TN 12th Question Paper 2023 Statistics

Tamil Nadu
State Board

2023
QUESTION
PAPER

No. of Printed Pages : 12
6669
!6669Statistics! £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.

[ v¸¨¦P / Turn over

6669 2

1. ©õv› \µõ\›UPõÚ vmh¨¤øÇ :
σ n σ
(A) (B) σ2 (C) (D)
n σ n
Standard error of the sample mean is :

σ n σ
(a) (b) σ2 (c) (d)
n σ n

2. \›¯õÚ TØÓõP C¸US® ÷£õx, H0 Gߣøu ©ÖUS® ¤øÇ :
(A) ©õv›ö¯kzu¼À ¤øÇ (B) •uÀ ÁøP¨ ¤øÇ
(C) vmh¨¤øÇ (D) Cµshõ® ÁøP¨ ¤øÇ
Rejecting H0, when it is true is called :
(a) sampling error (b) type I error
(c) standard error (d) type II error

3. 5×4 Á›ø\²øh¯ ÷|ºÄ¨ £mi¯¾UPõÚ øPÁºUP ÷\õuøÚ°ß Pmißø©U
TÖPÒ :
(A) 12 (B) 18 (C) 25 (D) 17
The degrees of freedom of the chi-square test statistic for the contingency of order
5×4 :
(a) 12 (b) 18 (c) 25 (d) 17

4. C¸ÁÈ ©õÖ£õmk¨ £S¨£õ´ÂÀ TSS=
(A) SST+SSB−SSE (B) SST+SSB+SSE
(C) SST+SSB (D) SST−SSB+SSE
In two-way classification TSS=
(a) SST+SSB−SSE (b) SST+SSB+SSE
(c) SST+SSB (d) SST−SSB+SSE

5. ΣD2=0, GÛÀ uµ JmkÓÄ :
(A) 0.5 (B) 0 (C) −1 (D) 1
If ΣD2=0, then rank correlation is :

(a) 0.5 (b) 0 (c) −1 (d) 1

3 6669

6. bXY=0.7 ©ØÖ® ‘a’=8 GÛÀ Y &ß «uõÚ X &Cß Ehß öuõhº¦a \©ß£õk :

(A) Y=0.7+8X (B) Y=8+0.7X (C) X=0.7+8Y (D) X=8+0.7Y
If bXY=0.7 and ‘a’=8 then the regression equation of X on Y is :

(a) Y=0.7+8X (b) Y=8+0.7X (c) X=0.7+8Y (d) X=8+0.7Y

7. C¸ Ehß öuõhº¦U ÷PõkPÒ JßÖUöPõßÖ ö\[Szx GÛÀ, rXY Gߣx :
(A) −1 (B) 0 (C) 2 (D) +1
If the two lines of regression are perpendicular to each other, then rXY=

(a) −1 (b) 0 (c) 2 (d) +1

8. Gί ö©õzu •øÓ¨£i, öPõkUP¨£mh Bsiß AøÚzx ö£õ¸mPÎß
Âø»PÎß ö©õzu® A÷u÷£õßÓ Guß ö©õzuzvÀ \uÃu©õP öPõkUP¨&
£kQÓx ?
(A) Põ»õsk (B) |h¨¦ Bsk
(C) Aøµ¯õsk (D) Ai¨£øh Bsk
In simple aggregate method, the aggregate price of all items in the given year is
expressed as percentage of the same in the :

(a) Quarterly (b) Current year

(c) Half-yearly (d) Base year

9. J¸ {ÖÁÚzvß £zuõsk Põ» Á¸hõ¢vµ Á¸Áõ´ uPÁÀPÒ SÔ¨£x :
(A) •ß Po¨¦ (B) Põ»z öuõhº Á›ø\
(C) ©õv›¨ £s£ÍøÁ (D) SÔ±möhsPÒ
Data of annual turnover of a company over a period of ten years can be represented
by :

