TN 11th Question Paper 2022 Statistics

No. of Printed Pages : 11
6069
!6069IstYearStatistics! £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 the corresponding answer.

6069 2

1. J¸ Põ›ß {Ó® __________ AÍÃmk AÍøÁ¯õS®.
(A) CøhöÁÎ (B) £s¦
(C) ÂQu (D) Á›ø\
The colour of a car is in __________ of measurement.
(a) Interval scale (b) Nominal scale
(c) Ratio scale (d) Ordinal scale

2. B´Áõͺ J¸ {ÖÁÚzvß uµÂøÚ¨ £¯ß£kzxQÓõº GÛÀ, AzuµÁõÚx :
(A) Cµshõ®{ø» uµÄ (B) Gs AÍ»õÚ uµÄ
(C) •uÀ{ø» uµÄ (D) £s£Í»õÚ uµÄ
When the researcher uses the data of an agency, then the data is called :
(a) Secondary data (b) Quantitative data
(c) Primary data (d) Qualitative data

3. Kº AmhÁøn°À ÷©¼¸¢x RÇõP Ch¨£k® EÖ¨¦PÐUPõÚ uø»¨¦PÒ :
(A) SÔ¨¦ (B) {øµ
(C) AmhÁøn uø»¨¦ (D) {µÀ
The column heading of a table from top to bottom is known as :
(a) Note (b) Stub
(c) Table title (d) Caption

4. usk & Cø»¨ £vÄ •øÓ°À SÔ¨¤h¨£k® usk¨£Sv°À Ch®ö£Ö®
C»UP® __________.
(A) ¤ß C»UP® (B) |k C»UP®
(C) •ß C»UP® (D) HxªÀø»
In a stem and leaf plot, stem is the label for __________ digit.
(a) trailing (b) middle
(c) leading (d) none

3 6069

5. G¢u ÂÍUP¨£hzvÀ uµÄPÒ ÷Põn[PÍõP ©õØÓ¨£kQÓx ?
(A) Ámh ÂÍUP¨£h® (B) E¸Á ÂÍUP¨£h®
(C) £µÁÀ ö\ÆÁP¨£h® (D) ö£›m÷hõ Áøµ£h®
In which one of the following, data is transformed into angles ?
(a) Pie diagram (b) Pictogram
(c) Histogram (d) Pareto diagram

6. RÈÚ SÂÄ {PÌöÁs ÁøÍ÷Põk®, ÷©¼Ú SÂÄ {PÌöÁs ÁøÍ÷Põk®
öÁmiU öPõÒЮ ¦ÒÎ __________ BS®.
(A) •Pk (B) ö£¸US \µõ\›
(C) Cø\ \µõ\› (D) Cøh{ø» AÍÄ
Intersection of less than ogive and more than ogive gives __________.
(a) Mode (b) Geometric mean
(c) Harmonic mean (d) Median

7. vÓ¢u Â›Ä CøhöÁÎ öPõsh £µÁ¼À __________ Põn C¯»õx.
(A) Cµshõ® PõÀ©õÚ® (B) Tmk \µõ\›
(C) ‰ßÓõ® PõÀ©õÚ® (D) •uÀ PõÀ©õÚ®
In an open end distribution __________ cannot be determined.
(a) II Quartile (b) Mean
(c) III Quartile (d) I Quartile

8. uµÄ öuõSv \©a^µõ°ß A¢u ÁøÍÁøµ°ß Ea]¨¦ÒÎ :
(A) Cøh{ø» (B) \µõ\›
(C) •Pk (D) CøÁ AøÚzx®
When a distribution is symmetrical the highest point on the curve is called the :
(a) Median (b) Mean
(c) Mode (d) All of these

9. PõÀ©õÚ»UP® 8 GÛÀ vmh »UPzvß ©v¨¦ :
(A) 24 (B) 12 (C) 22 (D) 16
If a Quartile deviation is 8, then value of the standard deviation will be :
(a) 24 (b) 12 (c) 22 (d) 16

6069 4

10. Á›ø\U Põµo¨ ö£¸UPÀ n __________ GÚÄ® GÊu¨£kQÓx.
(A) (n−1)! (B) n(n−1)! (C) (n+1)! (D) n(n+1)!
The factorial n is also written as :
(a) (n−1)! (b) n(n−1)! (c) (n+1)! (d) n(n+1)!

