TN 12th Question Paper 2022 Statistics

No. of Printed Pages : 12
5969
!5969Statistics! £vÄ Gs
Register Number

PART - III
¦Òΰ¯À / STATISTICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version)

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 70
Time Allowed : 3.00 Hours ] [Maximum Marks : 70

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP £vÁõQ EÒÍuõ GߣuøÚ \›£õºzxU
öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU PsPõo¨£õÍ›h®
EhÚi¯õPz öu›ÂUPÄ®.
(2) }»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ö£ß]À £¯ß£kzuÄ®.

Instructions : (1) Check the question paper for fairness of printing. If there is any lack of
fairness, inform the Hall Supervisor immediately.
(2) Use Blue or Black ink to write and underline and pencil to draw
diagrams.

£Sv & I / PART - I

SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 15x1=15

(ii) öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯ Âøhø¯z
÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx GÊuÄ®.
Note : (i) Answer all the questions.
(ii) Choose the most appropriate answer from the given four alternatives
and write the option code and corresponding answer.

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1. Cßø© P¸x÷PõÒ H0 Gߣøu¨ ö£õ¸zx ©õv› ÂQu\©zvß vmh¨¤øÇ :

PQ PQ pq pq
(A) (B) (C) (D)
n n n n
What is the standard error of the sample proportion under H0 ?

PQ PQ pq pq
(a) (b) (c) (d)
n n n n

2. ö£¸[TÔÀ, 1% ªøPPõs {ø»°À C¸•øÚ ÷\õuøÚ°ß wº©õÛUS®
©v¨¦ :
(A) 2.58 (B) 1.645 (C) 1.96 (D) 2.33
Critical value at 1% level of significance for two tailed large sample test is :
(a) 2.58 (b) 1.645 (c) 1.96 (d) 2.33

3. 4×3 Á›ø\²øh¯ ÷|ºÄ £mi¯¾UPõÚ øPÁºUP ÷\õuøÚ°ß Pmißø©
TÖPÒ :
(A) 12 (B) 18 (C) 7 (D) 6
If the order of the contingency table is 4×3. Then the degree of freedom of the
corresponding Chi-square test statistic is :
(a) 12 (b) 18 (c) 7 (d) 6

4. ©õÖ£õmk¨ £S¨£õ´Ä •øÓ öuõh[P¨£mh PÍ® :
(A) ©¸zxÁ® (B) öuõÈÀ (C) ©µ¤¯À (D) ÂÁ\õ¯®
ANOVA technique originated in the field of :
(a) Medicine (b) Industry (c) Genetics (d) Agriculture

5. J¸ ÁÈ ©õÖ£õmk £S¨£õ´ÂÀ, v¸zuUPõµo C.F.=264.5 ©ØÖ® n=18 GÛÀ
G&ß ©v¨¦ :

(A) 69 (B) 4761 (C) 282.5 (D) 2380.5
In one-way ANOVA, the value of Correction Factor C.F.=264.5 and n=18. Find
the value of G.
(a) 69 (b) 4761 (c) 282.5 (d) 2380.5

3 5969

6. r=0 GÛÀ cov(x, y) =

(A) −1 (B) 0 (C) α (D) +1
If r=0 then cov(x, y) is :

(a) −1 (b) 0 (c) α (d) +1

7. bXY > 1 GÛÀ bYX Gߣx :

(A) > 1 (B) 1 (C) < 1 (D) 0
If bXY > 1 then bYX is :

(a) >1 (b) 1 (c) <1 (d) 0

8. ÁÇUP©õÚ SÔ±kPÎߣi Põ»® ©õØÖ ÷\õuøÚ §ºzv ö\´ÁuØPõÚ
{£¢uøÚ.
(A) P01+P10=1 (B) P01×P10=1 (C) P01/P10=1 (D) P01−P10=1
The condition for the time reversal test to hold good with usual notation is :

(a) P01+P10=1 (b) P01×P10=1 (c) P01/P10=1 (d) P01−P10=1

9. hõº¥ì&ö£Í¼ ©ØÖ® »õ줯›ß Âø»U SÔ±mk GsPÒ •øÓ÷¯ 122.5
©ØÖ® 122.3 GÛÀ £õ]°ß Âø» SÔ±mk Gs ©v¨¦ :
(A) 122.5 (B) 122.4 (C) 122.3 (D) 122.7
If Dorbish-Bowley's price index is 122.5 and Laspeyre's price index is 122.3, then
Paasche's price index is :

(a) 122.5 (b) 122.4 (c) 122.3 (d) 122.7

10. Põ»z öuõhº Á›ø\°À __________ TÖPÒ EÒÍÚ.
(A) |õßS (B) Cµsk (C) I¢x (D) ‰ßÖ
A time series consists of __________ components.