(a) a parameter (b) a time series

(c) a statistic (d) index numbers
[ v¸¨¦P / Turn over

6669 4

10. ÁoP •ßPo¨¦ ÷©ØöPõÒÍ Ai¨£øh¯õÚx :
(A) Á› •øÓ¨£kzxuÀ (B) GvºPõ» ÂÁµ[PÒ
(C) Aµ\õ[P öPõÒøPPÒ (D) Ph¢uPõ» ÂÁµ[PÒ
Business forecast is made on the basis of :

(a) tax regulations (b) future data
(c) Government policies (d) past data

11. C¢v¯õÂÀ ¤Ó¨¦ CÓ¨¦ £vÄPÒ Pmhõ¯©õUSuÀ ö\¯À£kzu¨£mh
Bsk :
(A) 1969 (B) 1947 (C) 1970 (D) 1951
Compulsory registration of births and deaths was implemented in India, during
the year :
(a) 1969 (b) 1947 (c) 1970 (d) 1951

12. C¢v¯ Aµ]ß •uÀ öP͵Á ¦Òΰ¯À B÷»õ\PµõP C¸¢uÁº :
(A) ]. µ[Pµõáß (B) ¤.]. ©P»õ÷Úõ¤ì
(C) hõUhº ¤µõß]ì ¦UPõÚß (D) PºÚÀ ø\Uì
The first Honorary Statistical Advisor to Government of India is :

(a) C. Rangarajan (b) P.C. Mahalanobis
(c) Dr. Francis Buchanan (d) Col. Sykes

13. £s¦\õº uµÄPÒ Gߣx :
(A) AÍÂh •i¯õux (B) £Sv¯õP AÍÂhU Ti¯x
(C) AÍÂhU Ti¯x (D) ÷©ØTÔ¯ AøÚzx®
Qualitative data implies :

(a) Non-Measurable (b) Partly Measurable

(c) Measurable (d) All of the above

5 6669

14. ©õÖ£õmk¨ £S¨£õ´ÂÀ ©õv› ÂÁµ[PÒ :
(A) \©® (B) JßøÓ JßÖ \õº¢uøÁ
(C) \©©ØÓøÁ (D) \õº£ØÓøÁ
In ANOVA, the sample observations are :
(a) equal (b) dependent
(c) unequal (d) independent

15. F -÷\õuøÚ __________ GÚÄ® AøÇUP¨£kQÓx.
(A) ©õÖ£õmk ÷\õuøÚ
(B) \µõ\› ÂQu ÷\õuøÚ
(C) vmh»UP ÂQu ÷\õuøÚ
(D) ©õÖ£õmk ÂQu ÷\õuøÚ
F-test is also called as __________.
(a) Variance test
(b) Mean ratio test
(c) Standard deviation ratio test
(d) Variance ratio test

£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. ¦Òΰ¯¼À TÖöÁÎ Gߣøu Áøµ¯ÖUPÄ®.
Define sample space in Statistics.

17. øPÁºUP ©õv›¨ £s£ÍøÁø¯ Áøµ¯ÖUPÄ®.
Define chi-square Statistic.

18. ©õÖ£õmk¨ £S¨£õ´Ä GßÓõÀ GßÚ ?

What is Analysis of Variance ?

[ v¸¨¦P / Turn over

6669 6

19. H.G®. hmiÀ & Cß JmkÓÄ £ØÔ¯ Áøµ¯øÓø¯ GÊxP.
Write the definition of correlation by A.M. Tuttle.

20. Cµsk Ehß öuõhº¦ \©ß£õkPøÍ GÊxP.
Write the two simple linear regression equations.

21. _ÇÀ ÷\õuøÚ GßÓõÀ GßÚ ?
What is circular test ?

22. ÷£õUQøÚ AÍÂk® •øÓPøͨ ö£¯›kP.
Name the methods of estimating the trend.

23. Kº B´ÂÀ £[S ö£Ö® •Êø©z öuõSv AÀ»x C»US SÊ Gߣx £ØÔ
Áøµ¯ÖUPÄ®.
Define population or target group under study.

24. J¸ |P›À J¸ SÔ¨¤mh Põ»zvÀ ¤Ó¢u SÇÂPÎß GsoUøP²® A÷u Põ»
CøhöÁΰÀ CÓ¢u SÇÂPÎß GsoUøP²® •øÓ÷¯ 500 BPÄ®
75 BPÄ® £vÄ ö\´¯¨£mkÒÍÚ. A¢|P›ß SÇ CÓ¨¦ ÂQuzøuU
PnUQkP.
The number of live births recorded and the number of Infants died in a town
during a given period are 500 and 75 respectively. Calculate the Infant mortality
rate of the town.

