TN 12th Question Paper 2024 Statistics

TN PUBLIC EXAM

QUESTION
PAPER
2024

No. of Printed Pages : 12
7469
!7469Statistics! £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.

[ v¸¨¦P / Turn over

7469 2

1. H1 Gߣx J¸•øÚ (Á»x) ©õØÖ Gk÷PõÍõP C¸US®÷£õx, wº©õÛUS®
£Svø¯ {ºn°US® ÷\õuøÚ :
(A) Á»•øÚ ÷\õuøÚ
(B) Á», Ch C¸•øÚ ÷\õuøÚ
(C) Ch•øÚ ÷\õuøÚ
(D) Á» ©ØÖ® Ch•øÚ ÷\õuøÚ AÀ»
When H1 is a one-sided (right) alternative hypothesis, the critical region is determined by :
(a) right tail
(b) both right and left tails
(c) left tail
(d) neither right nor left tail

2. ©õv› AÍÁõÚx 30 -I Âh AvP©õS®÷£õx, t-£µÁÀ ö|¸[SÁx :
(A) øP ÁºUP¨ £µÁÀ (B) C¯À{ø» £µÁÀ
(C) F-£µÁÀ (D) £õ´\õß £µÁÀ
If the size of sample is larger than 30, the t-distribution tends to :
(a) Chi-square distribution (b) Normal distribution
(c) F-distribution (d) Poisson distribution

3. ö£¸[TÔÀ, 5% 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 5% level of significance for two-tailed large sample test is :
(a) 2.58 (b) 1.645 (c) 1.96 (d) 2.33

4. ©õÖ£õmk¨ £S¨£õ´Âß Cßø© Gk÷PõÎÀ AøÚzx •Êø©z öuõSvPÎß
\µõ\›PЮ :
(A) \©©À» (B) \©®
(C) \©® AÀ»x \©©À» (D) ©õÔPÒ
The null hypothesis in the ANOVA is that all the population means are :
(a) Unequal (b) Equal
(c) Either equal or unequal (d) Variable

3 7469

2
5. m×n Á›ø\ Eøh¯ ÷|ºÄ £mi¯¾UPõÚ, χ &©õv›¨ £s£ÍøÁ¯õÚx :

2
k O −E
( i i) 2
m n ( Oij − Eij )2
χ
(A) 0 = ∑ Ei
χ
(B) 0 = ∑∑ Eij
i=1 i =1 j=1

k k  O − E 2
2 i O 2 ( i)
(C) χ0 = ∑ E (D) χ0 =  i∑ 
i=1 i i =1  Ei 
2
The statistic χ , with usual notations, in case of contingency table of order (m×n) is given
by :

2
χ0 = ∑
k
( O i − Ei ) 2
χ0 = ∑ ∑
m n ( Oij − Eij )2
(a) Ei (b) Eij
i=1 i =1 j=1

k k 2
2 Oi 2  ( O i − Ei ) 
(c) χ0 = ∑ (d) χ0 = ∑  
i=1 Ei i =1  Ei 

6. ©õÖ£õmk¨ £S¨£õ´Ä •øÓPøÍ Â›Ä£kzv¯Áº :
(A) W.S. Põö\m (B) S.D. £õ´\õß
(C) PõºÀ&¤¯º\õß (D) R.A. L¤åº
ANOVA was developed by :
(a) W.S. Gosset (b) S.D. Poisson
(c) Karl Pearson (d) R.A. Fisher

7. r=+1 GÛÀ C¢u JmkÓøÁ¨ ¤ßÁ¸©õÖ TÓ»õ® :
(A) •Êø©¯õÚ Gvº JmkÓÄ (B) •Êø©¯õÚ ÷|º JmkÓÄ
(C) ÷|º JmkÓÄ (D) Gvº JmkÓÄ
If r=+1, then the correlation is called :
(a) Perfect negative correlation (b) Perfect positive correlation
(c) Positive correlation (d) Negative correlation