(a) four (b) two (c) five (d) three

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5969 4

11. __________ AÍÂkÁuØS AÀ»x uÛø©¨£kzxÁuØS ¦Òΰ¯À ²zv
GxÄ® CÀø».
(A) •øÓ¯ØÓ ©õÖ£õkPÒ (B) _ÇÀ ©õÖ£õkPÒ
(C) }shPõ» ÷£õUS (D) £¸ÁPõ» ©õÖ£õkPÒ
There is no statistical techniques for measuring or isolating __________.
(a) Erratic fluctuation (b) Cyclical variation
(c) Secular trend (d) Seasonal variation

12. ÷u]¯ ¦Òΰ¯À Bøn¯® Aø©UP¨£mh Bsk :
(A) áúß 12, 2006 (B) áÚÁ› 12, 2006
(C) áüø» 12, 2006 (D) H¨µÀ 12, 2006
National Statistical Commission was formed on :
(a) June 12, 2006 (b) January 12, 2006
(c) July 12, 2006 (d) April 12, 2006

13. ©UPÒ öuõøP°¯¼ß ¤›ÄPÎÀ JßÖ :
(A) {ºÁõP¨ ¦Òΰ¯À (B) ö£õ¸Íõuõµ¨ ¦Òΰ¯À
(C) ÷ÁÍõsø©¨ ¦Òΰ¯À (D) ÁõÌ{ø»¨ ¦Òΰ¯À
One of the branches of Demography is :
(a) Official Statistics (b) Economic Statistics
(c) Agricultural Statistics (d) Vital Statistics

14. ""Põ¨¤°ß _øÁ'' Gߣøu AÍÂhUTi¯ AÍÄ :
(A) CøhöÁÎ AÍÄ (B) ö£¯µÍÄ AÍÄ
(C) ÂQu AÍÄ (D) Á›ø\¨£kzx® AÍÄ
The measurement scale of "taste of a coffee" is :
(a) Interval (b) Nominal

(c) Ratio (d) Ordinal

5 5969

15. C¸ Ehß öuõhº¦U÷PõkPЮ JßÖUöPõßÖ ö\[SzuõP C¸US® GÛÀ rXY
Gߣx :
(A) rXY=−1 (B) rXY=0 (C) rXY=±1 (D) rXY=+1
If the two regression lines are perpendicular to each other then,
(a) r XY =−1 (b) r XY =0 (c) r XY =±1 (d) r XY =+1

£Sv & II / PART - II
SÔ¨¦ : H÷uÝ® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 24 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 6x2=12
Note : Answer any six from the following questions. Question No. 24 is compulsory.

16. Cßø© P¸x÷PõÒ (Null hypothesis) GßÓõÀ GßÚ ?
What is Null hypothesis ?

17. t-©õv›¨ £s£ÍøÁø¯ Áøµ¯ÖUPÄ®.
Define student's t-statistic.

18. ©õÖ£õmk¨ £S¨£õ´Âß AÝ©õÚ[PÒ ¯õøÁ ?
What are the assumptions of ANOVA ?

19. JmkÓÂß £À÷ÁÖ ÁøPPøͨ £ØÔ GÊxP.
Write about the different types of Correlation.

20. SÔ±mk Gsøn Áø¯ÖUPÄ®. Auß ÁøPPøÍ GÊxP.
Define Index number. State the types of Index numbers.

21. «a]Ö ÁºUP •øÓ°À £¯ß£kzu¨£k® C¯À{ø»a \©ß£õkPøÍ GÊxP.
Write the normal equations used in method of least squares.

22. vmh¨£o uø»¨ø£z öu›Ä ö\´ÁuØS •ß PÁÛUP ÷Ási¯ÁØøÓ¨
£mi¯¼kP.
List the points to be noted before fixing the project topic.

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5969 6

23. ~Pº÷Áõº Âø»U SÔ±mk GsPÎß £¯ß£õkPøÍ GÊxP.
Write the significance of the consumer price indices.