£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. J¸•øÚ ÷\õuøÚ, C¸•øÚ ÷\õuøÚ GߣøÁ £ØÔ ÂÍUSP.

Explain one-tailed and two-tailed tests.

7 6669

26. ö£õ¸zxu¼ß ö\®ø© ußø©ø¯ AÔ²® ÷\õuøÚ £ØÔ ]Ö SÔ¨¦ ÁøµP.
Write short note on testing the significance of goodness of fit.

27. J¸ ÁÈ ©õÖ£õmk¨ £S¨£õ´Âß Pmhø©¨ø£ GÊxP.
Write the model ANOVA table for one-way classification.

28. ÁÇUP©õÚ SÔ±kPÎÀ R÷Ç öPõkUP¨£mkÒÍ ÂÁµ[PÎß ö£õ¸zu&
•øhø©ø¯ Bµõ´P. N=1000, (A)=600, (B)=500, (AB)=50.
Test the consistency of the following data with the symbols having their usual
meaning. N=1000, (A)=600, (B)=500, (AB)=50.

29. Y &ß «uõÚ X &Cß Ehß öuõhº¦ \©ß£õk ©ØÖ® Auß C¯À \©ß£õkPøÍ
GÊxP.
Write the regression equation of X on Y and its normal equations.

30. J¸ SÔ¨¤mh Põ»zvÀ, J¸ ]Ø×›À ÁõÌ¢u ©UPÎß GsoUøP 15,000. A÷u
Põ»zvÀ AÆÅ›À CÓ¢uÁºPÒ GsoUøP 98 GÛÀ, AÆÅ›ß ö\¨£Ûhõ
CÓ¨¦ ÂQu® PõsP.
There were 15,000 persons living in a village during a period and the number of
persons died during the same period was 98. Find the crude death rate ?

31. ÁÚzxøÓ°À ö£Ó¨£k® Á¸©õÚ ÂÁµzvØS Aøµ \µõ\› •øÓø¯¨
£¯ß£kzv ÷£õUS ©v¨¦PÒ PõsP.

Á¸h® 2008 2009 2010 2011 2012 2013

Á¸©õÚ®
46.17 51.65 63.81 70.99 84.91 91.64
(÷Põi°À)
Calculate the trend values using semi-average method for the income from the
forest department.

Year 2008 2009 2010 2011 2012 2013
Income
46.17 51.65 63.81 70.99 84.91 91.64

(in crores)

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6669 8

32. vmh¨£oø¯ ÷©ØöPõÒÁuõÀ HØ£k® |ßø©Pøͨ £mi¯¼kP.
List the benefits derived by doing a project work.

33. RÌUPõq® SÔ±kPøͨ £¯ß£kzv hõº¥ì & ö£Í¼ ©ØÖ® ¤å›ß ÂÊ«¯
SÔ±mk GsPøÍU PõsP.

P 01L =125, P 01P =126.21

Find the Dorbish Bowley’s Index and Fisher’s Ideal Index by using the following
Index numbers.

P 01L =125, P 01P =126.21

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

Note : Answer all the following questions.

34. (A) J¸ {ÖÁÚ® u¯õ›zu AøÚzx LED ÂÍUSPÎß \µõ\› B²mPõ»®
2000 ©oPÒ. Auß vmh»UP® 150 ©oPÒ. \©Áõ´¨¦ •øÓ°À
GkUP¨£mh 100 ÂÍUSPøÍU öPõsh J¸ ©õv› öuõS¨¤ß \µõ\›
B²mPõ»® 1950 ©oPÒ. JÆöÁõ¸ öuõS¨¤À EÒÍ ÂÍUSPÎß \µõ\›
B²mPõ»® 2000 ©oPÒ GßÓ P¸zv¼¸¢x AøÁ SÔ¨¤hzuUP
Âzv¯õ\zøu¨ ö£ØÔ¸UQÓuõ Gߣøu 5% ªøP Põs {ø»°À ÷\õvzx
AÔP.
AÀ»x
(B) P¸x÷PõÒ ÷\õuøÚ°ß÷£õx ¤ß£ØÓ¨£k® ö£õxÁõÚ ÁÈ•øÓPøÍ
ÂÍUSP.
(a) A company producing LED bulbs finds that mean life span of the population of
its bulbs is 2000 hours with a standard derivation of 150 hours. A sample of
100 bulbs randomly chosen is found to have the mean life span of 1950
hours. Test at 5% level of significance, whether the mean life span of the
bulbs is significantly different from 2000 hours.

