Tamil Nadu 12th Std Model Question Paper 2026 Statistics

Tamil Nadu Board Model Question Paper

No. of Printed Pages : 12
8369
!8369Statistics! £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 |õßS ©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) n
(B) (C) n
(D)
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£¸[TÖPÎÀ, Cßø© P¸x÷PõÒ H0 GߣuØS Cø\¢u J¸£UP & Chx ©õØÖ
P¸x÷PõÒ Aø©US®÷£õx, AuØPõÚ ©ÖUS® Âv (Rejection rule) :
(A) Z 0 ≤−Z α 2 (B) Z0 ≥ Z α 2 (C) Z0>Z α (D) Z 0 <−Z α

What is the rejection rule, based on large sample, for testing H0 against one-sided (left)
alternative hypothesis ?

(a) Z 0 ≤−Z α (b) Z0 ≥ Z α (c) Z 0>Z α (d) Z 0 <−Z α
2 2

3. J¸ C¯À{ø» •Êø©öuõSv°ß ©õÖ£õmhÍøÁ \õº¢u P¸x÷PõøÍ
÷\õv¨£uØS __________ £¯ß£kzu¨£kQÓx.
(A) Z & ÷\õuøÚ (B) t & ÷\õuøÚ
(C) øPÁºUP ÷\õuøÚ (χ2) (D) F & ÷\õuøÚ
For testing the hypothesis concerning variance of a normal population _________ is used.
(a) Z-test (b) t-test
(c) χ2-test (d) F-test

4. ©õÖ£õmk¨ £S¨£õ´Ä Gߣx ‰ßÖ AÀ»x AuØS ÷©Ø£mh •Êø©z
öuõSv __________ ÷\õuøÚ ö\´¯ ]Ó¢u ÁȯõS®.
(A) \µõ\›PøÍ (B) ©õÖ£õmk AÍøÁPøÍ
(C) ÂÁµ[PøÍ (D) ÂQu[PøÍ
The Analysis of Variance procedure is appropriate for testing the equivalence of three or
more population ___________.
(a) means (b) variances
(c) observations (d) proportions

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5. C¸ ÁÈ ©õÖ£õmk¨ £S¨£õ´ÂÀ TSS=320, SST=45, SSB=70 GÛÀ, SSE Gߣx :
(A) 250 (B) 205 (C) 435 (D) 115
In two-way classification if TSS=320, SST=45, SSB=70 then SSE=____________.
(a) 250 (b) 205 (c) 435 (d) 115

6. r=−1 GÛÀ C¢u JmkÓøÁ¨ ¤ßÁ¸©õÖ TÓ»õ®.

(A) ÷|º JmkÓÄ (B) •Êø©¯õÚ ÷|º JmkÓÄ
(C) Gvº JmkÓÄ (D) •Êø©¯õÚ Gvº JmkÓÄ
If r=−1, then the correlation is called :
(a) positive correlation (b) perfect positive correlation
(c) negative correlation (d) perfect negative correlation

7. JmkÓÄUöPÊ Aø©²® CøhöÁÎ :
(A) 0 ≤ r ≤ 1 (B) −1 ≤ r ≤ 0 (C) −1 ≤ r ≤ 1 (D) −1< r < 1
The correlation coefficient lies in the interval :

(a) 0≤r≤1 (b) −1 ≤ r ≤ 0 (c) −1 ≤ r ≤ 1 (d) −1 < r < 1

8. C¸ Ehß öuõhº¦U ÷PõkPÒ JßÖUöPõßÖ ö\[Szx GÛÀ rxy Gߣx :
(A) −1 (B) 0 (C) 0.5 (D) 1
If the two lines of regression are perpendicular to each other then rxy=________.

(a) −1 (b) 0 (c) 0.5 (d) 1

9. Y=a+bx GßÓ ÷|º÷Põk __________ Ehß öuõhº¦ GÚ AøÇUP¨£kQÓx.

(A) X ©ØÖ® Y &US Cøh÷¯ (B) Y &Cß «uõÚ X &ß
(C) b &Cß «x a &Cß (D) X &Cß «uõÚ Y &ß
The linear equation Y=a+bx is called as regression equation of _____________.
(a) between X and Y (b) X on Y

(c) ‘a’ on ‘b’ (d) Y on X

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10. Põ» ©õØÖ ÷\õuøÚø¯ §ºzv ö\´²® SÔ±mk Gs Gߣx :
(A) ¤å›ß Âʪ¯ SÔ±möhs
(B) £õ]°ß SÔ±mk Gs
(C) ÁõÀì Âø»U SÔ±mk Gs
(D) »õ줯›ß SÔ±mk Gs
The index that satisfies time reversal test is :
(a) Fisher’s Ideal Index
(b) Paasche’s Index
(c) Walsh price Index
(d) Laspeyre’s Index

