�$� GH� YROXP�Q� vQ� ED]D� F UXLD� VH� HVWLPHD] �PHGLD�P�D� SRSXOD LHL� VWDWLVWLFH� SHQWUX�

YDULDELOD�;�SULQ� HVWLPD LD� ax � HVWH�PDL� HILFLHQW� GHFkW� VRQGDMXO�%� GH� DFHODúL� YROXP�Q� vQ� ED]D�

F UXLD�VH�HVWLPHD] �DFHHDúL�PHGLH�P�SULQ�HVWLPD LD� bx ��GDF �H[LVW �UHOD LD�

a) )()()()( baba xDxDsimxMxM <== ;

b) )()()()( baba xDxDsauxMxM <= ;

c) )()()()( baba xDxDsimxMxM >= ;

d) )()()()( baba xDxDsixMxM << ;

e) )()()()( baba xDxDsauxMxM << .

1RW ��0�[��úL�'�[��UHSUH]LQW �PHGLD�úL�GLVSHUVLD�OXL�;�

3) Dintre conturile macroeconomice, din SCN, nu are sold:

a) FRQWXO�GH�UHSDUWL LH�D�YHQLWXULORU� b) contul de creare a veniturilor; c) FRQWXO�SURGXF LH� d) contul sintetic de bunuri; e) contul de modificare a patrimoniului;

4) 3H�ED]D�YDORULORU�LQGLYLGXDOH�DOH�DFHOHLDúL�YDULDELOH�QXPHULFH�;��vQUHJLVWUDWH�OD�FHOH�Q�XQLW L�DOH�

SRSXOD LHL�VWDWLVWLFH�3�V-D�FDOFXODW�PHGLD�DULWPHWLF �� x ���YDORDUHD�PHGLDQ ��0H��úL�XQLFD�YDORDUH�PRGDO � �0R��� ÌQWUH� FHOH� WUHL� YDORUL� VLQWHWLFH� V-D� VWDELOLW� F � H[LVW � XUP WRDUHD� LQHJDOLWDWH��

Page 138: STATISTICA - TESTE GRILA

MoMex << ��$FHDVW �LQHJDOLWDWH�

a) VXJHUHD] �F �FHOH�PDL�PXOWH�XQLW L�GLQ�3�vQUHJLVWUHD] �YDORUL�LQGLYLGXDOH�GHSODVDWH�F WUH�valorile mari;

b) VXJHUHD] �F �FHOH�PDL�PXOWH�YDORUL�LQGLYLGXDOH�GLQ�FHOH�vQUHJLVWUDWH�VXQW�GHSODVDWH�F WUH�valorile mici;

c) HYLGHQ LHD] �FRQFHQWUDUHD�YDORULORU�LQGLYLGXDOH�F WUH�0R�

d) HYLGHQ LHD] �VLPHWULD�UHSDUWL LHL�VWDWLVWLFH�

e) QX�DUH�QLFL�R�VHPQLILFD LH�HFRQRPLF �

5) Soldul contului macroeconomic „Crearea veniturilor” este:

a) 9DORDUHD�DG XJDW �EUXW �

b) 3URGXVXO�LQWHUQ�EUXW�OD�SUH XULOH�IDFWRULORU�

c) 3URGXVXO�LQWHUQ�EUXW�OD�SUH XULOH�SLH HL�

d) 3URGXVXO�LQWHUQ�QHW�OD�SUH XULOH�IDFWRULORU�

e) 3URGXVXO�QD LRQDO�QHW�OD�SUH XULOH�IDFtorilor.

6) 6H�FRQVLGHU �R�SRSXOD LH�VWDWLVWLF �3�GH�YROXP�1 Q.k: unde, n-�YROXPXO�HúDQWLRQXOXL�úL�N- un QXP U�QDWXUDO�QHQXO�GLIHULW�GH����/D�XQLW LOH�GH�REVHUYDUH�D�HúDQWLRQXOXL�GH�YROXP�Q�– normal –

s-D� XUP ULW� YDULDELOD� QXPHULF � ;� DOH� F UHL� YDORUL� LQGLYLduale au fost ixi = (cu I=1,2,…,N). 'LVSHUVLD�PHGLHL�GH�VHOHF LH��vQ�FD]XO�vQ�FDUH�HúDQWLRQXO�D�IRVW�IRUPDW�DOHDWRU�úL�I U �UHYHQLUH��este:

a). ;