8. JmkÓÄU öPÊ Gߣx Ehßöuõhº¦U öPÊUPÎß __________ BS®.
(A) Cø\a \µõ\› (B) Tmka \µõ\›
(C) Cøn¢u \µõ\› (D) ö£¸USa \µõ\›
Correlation co-efficient is the __________ between the regression coefficients.
(a) harmonic mean (b) arithmetic mean
(c) combined mean (d) geometric mean
[ v¸¨¦P / Turn over

7469 4

9. ©õÔPÒ x ©ØÖ® y &ß JmkÓÄU öPÊUPÒ \©a^º GÛÀ :
(A) rxy < ryx (B) rxy=ryx (C) rxy ≠ ryx (D) rxy > ryx
The correlation coefficient of x and y is symmetric. Hence :
(a) rxy < ryx (b) rxy=ryx (c) rxy ≠ ryx (d) rxy > ryx

10. J¸ ö£¸[SÊ (cohort) £ØÔ¯ Áµ»õÖ AÔ¯ EuÄÁx :
(A) P¸ÄÖuÀ ÂQu[PÒ (B) CÓ¨¦ ÂQu[PÒ
(C) ©UPÒ öuõøP Áͺa] (D) ÁõÌ{ø» AmhÁøn
History of a cohort can be understood from :
(a) Fertility rates (b) Mortality rates
(c) Population growth (d) Life table

11. Põ»zöuõhº Á›ø\°À JÊ[PØÓ ©õÖ£õkPÒ HØ£kÁuØPõÚ Põµn® :
(A) _ÇÀ ©õÖ£õkPÒ (B) }sh Põ» ÷£õUS
(C) PoUP •i¯õu PõµoPÒ (D) £¸Á Põ» ©õÖ£õkPÒ
Irregular variation in a time series can be due to :
(a) cyclical variations (b) trend variations
(c) unpredictable causes (d) seasonal variations

12. ÁÇUP©õÚ SÔ±kPÎߣi Põ»® ©õØÖ ÷\õuøÚ §ºzv ö\´ÁuØS BÚ
{£¢uøÚ :
P01
(A) P01+P10=1 (B) P01×P10=1 (C) P =1 (D) P01−P10=1
10

The condition for the time reversal test to hold good with usual notation is :

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

13. C¢v¯õÂß •uÀ ©UPÒöuõøP AÔUøP öÁΰh¨£mh Bsk :
(A) 1948 (B) 1858 (C) 1958 (D) 1848
The first Census Report of India was published in :
(a) 1948 (b) 1858 (c) 1958 (d) 1848

5 7469

14. ¤ßÁ¸ÁÚÁØÖÒ Gx vmh¨£o°ß öuõhº ö\¯ÀPÍõPU SÔ¨¤h¨£k® ?
(A) SÔU÷PõÒPÒ E¸ÁõUSuÀ, uµÄ¨ £S¨£õ´Ä ö\´uÀ, AÔUøP u¯õ›zuÀ,
vmh¨£oUSz vmhªhÀ
(B) SÔU÷PõÒPÒ E¸ÁõUSuÀ, AÔUøP u¯õ›zuÀ, uµÄ¨ £S¨£õ´Ä ö\´uÀ,
vmh¨£oUSz vmhªhÀ
(C) SÔU÷PõÒPÒ E¸ÁõUSuÀ, vmh¨£oUSz vmhªhÀ, uµÄ¨ £S¨£õ´Ä
ö\´uÀ, AÔUøP u¯õ›zuÀ
(D) AÔUøP u¯õ›zuÀ, uµÄ¨ £S¨£õ´Ä ö\´uÀ, vmh¨£oUSz vmhªhÀ,
SÔU÷PõÒPÒ E¸ÁõUSuÀ
Which one is the correct sequence of activities in project work ?
(a) formulating objectives, data analysis, report writing, project work plan
(b) formulating objectives, report writing, data analysis, project work plan
(c) formulating objectives, project work plan, data analysis, report writing
(d) report writing, data analysis, project work plan, formulating objectives

15. Põ»zöuõhº 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

£S-v & II / PART - II

SÔ¨¦ : H÷uÝ® 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. Cßø© P¸x÷PõÒ GßÓõÀ GßÚ ?
What is null hypothesis ?