11. 1974 B® Bsøh Ai¨£øh BshõPU öPõsk, 1981 ©ØÖ® 1982 B®
BsiØPõÚ ~Pº÷Áõº Âø»U SÔ±mk GsPÒ 320 ©ØÖ® 400 BS® GÛÀ,
1982 B® Bsøh Ai¨£øh BshõPU öPõsk 1981 B® BsiØPõÚ
~Pº÷Áõº Âø»U SÔ±mk Gs :
(A) 125 (B) 80 (C) 85 (D) 128
The consumer price index numbers for 1981 and 1982 to the base 1974 are 320 and 400
respectively. The consumer price index for 1981 to the base 1982 is :
(a) 125 (b) 80 (c) 85 (d) 128

12. Põ»z öuõhº Á›ø\°ß TÖPÒ T, S, C ©ØÖ® I EÒÍhUQ¯ Tmk ÁiÁø©¨¦ :
(A) Y=T×S+C×I (B) Y=T×S×C×I
(C) Y=T×S×C+I (D) Y=T+S+C+I
An additive model of time series with components, T, S, C and I is :
(a) Y=T×S+C×I (b) Y=T×S×C×I
(c) Y=T×S×C+I (d) Y=T+S+C+I

13. •uÀ ÷u]¯¨ ¦Òΰ¯À vÚ® __________ CÀ öPõshõh¨£mhx.
(A) áüß 29, 2007 (B) H¨µÀ 29, 2007
(C) áüø» 29, 2007 (D) ÷© 29, 2007
The first National Statistics Day was celebrated on ____________.
(a) June 29, 2007 (b) April 29, 2007
(c) July 29, 2007 (d) May 29, 2007

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14. ÁõÌ{ø»U SÔ±k AÍÂkÁx :
(A) SÇ CÓ¨¦ ÂQu® (B) ¤Ó¨¦ & CÓ¨¦ ÂQu®
(C) ö£õxÁõÚ P¸ÄÖuÀ ÂQu® (D) ÁõÌ{ø» {PÌÂß ÂQu®
Vital Index measures :
(a) infant mortality rate (b) birth - death ratio
(c) general fertility rate (d) rate of vital event

15. ÁõÌ{ø» {PÌÄPÎß ÂQu[PÒ ö£õxÁõP AÍÂkÁx :
(A) B°µ® ÷£¸US (B) £zx »m\® ÷£¸US
(C) ¡Ö ÷£¸US (D) £zuõ°µ® ÷£¸US
Rates of Vital events are usually measured as :
(a) per thousand (b) per ten lakh
(c) per hundred (d) per ten thousand

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

16. Asø©°À J¸ ©õÁmhzvÀ |hzv¯ PÍ B´ÂÀ, \©Áõ´¨¦ •øÓ°À
2000 £mhuõ›PÒ öu›Ä ö\´¯¨£mk, AÁºPÐUQøh÷¯ 367 ÷£º C¢v¯
Bm]¨£o ÷uºÄ GÊxÁuØS BºÁ•øh¯ÁµõP C¸UQßÓÚº GßÖ
PshÔ¯¨£mkÒÍx. AÆÁõöÓÛß AÁºPÍx ÂQu\© ©v¨ø£U PõsP.
In a recent survey, conducted among 2000 randomly selected graduates in a district, 367 of
them are IAS aspirants. Calculate the proportion of IAS aspirants among the graduates in
the district.

17. Pmißø© TÖPÒ & Áøµ¯ÖUPÄ®.
Define degrees of freedom.

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

19. cov (x, y)=9.3, x &Cß ©õÖ£õk = 10.1, y &ß ©õÖ£õk = 11.9 GÛÀ r &Cß ©v¨¦
PõsP.
Given that cov (x, y)=9.3, variance of x=10.1 variance of y=11.9. Find r.

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20. Ehß öuõhº¤ß ÁøPPÒ ¯õøÁ ?
What are the types of regression ?

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

22. Põ»zöuõhº Á›ø\ GßÓõÀ GßÚ ?
What is a time series ?

23. SÇ CÓ¨¦ ÂQu® PnUQk® Âvø¯U TÖP.
What is the formula used to compute infant mortality rate ?

24. J¸ ©õ|P›À J¸ SÔ¨¤mh Põ»zvÀ ¤Ó¢u SÇ¢øuPÎß GsoUøP 3,907
BS®. A®©õ|P›À AUPõ»zvØS›¯ ©UPÒöuõøP 20,00,000 BS®.
AÆÁõÓõ°ß A®©õ|P›ß ö\¨£Ûhõ ¤Ó¨¦ ÂQuzøuU (CBR) Psk¤i.
The number of children born in a city during a period was 3,907 and the total population of
the city in that period was 20,00,000. Find the crude birth rate of the city.