OR

(b) Explain the general procedures to be followed for testing of hypotheses.

9 6669

35. (A) uÛ|£ºPÎß E¯º Cµzu AÊzuzøuU SøÓ¨£uØPõP AÁºPÐUS ‰ßÖ
öÁÆ÷ÁÖ ~m£[PÒ •øÓ÷¯, ©¸¢uÎzuÀ, EhØ£°Ø] ©ØÖ® ]Ó¨¦
EnÄ BQ¯øÁ Áõ´¨¦ •øÓ°À AÎUP¨£kQßÓx. |õßS
Áõµ[PÐUS¨ ¤ÓS AÁºPÎß Cµzu AÊzu® £›÷\õvUP¨£mk £vÄ
ö\´¯¨£mk RÌUPõq® AmhÁøn°À öPõkUP¨£mkÒÍx. ‰ßÖ
öÁÆ÷ÁÖ ~m£[PÎÚõÀ uÛ|£ºPÎß Cµzu AÊzu \µõ\›PÐUQøh÷¯
H÷uÝ® SÔ¨¤hzuUP Âzv¯õ\® HØ£mkÒÍuõ GÚ 5% ªøPPõs
{ø»°À ÷\õvUP.

©¸¢uÎzuÀ 10 12 9 15 13

EhØ£°Ø] 6 8 3 0 2

]Ó¨¦ EnÄ 5 9 12 8 4

AÀ»x
(B) ¤ßÁ¸® uµÄPÐUS PõºÀ ¤¯º\õÛß JmkÓÄU öPÊøÁ PnUQmk
ÂÍUP® u¸P.

x 9 8 7 6 5 4 3 2 1

y 15 16 14 13 11 12 10 8 9

(a) Three different Techniques namely medication, exercises and special diet
are randomly assigned to lower the blood pressure of individuals diagnosed
with high blood pressure. After four weeks the reduction in each person’s
blood pressure is tested and recorded and is given below. Test at 5% level,
whether there is any significant difference in mean reduction of blood
pressure among the three techniques.

Medication 10 12 9 15 13
Exercise 6 8 3 0 2
Diet 5 9 12 8 4

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

x 9 8 7 6 5 4 3 2 1

y 15 16 14 13 11 12 10 8 9

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6669 10

36. (A) \µõ\› vmh»UP®
÷Põxø© ÂøÍa\À (Q.Q./J¸ \xµ A»S) 10 8

Kµõsk ©øÇ AÍÄ (ö\.«.) 8 2
JmkÓÄU öPÊ : 0.5.
©øÇ AÍÄ 9 ö\.«. BP C¸US® ÷£õx ÂøÍa\ø»U PõsP.
AÀ»x
(B) HÇõ® ÁS¨¤À EÒÍ 8 ©õnÁºPÎß GøhPÒ (Q.Q.) 38, 42, 43, 50, 48,
45, 52 ©ØÖ® 50. •Êø©z öuõSv°ß ©õÖ£õk 48 Q.Q. GßÓ
P¸x÷PõøÍ ÷\õvUPÄ®. •Êø©zöuõSv C¯À{ø» öuõSv GßÖ® Auß
\µõ\› µ Gߣx öu›¯õux GߣuõPÄ® öPõÒP.
(a) Mean S.D.
Yield of wheat (kg/unit area) 10 8
Annual Rainfall (cm) 8 2
Correlation Co-efficient : 0.5.
Find the yield when rainfall is 9 cm
OR
(b) The weight (in kg) of 8 students of class VII are 38, 42, 43, 50, 48, 45, 52 and
50. Test the hypothesis that the variance of the population is 48 kg, assuming
that the population is normal and µ is unknown.