17. F-©õv›¨£s£ÍøÁa ÷\õuøÚ°ß £¯ß£õkPøÍ GÊxP.
Write the applications of F-statistic.

18. £s¦ – Áøµ¯ÖUPÄ®.
Define an attribute.

[ v¸¨¦P / Turn over

7469 6

19. Ehßöuõhºø£ Áøµ¯ÖUPÄ®.
Define regression.

20. JmkÓÂß £À÷ÁÖ ÁøPPøÍ GÊxP.
Write the different types of correlation.

21. SÖQ¯ Põ» •ßPo¨¦ Gߣx ¯õx ?
What is a short-term forecast ?

22. ö\¨£Ûhõ CÓ¨¦ ÂQu® Põs£uØPõÚ `zvµzøu GÊxP.
Write down the formula to find crude death rate.

23. SÔ±mk GsPÎß £¯ßPøÍ GÊxP.
Write the uses of Index numbers.

24. C¸ Ehßöuõhº¦U ÷PõkPÎß öPÊUPÒ b yx = 4 ©ØÖ® b xy = 9 GÛÀ,
5 20
rxy &Cß ©v¨¦ PõsP.
4 9
If two regression coefficients are b yx = and b xy = , what would be the value of rxy ?
5 20

£S-v & III / PART - III
SÔ¨¦ : H÷uÝ® 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¸ ÁÈ ©ØÖ® C¸ ÁÈ ©õÖ£õmk¨ £S¨£õ´ÂøÚ J¨¤kP.
Compare one-way and two-way ANOVA.

26. ªøPPõs {ø» Gߣuß ö£õ¸Ò ¯õx ?
What do you mean by level of significance ?

27. t-£µÁ¼ß £s¦Pøͨ £mi¯¼kP.
List out the properties of t-distribution.

7 7469

28. Ehßöuõhº¤ß £¯ßPøÍ GÊxP.
Write uses of regression.

29. vmh¨£o AÔUøP°ß öuõhUP {ø»¨¤›ÂÀ Ch® ö£ÖÁÚ ¯õøÁ ?
What are things to be included in the primary section of a project report ?

30. uµ JmkÓÄUöPÊ r=0.8, ∑D2=33 GÛÀ n&Cß ©v¨¦ PõsP.
If rank correlation coefficient r=0.8, ∑D2=33 then find value of n ?

31. J¸ ]Ø×›À EÒÍ Bµ®£ _Põuõµ ø©¯zvÀ KµõsiÀ ¤Ó¢u SÇ¢øuPÎß
GsoUøP 135 BS®. AÆÅ›À AÆÁõsiÀ 300 ÷£º CÓ¢xÒÍÚº.
AÁºPÐÒ Kµõsøh {øÓÄ ö\´¯õu 5 ]Ö SÇ¢øuPЮ CÓ¢xÒÍÚº.
AÆÁõÓõ°ß AÆÅ›ß SÇ CÓ¨¦ ÂQuzøuU PõsP.
A Primary Health Centre located in a village has a record of 135 live births during a year.
The number of deaths recorded in the village during that year was 300. Among them, 5 are
newborn babies of age less than a year. Measure the infant mortality rate of the village.

32. RÌUPsh uµÄPÐUSz uS¢u Âø»U SÔ±mk GsønU PnUQkP.

Âø»
ö£õ¸mPÒ AÍÄPÒ
2007 2010
X 25 3 4
Y 12 5 7
Z 10 6 5

Calculate a suitable price index from the following data.

Price
Commodity Quantity
2007 2010
X 25 3 4
Y 12 5 7
Z 10 6 5

[ v¸¨¦P / Turn over

7469 8

33. Aøµ \µõ\› •øÓø¯ £¯ß£kzv ÷£õUS ©v¨¦PÒ PõsP.
Á¸h® 1994 1995 1996 1997 1998 1999

EØ£zv (B°µ® hß) 20 25 24 24 23 25

Calculate trend values using semi-averages methods.