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

Note : Answer any six questions. Question No. 33 is Compulsory.

25. J¸ ¦Òΰ¯À ÷\õuøÚUS, •iøÁz u¸® ÂvPøÍ AmhÁøn¨£kzv
ÂÁ›UP.
Describe Decision Table.

26. øP & ÁºUP (χ2) &£µÁ¼ß £s¦PøÍ TÖP.
State the properties of χ2 distribution.

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

28. JmkÓÂß GøÁ÷¯Ý® ‰ßÖ £¯ßPøÍ GÊxP.
Write any three uses of correlation.

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29. _ÇÀ ©õÖ£õkPÒ GßÓõÀ GßÚ ?
What is cyclical variation ?

30. J¸ ö\¯Àvmhzvß £s¤¯À¦PøÍU TÖP.
State the characteristics of a project.

31. 2000 B® Bsøh Ai¨£øh BshõPU öPõsk 2015 &B® BsiØS ö©õzu
ö\»ÂÚ •øÓø¯ £¯ß£kzv ~Pº÷Áõº Âø» SÔ±mk GsPøÍ RÌUPsh
uµÄPÐUS PõsP.

Âø»
ö£õ¸mPÒ AÍÄ
2000 2015

÷Põxø© 10 15 20

A›] 12 30 36

ö|´ 2 160 200

\ºUPøµ 4 40 40

Calculate the consumer price index number for 2015 on the basis of 2000 from the following
data by using the Aggregate Expenditure method.

Price
Commodity Quantity
2000 2015
Wheat 10 15 20
Rice 12 30 36
Ghee 2 160 200
Sugar 4 40 40

32. J¸ ©õÁmhzvÀ CÚ¨ö£¸UP Á¯xøh¯ ö£sPÎß GsoUøP 70,000 .
A®©õÁmhzvÀ ¤Ó¢u SÇ¢øuPÎß GsoUøP²®, SÇ CÓ¨¦® •øÓ÷¯
10,000 ©ØÖ® 70 BP EÒÍx. CÁØÔØS G¢u CÓ¨¦ ÂQuzøuU PnUQkÁõ´ ?
Auß ©v¨¦ GßÚ ?
The number of women at reproductive age in a district is 70,000. Also the number of live
births and infant deaths registered in the district are respectively 10,000 and 70. Which
mortality rate you will calculate ? What is its value ?

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33. 4X−5Y=−33 ©ØÖ® 20X−9Y=107 GßÓ Ehß öuõhº¦ ÷PõmiØS X ©ØÖ® Y
&Cß \µõ\›PøÍ PnUQkP.
Given the following lines of regression 4X−5Y=−33 and 20X−9Y=107. Find the mean
values of X and Y.
£Sv & IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS Âøh¯ÎUPÄ®. 5x5=25
Note : Answer all the questions.

34. (A) J¸ {ÖÁÚ® u¯õ›zu AøÚzx LED ÂÍUSPÎß \µõ\› B²mPõ»®
2000 ©oPÒ. Auß vmh »UP® 150 ©oPÒ. u¯õ›UP¨£mh ÂÍUSPÒ
AøÚzx® £» öuõS¨¦PÍõP EÒÍÚ. \© 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) RÌPõq® uµÄPÐUS «a]Ö ÁºUP •øÓø¯¨ £¯ß£kzv 1995 &B®
Á¸hzvØPõÚ EØ£zvø¯U PnUQkP.

Á¸h® 1990 1991 1992 1993 1994

EØ£zv
70 72 88 90 92
(B°µ® hß)

(a) A company producing LED bulbs finds that mean life span of the population of its
bulbs is 2000 hours with a standard deviation 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) Estimate the value of production for the year 1995 by using the method of least squares
from the following data.

Year 1990 1991 1992 1993 1994

Production
70 72 88 90 92
(1000 tons)

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35. (A) J¸ |P›À EÒÍ ‰ßÖ £ÒÎPÎÀ £°¾® 12 B® ÁS¨¦ ©õnÁºPÒ
Áõ´¨¦ •øÓ°À JÆöÁõ¸ £Òΰ¾® 5 ÷£º ÷uº¢öukUP¨£mk ÷uºÄ
|hzu¨ö£ØÓx. AÁºPÒ ö£ØÓ ©v¨ö£s ¤ßÁ¸©õÖ :

£ÒÎ I 9 7 6 5 8

£ÒÎ II 7 4 5 4 5

£ÒÎ III 6 5 6 7 6

J¸ ÁÈ ©õÖ£õmk¨ £S¨£õ´Ä ö\´P.
AÀ»x

(B) 1990 - 91 •uÀ 1999 - 2000 Áøµ°»õÚ C¢v¯õÂß EnÄ EØ£zv ÂÁµ®
R÷Ç öPõkUP¨£mkÒÍx. 4 Á¸h |P¸® \µõ\›ø¯¨ £¯ß£kzv ÷£õUS
©v¨¦PÒ Põs.