24. J¸ ©ø»¨¤µ÷u\zvÀ, 75,000 ÷£º Á]US® F›À, KµõsiÀ ¤Ó¢u SÇ¢øuPÎß
GsoUøP 218 GÛÀ AÆÅ›ß ö\¨£Ûhõ ¤Ó¨¦ ÂQuzøuU [CBR] PõsP.
Population size of a hamlet during a calendar year was 75,000 and the number of
children born in the hamlet during the same year was 218. What is the Crude
Birth Rate [CBR] of the village ?

£Sv & III / PART - III
SÔ¨¦ : H÷uÝ® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs. 33 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 6x3=18

Note : Answer any six of the following questions. Question No. 33 is compulsory.

25. n=500, np=383 GߣÁØÔØS, H 0 : P=0.68 GÝ®÷£õx Auß ©õv›¨
£s£ÍøÁa ÷\õuøÚ°ß ©v¨ø£U PnUQkP.
In test for population proportion, if n=500 and np=383, then calculate the value
of the test statistic under H0 : P=0.68.

26. øPÁºUP £µÁ¼ß £s¦PøÍU TÖP.
State the properties of Chi-square distribution.

27. J¸ÁÈ ©õÖ£õmk¨ £S¨£õ´Âß {øÓ SøÓPøÍ GÊxP.
Write the merits and demerits of one-way classification.

28. ÁÇUP©õÚ SÔ±kPÎÀ R÷Ç öPõkUP¨£mkÒÍ ÂÁµ[PÎß
ö£õ¸zu•øhø©ø¯ Bµõ´P.
N=200, (A)=80, (B)=60, (αβ)=100
Test the consistency of the following data with the symbols having their usual
meaning.
N=200, (A)=80, (B)=60, (αβ)=100

7 5969
29. »õ줯º ©ØÖ® £õ]°ß SÔ±k `zvµzøu u¸P.
Give the formula for Laspeyre's and Paasche's method.

30. Aøµ \µõ\› •øÓø¯ £¯ß£kzv ÷£õUS ÷Põk ÁøµP.

Á¸h® 2013 2014 2015 2016 2017 2018

EØ£zv
59 62 69 72 78 79
(B°µ® hß)

Draw a trend line by the method Semi averages.

Year 2013 2014 2015 2016 2017 2018

Production
59 62 69 72 78 79
[1000 tons]

31. 1,50,000 ©UPÒ öuõøP²ÒÍ J¸ |P›À, J¸ SÔ¨¤mh Põ»zvÀ HØ£mh
CÓ¨¦PÒ 980 GÛÀ, ö£õ¸zu©õÚ Âvø¯¨ £¯ß£kzv A¢|P›ß CÓ¨¦
ÂQuzøuU PnUQkP.
If the number of deaths occurred is 980 in a town consisting of 1,50,000 persons
during a period, quantify the death rate of the town using suitable formula.

32. vmh¨£oø¯ ö\¯À£kzxu¼À EÒÍ {ø»PøÍU TÖP.
State the stages involved in doing a project work.

−7 −5
33. C¸ Ehßöuõhº¦U ÷PõkPÎß öPÊUPÒ bXY = ©ØÖ® bYX = GÛÀ
10 4
rXY Cß ©v¨¦ PõsP.

−7 −5
If two regression coefficients are bXY = and b YX = , what would be the
10 4
value of rXY ?

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5969 8

£Sv & IV / PART - IV
SÔ¨¦ : RÌUPõq® AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 5x5=25

Note : Answer all the following questions.