Year 1994 1995 1996 1997 1998 1999

Production (1000s tons) 20 25 24 24 23 25

£S-v & IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 5x5=25
Note : Answer all the questions.
34. (A) Kº B´ÄU Pmkøµ°À ©õnÁºPÒ HØ£kzv¯ GÊzx¨ ¤øÇ°øÚ ‰ßÖ
Aø©¨¦ £°ØÖ|ºPÒ £vÄ ö\´u ÂÁµ® ¤ßÁ¸©õÖ. ‰ßÖ
ÁS¨¦Pξ® HØ£mh GÊzx¨ ¤øÇPÎß \µõ\›PÐUQøh÷¯ Âzv¯õ\®
EÒÍuõ GÚ 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¸® uµÄPμ¸¢x öí¨£õimiì B (Hepatitis B) GßÓ ÷|õø¯ ukUP
uk¨§], uk¨¦ •øÓ¯õP HØÖUöPõÒÍ»õ©õ ? ""1500 ÷£º öPõsh £Sv°À
400 ÷£øµ öí¨£õimiì B GßÓ ÷|õ´ uõUQ¯x. 750 ÷£º uk¨§] ÷£õmkU
öPõshÚº. AÁºPÎÀ 75 ÷£øµ ©mk® A¢u ÷|õ´ uõUQ¯x''.
(a) Three composition instructors 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) Can vaccination be regarded as a preventive measure of Hepatitis B from the data
given below ?
Of 1500 persons in a locality, 400 were attacked by Hepatitis B. 750 has been vaccinated.
Among them only 75 were attacked.

9 7469

35. (A) J¸ u¯õ›¨£õͺ ÁÇ[Q²ÒÍ P®¤Áhzvß \µõ\› Eøh£k® vÓß
1900 n/m2 A»SPÒ ©ØÖ® vmh»UP® 120 n/m2. Azu¯õ›¨£õͺ, u©x
¦v¯ u¯õ›¨¤À, J¸ ¦v¯ öuõÈÀ ~m£zøu¨ £¯ß£kzvz u¯õ›UP¨£mh
P®¤Áhzvß Eøh£k® vÓß AvP›zxÒÍuõPU TÖQÓõº. AUTØøÓa
÷\õuøÚ ö\´¯ 60 P®¤Áh[PøÍU öPõsh ©õv› GkzxU öPõÒͨ&
£kQÓx. Aa÷\õuøÚ°À \µõ\› Eøh£k® vÓß 1960 n/m 2 GÚU
QøhUQÓx. AÆÁõöÓÛÀ 1% ªøPPõs {ø»°À Azu¯õ›¨£õÍ›ß
TØÖ HØP¨£k©õ ?

AÀ-»-x

(B) 5 |£ºPÎß ~snÔÄ vÓøÚ AÔÁuØPõP, ÷\õuøÚPÒ J¸ £°Ø]US
•ßÝ® ¤ßÝ® |hzu¨£mhx. AÁØÔß •iÄPÒ RÌUPshÁõÖ
ö£Ó¨£kQÓx.

|£ºPÒ I II III IV V
£°Ø]US •ß ~snÔÄ vÓß 110 120 123 132 125
£°Ø]US ¤ß ~snÔÄ vÓß 120 118 125 136 121

~snÔÄ vÓÛÀ H÷uÝ® •ß÷ÚØÓ® EÒÍuõ GÚ 1% ªøPPõs
{ø»°À ÷\õvUPÄ®.

(a) The mean breaking strength of cables supplied by a manufacturer is 1900 n/m2 with a
standard deviation of 120 n/m2. The manufacturer introduced a new technique in the
manufacturing process and claimed that the breaking strength of the cables has increased.
In order to test the claim, a sample of 60 cables is tested. It is found that the mean
breaking strength of the sampled cables is 1960 n/m2. Can we support the claim at
1% level of significance ?

OR

(b) An IQ test was conducted to 5 persons before and after they were trained. The results
are given below :

Candidates I II III IV V
IQ before training 110 120 123 132 125
IQ after training 120 118 125 136 121

Test whether any improvement in IQ at 1% level of significance.