37. (A) 2014 &B® Bsøh Ai¨£øh BshõPU öPõsk RÌUPsh uµÄPÐUS
(1) »õ줯ºì SÔ±k (2) £õ]°ß SÔ±k (3) ©õºåÀ&GmäöÁõºz SÔ±k
©ØÖ® (4) ¤åº Âʪ¯ SÔ±k PnUQkP.
Á¸h® 2014 Á¸h® 2015
ö£õ¸mPÒ
Âø» AÍÄ Âø» AÍÄ
A 6 50 10 56
B 2 100 2 120
C 4 60 6 60
D 10 30 12 24
E 8 40 12 36
AÀ»x
(B) RÌUPõq® öuõÈÀxøÓ öuõÈ»õͺPÎß ~Pº÷Áõº Âø» SÔ±mk
GsPÐUS «a]Ö ÁºUP•øÓ°À ÷£õUS ÷Põk ö£õ¸zxP.
Á¸h® 2010 2011 2012 2013 2014

SÔ±mk Gs 166 177 198 221 225

11 6669
(a) Calculate (1) Laspeyre’s Index (2) Paasche’s Index (3) Marshall-Edgeworth
Index and (4) Fisher Ideal Index for the following data taking 2014 as base
year.
Year 2014 Year 2015
Items
Price Quantity Price Quantity
A 6 50 10 56
B 2 100 2 120
C 4 60 6 60
D 10 30 12 24
E 8 40 12 36
OR
(b) Fit a straight line trend by the method of least squares for the following
consumer price index numbers of the industrial workers.

Year 2010 2011 2012 2013 2014

Index number 166 177 198 221 225

38. (A) uªÌ|õmiÀ ÷PÌÁµS EØ£zvUPõP £¯ß£kzu¨£k® {»¨£µ¨¦ AÍÂß
(B°µ® öíU÷h›À) ÂÁµ® ¤ßÁ¸©õÖ :
Á¸h® 2003 2004 2005 2006 2007 2008 2009 2010

£µ¨¦ (B°µ® öíU÷h›À) 118 109 100 95 94 90 82 76
Aøµ \µõ\› •øÓø¯¨ £¯ß£kzv ÷£õUS ©v¨¦PÒ PõsP.
AÀ»x
(B) C¸ £SvPξÒÍ ©UPÒ öuõøP GsoUøP, A¨£SvPξÒÍ
Á¯xU÷PØÓ SÊUPÒ, AÁØÔÀ HØ£mh CÓ¨¦PÒ BQ¯øÁ RÌUPsh
AmhÁøn°À uµ¨£mkÒÍÚ. ö\¨£Ûh¨£hõ CÓ¨¦ ÂQuzøu²®,
Á¯øuU SÔzu CÓ¨¦ ÂQuzøu²® £Sv I ©ØÖ® £Sv II &ØS PõsP.

£Sv I £Sv II
Á¯x
(BskPÎÀ) ©UPÒ CÓ¨¦PÎß ©UPÒ CÓ¨¦PÎß
öuõøP GsoUøP öuõøP GsoUøP
0 - 10 3000 55 7500 300
10 - 25 4500 30 6000 50
25 - 45 6000 40 8000 40

45 &US ÷©À 1000 15 2000 64

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6669 12
(a) The following table shows the area covered for cultivation of Ragi in Tamil
Nadu (in '000 hectares)

Year 2003 2004 2005 2006 2007 2008 2009 2010

Area (in '000 hectares) 118 109 100 95 94 90 82 76

Find the trend values using semi averages method.
OR
(b) Number of deaths recorded in various age groups in two areas and the
population size in each age group are given in the following table.

Area I Area II
Age group (in years) No. of No. of
Population Population
Deaths Deaths
0 - 10 3000 55 7500 300
10 - 25 4500 30 6000 50
25 - 45 6000 40 8000 40
45 and over 1000 15 2000 64

Find the crude death rate and age specific death rate of Area I and Area II.

-oOo-