34. (A) PõºPÒ u¯õ›US® J¸ {ÖÁÚ®, J¸ ¦v¯ ÁøP Põøµ AÔ•P® ö\´¯
EÒÍx. A¢{ÖÁÚ® uØ÷£õøu¯ £¯ß£õmiÀ C¸US® Põøµ Âh
AÔ•P¨£kzu¨ ÷£õS® Põ›À G›ö£õ¸Ò SøÓÁõPa ö\»ÁõS® GßÖ®
Auß \µõ\› G›ö£õ¸Ò vÓß ¼mh¸US 27 Q.« GßÖ® TÖQÓx. 100
¦v¯ PõºPøÍU öPõsh J¸ ©õv› GkUP¨£mk Auß G›ö£õ¸Ò vÓß
÷\õvUP¨£kQÓx. A®©õv›a ÷\õuøÚ°À 100 ¦v¯ PõºPÎß \µõ\›
G›ö£õ¸Ò vÓß ¼mh¸US 30 Q.«, vmh»UP® ¼mh¸US 3 Q.« BPÄ®
QøhUP¨ ö£ÖQÓx. {ÖÁÚzvß TØøÓ HØP»õ©õ Gߣøu 5% ªøPPõs
{ø»°À ÷\õvzxU TÖP.
AÀ»x
(B) 5 umha\ºPÒ •Ø£P¼À 1 ©o ÷|µzvÀ umha_ ö\´u £UP[PÎß
GsoUøP 10, 12, 13, 8, 9 ©ØÖ® AÁºPÒ ¤Ø£P¼À 1 ©o ÷|µzvÀ
umha_ ö\´u £UP[PÎß GsoUøP 11, 15, 12, 10, 8. umha_ ö\´¯¨£mh
£UP[PÎß GsoUøP°À EÒÍ Âzv¯õ\® SÔ¨¤hzuUPuõ Gߣøu
B´Ä ö\´P. (α=5% GßP).
(a) A car manufacturing company desires to introduce a new model car. The
company claims that the mean fuel consumption of its new model car is
lower than that of the existing model of the car which is 27 kms/litre. A
sample of 100 cars of the new model is selected randomly and their fuel
consumptions are observed. It is found that the mean fuel consumption of
the 100 new model cars is 30 kms/litre with a standard deviation of
3 kms/litre. Test the claim of the company at 5% level of significance.
OR
(b) The number of pages typed by 5 DTP-operators for 1 hour in the morning
sessions are 10, 12, 13, 8, 9 and the number of pages typed by them in the
afternoon are 11, 15, 12, 10, 8. Is there any significant difference in the

mean number of pages typed ? (α=5%)

9 5969

35. (A) 500 ©õnÂPÒ öPõsh J¸ SÊÂÀ |hzu¨£mh B´ÂÀ 60%
¦zv\õ¼¯õÚÁºPÒ. AÁºPÎÀ 40% ©õnÂPÎß u¢øu¯ºPÒ £i¨£ÔÄ
CÀ»õuÁºPÒ. ¦zv\õ¼°À»õu ©õnÂPÎÀ 30% u¢øu¯ºPÒ
£izuÁºPÒ. CzuµÄPμ¸¢x £izu u¢øu¯ºPÎß SÇ¢øuPÒ
¦zv\õ¼¯õÚÁºPÍõ GßÓ P¸x÷PõÎß •UQ¯zxÁzøu 5% ªøPPõs
{ø»°À ÷\õvUP.
AÀ»x
(B) ¤ßÁ¸® uµÄPÐUS uµ •øÓø¯¨ £¯ß£kzv JmkÓÄU öPÊøÁU
PnUQkP.

uªÌ ©v¨ö£s 29 24 25 27 30 31

B[Q» ©v¨ö£s 29 19 30 33 37 36

(a) A survey was conducted with 500 female students of which 60% were
intelligent, 40% had uneducated fathers, while 30% of the not intelligent
female students had educated fathers. Test the hypothesis that the education
of fathers and intelligence of female students are independent at 5% of
significance.
OR
(b) Calculate the coefficient of correlation for the following data using ranks.
Marks in Tamil 29 24 25 27 30 31

Marks in English 29 19 30 33 37 36

36. (A) Kº B´ÄUPmkøµ°À ©õnÁºPÒ HØ£kzv¯ GÊzx¨ ¤øÇø¯ ‰ßÖ
Aø©¨¦ £°ØÖ|ºPÒ £vÄ ö\´u ÂÁµ® ¤ßÁ¸©õÖ. ‰ßÖ
ÁS¨¦Pξ® HØ£mh GÊzx¤øÇPÎß \µõ\›PÐUQøh÷¯ Âzv¯õ\®
EÒÍuõ GÚ α=5% ªøPPõs {ø»°À Bµõ´P.

£°ØÖ|º 1 2 3 5 0 8

£°ØÖ|º 2 4 6 8 4 9 0 2

£°ØÖ|º 3 5 2 3 2 3 3

AÀ»x
(B) ¤ßÁ¸® uµÄPÐUS PõºÀ ¤¯º\Ûß JmkÓÄU öPÊøÁ PnUQmk
ÂÍUP® u¸P.
X 13 15 11 16 13 19
Y 16 17 10 19 15 21

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5969 10

(a) Three composition instructions recorded the number of spelling errors which
their students made on a research paper. At 5% level of significance test
whether there is significant difference in the average number of errors in
the three classes of students.