Á¸h® 1990-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 1999-2000

ÂøÍa\À
626 734 535 727 652 715 756 860 909 798
(Q.Q/öíU÷hº)

(a) A test was given to five students taken at random from XII class of three schools of a
town. The individual scores are :

School I 9 7 6 5 8
School II 7 4 5 4 5
School III 6 5 6 7 6

Carry out the one-way ANOVA.
OR
(b) Following data gives the yield of foodgrains in India for the years 1990 - 91
to 1999 - 2000. Find the trend values using 4 - year moving averages.

Year 1990-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 1999-2000

Yield
626 734 535 727 652 715 756 860 909 798
(kg / hectare)

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36. (A) ¤ßÁ¸® uµÄPÐUS Y &Cß «uõÚ X &Cß Ehßöuõhº¦ \©ß£õmøhU
PõsP.
x 7 4 6 9 3 8
y 8 5 4 8 3 6
AÀ»x
(B) \© Áõ´¨¦ •øÓ°À ÷uº¢öukUP¨£mh 5 PÀ¿› ©õnÁºPÎß uªÌ,
B[Q» ©v¨ö£sPÒ ¤ß Á¸©õÖ öPõkUP¨£mkÒÍx. 줯º÷©Ûß
uµ JmkÓÄ öPÊ PõsP.
uªÌ 85 60 73 40 90

B[Q»® 93 75 65 50 80

(a) Calculate the regression equation of X on Y from the data given below,
x 7 4 6 9 3 8
y 8 5 4 8 3 6
OR
(b) A random sample of 5 college students is selected and their marks in Tamil and English
are found to be :
Tamil 85 60 73 40 90
English 93 75 65 50 80
Calculate Spearman’s rank correlation coefficient.

37. (A) J¸ C¯À{ø» öuõSv°ß \µõ\› µ (öu›¯õux) ©ØÖ® ©õÖ£õk 9. ©õv›
AÍÄ 9 EÒÍ J¸ ©õv› GkUP¨£mk Auß ©õÖ£õmk AÍøÁ°ß AÍÄ
5.4 GÚU PnUQh¨£kQÓx. H1 : σ2>9 GßÓ ©õØÖ P¸x÷PõÐUS GvµõP
5% ªøP Põs {ø»°À Cßø© P¸x÷PõÒ H0 : σ2=9 Gߣøu ÷\õvUP.
AÀ»x
(B) RÌUPsh uµÄPÐUS, 2010 B® Bsøh Ai¨£øh BshõPU öPõsk
(1) »õ줯º •øÓ (2) £õ] •øÓ ©ØÖ® (3) ¤å›ß Âʪ¯ •øÓ°À Âø»
SÔ±mk GsPøÍU PnUQkP.
2010 2011
ö£õ¸mPÒ
Âø» AÍÄPÒ Âø» AÍÄPÒ
A 20 10 25 13
B 50 8 60 7
C 35 7 40 6
D 25 5 35 4

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(a) A normal population has mean µ (unknown) and variance 9. A sample of size
9 observations has been taken and its variance is found to be 5.4. Test the null hypothesis
H0 : σ2=9 against H1 : σ2>9 at 5% Level of significance.
OR
(b) Calculate the price indices from the following data by applying (1) Laspeyre’s method
(2) Paasche’s method and (3) Fisher ideal number by taking 2010 as the base year.
2010 2011
Commodity
Prices Quantities Prices Quantities
A 20 10 25 13
B 50 8 60 7
C 35 7 40 6
D 25 5 35 4

38. (A) 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 RÌPsh 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£õ¸zx, EhÀ|»® ÷£nÀ SÔzx CƸ
©õÁmh[PøͲ® J¨¤kP.
AÀ»x
(B) 6 ©õnÁºPÐUS J¸ £°Ø]US •ßÝ®, ¤ßÝ® |hzu¨£mh ÷uºÂÀ
AÁºPÒ ö£ØÓ ©v¨ö£sPÒ £vÂh¨£mk RÌUPshÁõÖ AmhÁøn¨&
£kzu¨£mkÒÍx. C¨£°Ø] BÚx AÁºPÎß ©v¨ö£sPøÍ
E¯ºzxÁuØS EuÂPµ©õP C¸¢uuõ GÚ ÷\õvUP.

£°Ø]US •ß 100 160 113 122 120 105

£°Ø]US ¤ß 120 155 120 128 115 100

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(a) 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 Death No. of persons No. of persons
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.

OR

(b) A test was conducted with 6 students before and after the training programme. Their
marks were recorded and tabulated as shown below. Test whether the training was
helpful in improving their scores.

Before training 100 160 113 122 120 105

After training 120 155 120 128 115 100

-oOo-