2

1+N

b). 12

)1( +NN

; c). 2)1(

Nk −

; d). 12

)1)(1( +− Nk

; e). 12

1−k

;

7) 3HQWUX�YHULILFDUHD�OHJ WXULL�DXWRUHJUHVLYH��GH�RUGLQXO�vQWkL��GLQWUH�WHUPHQLL�XQHL�VHULL�FURQRORJLFH�VH�XWLOL]HD] �FHO�PDL�IUHFYHQW�

a) WHVWXO�GH�YHULILFDUH�D�QRUPDOLW LL�UH]LGXXULORU�

b) testul Durbin-Watson definit prin ∑

=

=−−

= n

tt

n

ttt

e

eed

1

2

2

21)(

, unde ttt yye ˆ−= este eroarea de PRGHO��UH]LGXDO ��DIHUHQW �YDORULL�W�D�YDULDELOHL�WLPS�

c) testul Durbin-Watson definit prin ∑

=

=−−

= n

tt

n

ttt

e

eed

1

2

3

21)(

;

Page 139: STATISTICA - TESTE GRILA

d) testul Durbin-Watson definit prin ∑

=

=−−

= n

tt

n

ttt

e

eed

1

2

21)(

;

e) testul Student.

8) $QDOL]kQG� OHJ WXUD� GLQWUH� 6&1� úL� WDEHOXO� LQSXW-RXWSXW� �7,2�� FRQVWDW P� F � SULQ� vQVXPDUHD�FRPSRQHQWHORU�FDGUDQXOXL���DO�7,2�VH�RE LQH�

a) 3,%�OD�SUH XULOH�SLH HL�SULQ�PHWRGD�XWLOL] ULL�ILQDOH�

b) 3,%�OD�SUH XULOH�SLH HL�SULQ�PHWRGD�GH�SURGXF LH�

c) P1%�OD�SUH XULOH�SLH HL�SULQ�PHWRGD�XWLOL] ULL�ILQDOH�

d) 3,%�OD�SUH XULOH�SLH HL�SULQ�PHWRGD�YHQLWXULORU�

e) 311�OD�SUH XULOH�IDFWRULORU�

9) 3HQWUX�DFHHDúL�VHULH�FURQRORJLF �WUHQGXO�V-a determinat prin mai multe metode. Pentru fiecare PHWRG �V-a calculat eroarea mHGLH�S WUDWLF �D�DMXVW ULL��6-DX�RE LQXW�XUP WRDUHOH�UH]XOWDWH�

0HWRGD�GH�DMXVWDUH�XWLOL]DW (URDUHD�PHGLH�S WUDWLF �D�DMXVW ULL��X�P��

• 0HWRGD�LQGLFHOXL�PHGLX�GH�GLQDPLF ��0,0� 29.51

• Metoda sporului mediu (MSM) 27.88

• Metoda mediilor mobile (MMM) cu periodicitatea p=5 ani

17.14

• MMM cu p=2 ani 5.97

3UHFL]D L�FDUH�GLQ�DILUPD LLOH�XUP WRDUH�HVWH�IDOV �

a) FHD�PDL��PLF �SUHFL]LH�vQ�DMXVWDUH�HVWH�RIHULW �GH�0,0�

b) FHYD�PDL�SUHFLV ��GDU�QX�VHPQLILFDWLY�PDL�EXQ ��HVWH�DMXVWDUHD�SULQ�06��

c) WHQGLQ D�GHWHUPLQDW �SULQ�000�FX�S ��HVWH�PDL�DSURSLDW �GH�HYROX LD�UHDO �GHFkW�FHD�RE LQXW �SULQ�000�FX�S ���GHRDUHFH�QHWH]LUHD�RVFLOD LLORU�HVWH�PDL�DFFHQWXDW �

d) DMXVWDUHD�SULQ�000�FX�S ��HVWH�PDL�EXQ �GHFkW�FHD�SULQ�000�FX�S ��

e) FHD�PDL�EXQ �DMXVWDUH�FRPSDUDWLY�FX�FHOHODOWH�PHWRGH�XWLOL]DWH�HVWH�FHD�RE LQXW �SULQ�000�FX�p=2.