Instructor 1 2 3 5 0 8

Instructor 2 4 6 8 4 9 0 2

Instructor 3 5 2 3 2 3 3

OR

(b) Calculate the Karl Pearson's coefficient of correlation for the following data
and interpret.

X 13 15 11 16 13 19
Y 16 17 10 19 15 21

37. (A) RÌUPsh uµÄPÐUS ¤ßÁ¸® AÍÄ SÔ±mk GsPøÍ PõsP.

(i) »õ줯›ß AÍÄ SÔ±mk Gs

(ii) £õ]°ß AÍÄ SÔ±mk Gs

(iii) ¤å›ß AÍÄ SÔ±mk Gs

1970 1980

Âø» ö©õzu ©v¨¦ Âø» ö©õzu ©v¨¦

A 10 80 11 110
B 15 90 9 108
C 8 96 17 340

AÀ»x

(B) JmkÓÄ ©ØÖ® Ehß öuõhºø£ ÷ÁÖ£kzxP.

11 5969
(a) Compute the following quantity indices from the data given below.
(i) Laspeyre's quantity index
(ii) Paasche's quantity index and
(iii) Fisher's quantity index
1970 1980
ity
od
m

Price Total Value Price Total Value
om
C

A 10 80 11 110
B 15 90 9 108
C 8 96 17 340
OR
(b) Distinguish between correlation and regression.

38. (A) uªÌ|õmiÀ ö£´u ©øÇ ÂÁµ[PÐUS (ª«À) £¸ÁPõ» SÔ±kPÒ
PõsP.
Á¸h® 2009 2010 2011 2012
Põ»õsk
I 38.2 38.5 55 50.5
II 166.8 250.9 277.7 197
III 612.6 773.1 717.8 706.1
IV 72.2 153.1 65.8 101.1
AÀ»x
(B) C¸ ©õÁmh[PÎÀ, J¸ |õmPõmi BsiÀ }›ÈÄ ÷|õ´, ~øµ±µÀ ¦ØÖ
÷|õ´ BQ¯ÁØÓõÀ £õvUP¨£mh ©UPøͲ®, A¢÷|õ´PÍõÀ CÓ¢uÁº
£ØÔ²® QøhUP¨ ö£ØÓ uPÁÀPÒ RÌUPsh AmhÁøn°À
uµ¨£mkÒÍÚ.
©õÁmh® A ©õÁmh® B
CÓ¨¤ØPõÚ
£õvUP¨£m÷hõº CÓ¢÷uõº £õvUP¨£m÷hõº CÓ¢÷uõº
Põµn®
GsoUøP GsoUøP GsoUøP GsoUøP
}›ÈÄ ÷|õ´ 20,000 325 22,000 400

~øµ±µÀ
19,500 300 21,225 380
¦ØÖ÷|õ´
CƸ ©õÁmh[PÐUS® ÷|õ´ SÔzu CÓ¨¦ ÂQu® PõsP.÷©¾®
CÓ¨¤ØPõÚ Põµn[Pøͨ ö£õÖzx EhÀ |»® ÷£nÀ SÔzx CƸ
©õÁmh[PøͲ® J¨¤kP.

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5969 12

(a) Find Seasonal Indices for the rainfall data in Tamil Nadu (in mm).

Year
2009 2010 2011 2012
Quarter
I 38.2 38.5 55 50.5
II 166.8 250.9 277.7 197
III 612.6 773.1 717.8 706.1
IV 72.2 153.1 65.8 101.1

OR
(b) The following are the information about the number of persons who are
affected by Diabetes and Lung Cancer and the number of persons died due
to each cause of death during a calendar year in two different districts.

District A District B
Cause of
No. of Persons No. of Persons
Death
Affected Died Affected Died
Diabetes 20,000 325 22,000 400

Lung Cancer 19,500 300 21,225 380

Find the illness specific death rates for the two districts. Also, compare
health conditions of both the districts with reference to these two causes of
death. Assume that a person affected by Diabetes is not affected by Lung
Cancer and Vice-Versa.

-oOo-