[ v¸¨¦P / Turn over

7469 10

36. (A) JmkÓÄ ©ØÖ® Ehßöuõhºø£ ÷ÁÖ£kzxP.

AÀ-»-x

(B) ¤ßÁ¸® Âø» ©ØÖ® AΨ¦ £ØÔ¯ uµÄPÐUS 줯º©õÛß uµ
JmkÓÄ öPÊøÁU PnUQkP.

Âø» 4 6 8 10 12 14 16 18
Aئ 10 15 20 25 30 35 40 45

(a) Distinguish between correlation and regression.

OR

(b) Calculate the Spearman's Rank Correlation Coefficient between price and supply from
the following data.

Price 4 6 8 10 12 14 16 18
Supply 10 15 20 25 30 35 40 45

37. (A) C¢v¯õÂÀ £vÁõÚ ©øÇ (ª.«) ÂÁµ® R÷Ç öPõkUP¨£mkÒÍx.
AÆÂÁµzvØS £¸ÁPõ» SÔ±k PõsP.

£¸Á[PÒ
Á¸h®
I II III IV
2009 38.2 166.8 612.6 72.2
2010 38.5 250.9 773.1 153.1
2011 55 277.7 717.8 65.8
2012 50.5 197 706.1 101.1

AÀ-»-x

11 7469

(B) J¸ |õmiÀ, J¸ SÔ¨¤mh Põ»zvÀ, CÚ¨ö£¸UP Á¯xøh¯ ö£sPÎß
SÊUPЮ, AÁºPÒ ö£ØöÓkzu SÇ¢øuPÎß GsoUøP²® RÌUPsh
AmhÁøn°À uµ¨£mkÒÍx. A¢|õmiß ö£õxÁõÚ P¸ÄÖuÀ
ÂQuzøu²®, Á¯x SÔzu P¸ÄÖuÀ ÂQu[PøͲ® PnUQkP.

SÊUPÎß Á¯x ö£sPÎß E°¸hß ¤Ó¢u
(BskPÒ) GsoUøP SÇ¢øuPÎß GsoUøP
15 - 20 2,16,410 20,468
20 - 25 2,13,610 26,983
25 - 30 2,02,930 22,522
30 - 35 1,93,300 17,083
35 - 40 1,73,920 13,456
40 - 45 1,62,870 11,140

(a) Obtain the seasonal indices for the rainfall (in mm) data in India given in the following
table.
Quarter
Year
I II III IV
2009 38.2 166.8 612.6 72.2
2010 38.5 250.9 773.1 153.1
2011 55 277.7 717.8 65.8
2012 50.5 197 706.1 101.1
OR
(b) The following is the data regarding the size of female population in a country at
reproductive age and the live births during a period.
Age Groups Female No. of Live
(Years) Population Births
15 - 20 2,16,410 20,468
20 - 25 2,13,610 26,983
25 - 30 2,02,930 22,522
30 - 35 1,93,300 17,083
35 - 40 1,73,920 13,456
40 - 45 1,62,870 11,140
Calculate the general fertility rate and age specific fertility rates of the country.
[ v¸¨¦P / Turn over

7469 12

38. (A) ÂÚõ¨£mi¯À u¯õ›US® ÷£õx {øÚÂÀ öPõÒÍ÷Ási¯øÁ ¯õøÁ ?
AÀ-»-x
(B) 2010 -B® Bsøh Ai¨£øh¯õPU öPõsk »õ줯ºì, £õ]°ß ©ØÖ®
¤å›ß Âʪ¯ SÔ±mk GsPøÍU PõsP.

2010 2011
ö£õ¸mPÒ
Âø» (` ) AÍÄ Âø» (` ) AÍÄ
A 15 15 22 12
B 20 5 27 4
C 4 10 7 5

(a) State the points to be kept in mind while writing the questionnaire.
OR
(b) Construct 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
Price (` ) Quantity Price (` ) Quantity
A 15 15 22 12
B 20 5 27 4
C 4 10 7 5

-o0o-

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