10) (IHFWXDUHD�FDOFXOHORU�PDFURHFRQRPLFH�vQ�6&1�QX�SRDWH�IDFH�DEVWUDF LH�GH�IOX[XULOH�JHQHUDWH�GH�DFWLYLWDWHD� VHFWRUXOXL� ÄVWDW´�� 5HIHULWRU� OD� DFHVW� VHFWRU� SUHFL]D L� FDUH� GLQ� XUP WRDUHOH� DILUPD LL�HVWH�IDOV �

a) veniturile sale provin din impozite de la menaje private )( StMI , de la firme )( St

FI �úL�SDU LDO�GLQ�SDUWLFLSDUHD�OD�DFWLYLWDWHD�HFRQRPLF �

Page 140: STATISTICA - TESTE GRILA

b) YHQLWXULOH� VDOH� VXQW� IRORVLWH� SHQWUX� UHPXQHUDUHD� DQJDMD LORU� GLQ� VHFWRUXO� SXEOLF� )( TSTV ,

SHQWUX� FXPS UDUHD� GH� EXQXUL� GH� OD� ILUPH� )( STPI �� SHQWUX� WUDQVIHUXUL� F WUH� ILUPH�

�VXEYHQ LL-6��úL�F WUH�PHQDMH�SULYDWH� )( MSTT ;

c) DFWLYLWDWHD� VWDWXOXL� GH� SURGXFHUH� D� EXQXULORU� FROHFWLYH�� GH� UHJXO �� VH� FRQFHQWUHD] � vQ�fluxuri bilaterale;

d) STM

STSTM

STSTF

STM ESTPIVII ++++=+ , unde EST GLIHUHQ D�GLQWUH�YHQLWXUL�úL�FKHOWXLHOL�

e) DFWLYLWDWHD�VWDWXOXL�JHQHUHD] �SUHSRQGHUHQW�IOX[XUL�vQWU-un singur sens.

11) În cazul sondajului simplu, de volum n, analizându-VH� DEDWHUHD�PHGLH� S WUDWLF � D�PHGLHL� GH�VHOHF LH�FD�P VXU WRU�DO�HURULL�PHGLL�GH�UHSUH]HQWDWLYLWDWH��VH�FRQVWDW �

a) FkQG�Q�FUHúWH�SUHFL]LD�HVWLP ULL�SDUDPHWULORU�FUHúWH�DSUR[LPDWLY�GH� n ori;

b) FkQG�Q�FUHúWH�SUHFL]LD�HVWLP ULL�SDUDPHWULORU�FUHúWH�H[DFW�GH� n ori;

c) FkQG�Q�VFDGH�SUHFL]LD�HVWLP ULL�SDUDPHWULORU�FUHúWH�DSUR[LPDWLY�GH� n ori;

d) FkQG�Q�FUHúWH�SUHFL]LD�HVWLP ULL�SDUDPHWULORU�FUHúWH�WRW�GH�Q�RUL�

e) FUHúWHUHD�VDX�UHGXFHUHD�OXL�Q�QX�DIHFWHD] �SUHFL]LD�HVWLP ULL�SDUDPHWULOor.

12) &RQFRUGDQ D�vQWUH�UDQJXULOH�GH�OD���OD�Q�DOH�YDORULORU�YDULDELOHL��IDFWRULDOH�úL�UDQJXULOH�GH�OD���OD�Q� DOH� YDORULORU� YDULDELOHL� HIHFW� VH� SRDWH� H[SULPD� QXPHULF� FX� FRHILFLHQWXO� GH� FRUHOD LH� DO� OXL�Spearman (rs��úL�FX�FHO�DO�OXL�.HQGDOO��Uk). În cazul îQ�FDUH�Q�HVWH�PDUH�vQWUH�FHL�GRL�FRHILFLHQ L�H[LVW �UHOD LD�

a) ks rr

3

2=; b)

sk rr3

2=; c) 132 =− sk rr ; d) 0=+ sk rr ; e) sk rr = .

13) &DOFXOXO�DYX LHL�SURGXFWLYH��VH�UHDOL]HD] �SH�ED]D�XUP WRDUHORU�HOHPHQWH�

a) UHVXUVHOH�QDWXUDOH��VWRFXUL�úL�UH]HUYH�úL�EXQXUL�GH�FDSLWDO�

b) VWRFXUL�úL�UH]HUYH��SUHFXP�úL�XWLODMH��PDúLQL�úL�HFKLSDPHQWH�

c) VWRFXUL��UH]HUYH�úL�PLMORDFH�IL[H�

d) DYX LD�GH�FRQVXP�D�PHQDMHORU�SULYDWH�úL�D�VWDWXOXL��VWRFXUL��UH]HUYH�úL�EXQXri de capital;

e) VWRFXUL�úL�UH]HUYH��XWLODMH��PDúLQL��HFKLSDPHQWH��FRQVWUXF LL�

14) 8Q� DQDOLVW� GH�PDUNHWLQJ� XUP UHúWH� HIHFWXO� FKHOWXLHOLORU� FX� UHFODPD� �[�� DVXSUD� YHQLWXULORU� GLQ�YkQ] UL� �\�� SH� R� SHULRDG � GH� ��� GH� OXQL�� ÌQ� XUPD� SUHOXFU ULL� GDWHORU� SULPDUH� V-au oE LQXW�

XUP WRDUHOH� UH]XOWDWH�� 44.3532 =xσ ; 09.222 =yσ

; cov(x,y)= 70.7; 2.75=x � úL� 84.18=y . În urma analizei statistice s-D�DMXQV�OD�FRQFOX]LD�F �GHSHQGHQ D�GLQWUH�FHOH�GRX �YDULDELOH�SRDWH�IL�modelat �SULQWU-R�IXQF LH�GH�JUDGXO�vQWkL��(FXD LD�PRGHOXOXL�GH�UHJUHVLH�úL�YDORDUHD�FDOFXODW �D�OXL�W��XWLOL]DW �SHQWUX�WHVWDUHD�VHPQLILFD LHL�FRHILFLHQWXOXL�GH�FRUHOD LH��vQ�DFHDVW �RUGLQH��HVWH�

Page 141: STATISTICA - TESTE GRILA

a) xy 2.08.3ˆ += úL�W ����

b) xy 2.08.3ˆ −= úL�W ��

c) xy 8.32.0ˆ += úL�W ���

d) xy 8.32.0ˆ += úL�W ��

e) xy 2.08.3ˆ += úL�W ��

15) Despre patru firme dintr-XQ�FRQFHUQ�VH�FXQRVF�XUP WRDUHOH�GDWH� Firma 6WUXFWXUD�SURGXF LH�

în perioada T0 (%) 3URGXF LD�UHDOL]DW �GH�ILUPH�vQ�T1 în raport cu cea a firmei A

'HS úLUHD��QHUHDOL]DUHD��SURJUDPXOXL�GH�SURGXF LH�vQ�71 (%)

A 15 1.0 +20 B 25 1.8 -10 C 20 1.4 0 D 40 2.5 +30

6H� PDL� FXQRDúWH�� GH� DVHPHQHD�� F � SURGXF LD� UHDOL]DW � GH� ILUPD� $� vQ� 71 a fost de 75 mld. lei, GHYDQVkQG�SURGXF LD�UHDOL]DW �GLn T0�FX������ÌQ�XUPD�SUHOXFU ULL�GDWHORU�SHQWUX�vQWUHJXO�FRQFHUQ�V-D�DMXQV�OD�XUP WRDUHD�FRQFOX]LH�

a) SURJUDPXO�GH�SURGXF LH�D�IRVW�GHS úLW�FX��������LDU�SURGXF LD�UHDOL]DW �GLQ�71�D�IRVW�HJDO �FX�FHD�din T0;

b) SURJUDPXO�GH�SURGXF LH�QX�V-a realizat cu 8.83%, LDU�SURGXF LD�UHDOL]DW �vQ�71 a fost mai mare decât cea din T0;

c) LQGLFHOH�UHDOL] ULL�SURJUDPXOXL�GH�SURGXF LH�vQ�71�D�IRVW�GH����������LDU�SURGXF LD�SURJUDPDW �pentru T1�D�FUHVFXW�ID �GH�70 cu 120%;

d) LQGLFHOH�UHDOL] ULL�SURJUDPXOXL�GH�SURGXF LH�D�IRVW�GH��������LDU�SURGXF LD�UHDOL]DW �vQ�71 a fost PDL�PDUH�GHFkW�FHD�UHDOL]DW �vQ�70 cu 117.9 mld. lei;

e) SURJUDPXO�GH�SURGXF LH�SHQWUX��71�D�IRVW�GHS úLW�FX�������POG��OHL�LDU�SURGXF LD�UHDOL]DW �vQ�71 a fost mai mare decât cea din T0 cu peste 5%.