11. x9 &ß ÁøPUöPÊ :
(A) 8x9 (B) x8 (C) 8x8 (D) 9x8
Derivative of x9 is :
(a) 8x9 (b) x8 (c) 8x8 (d) 9x8

12. A ©ØÖ® B Gß£Ú H÷uÝ® Cµsk {PÌa]PÒ. ÷©¾® P(A/B)=0.3 ©ØÖ®
P(A∩B)=0.2 GÛÀ P(B) =

6 2 1 5
(A) (B) (C) (D)
7 3 7 3
If A and B are two events with P(A/B)=0.3, P(A∩B)=0.2, then P(B) is :
6 2 1 5
(a) (b) (c) (d)
7 3 7 3

13. ©õÖ(4X+3)= __________.
(A) 256 ©õÖ(X) (B) 7 ©õÖ(X) (C) 0 (D) 16 ©õÖ(X)
Var(4X+3) is :
(a) 256 Var(X) (b) 7 Var(X) (c) 0 (d) 16 Var(X)

14. B(n, p) &CÀ, ‘n’ öÁØÔPÐUPõÚ {PÌuPÄ :
(A) pn (B) nCxpxqn−x (C) qn (D) 1
In B(n, p) the probability ‘n’ successes is :
(a) pn (b) nCxpxqn−x (c) qn (d) 1

15. £õ´éõß £µÁ»õÚx __________ Ehß öuõhº¦øh¯x.
(A) |hÁõ {PÌa] (B) A›uõÚ {PÌa]PÒ
(C) HÓzuõÇ {a\¯ {PÌa] (D) {a\¯©õÚ {PÌa]PÒ
Poisson distribution corresponds to :
(a) Impossible event (b) Rare events
(c) Almost sure event (d) Certain events

5 6069

£Sv & II / PART - II
SÔ¨¦ : H÷uÝ® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. 24 &Áx ÂÚõÂØS
Psi¨£õP Âøh¯ÎUP ÷Ásk®. 6x2=12

Note : Answer any six questions. Question No. 24 is Compulsory.

16. {¦nzxÁ ©v¨¥mk AÔ¯¼À ¦Òΰ¯À £¯ß£õkPøÍU TÖP.
State the role of statistics in Actuarial Science.

17. ÂÚõz öuõS¨¦ £mi¯À Gߣx GßÚ ?
What is a schedule ?

18. ¦Òΰ¯À AmhÁøn°øÚ Áøµ¯øÓ ö\´P.
Define a statistical table.

19. ÷Põmh AÍøÁPÒ GßÓõÀ GßÚ ?
What are the measures of skewness ?

20. J¸ ]ÖÁß 6 PõÀ \møhPЮ, 10 ÷©À \møhPЮ øÁzv¸UQÓõß. AÁß
AÁØøÓ GzuøÚ ÁÈPÎÀ Ao¢x öPõÒÍ •i²® ?
A boy has 6 pants and 10 shirts. In how many ways can he wear them ?

21. E 1 ©ØÖ® E 2 Gß£Ú Cµsk® JßøÓ JßÖ Â»US® {PÌa]PÒ. ÷©¾®
P(E2)=0.5, P(E1∪E2)=0.7 GÛÀ P(E1) PõsP.
If E1 and E2 are two mutually exclusive events and given that P(E 2)=0.5 and
P(E1∪E2)=0.7 then find P(E1).

22. f (x)=5x4, 0 < x < 1 Gߣx {PÌuPÄ Ahºzv \õº£õS©õ GÚ {¹¤UPÄ®.
Verify whether the following is a p.d.f. f (x)=5x4, 0 < x < 1.

23. 2, 7, 10, 12, 10, 19, 2, 11, 3, 12 GßÓÁØÔØS •Pk PõsP.
Compute mode value for the following observations.
2, 7, 10, 12, 10, 19, 2, 11, 3, 12

24. 2, 4 ©ØÖ® 8 &ß ö£¸US \µõ\› PõsP.
Find the G.M of 2, 4 and 8.

6069 6

£Sv & III / PART - III
SÔ¨¦ : H÷uÝ® BÖ ÂÚõUPÐUS Âøh¯ÎUPÄ®. 33 &Áx ÂÚõÂØS
Psi¨£õP Âøh¯ÎUP ÷Ásk®. 6x3=18

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

25. ©õv›US®, ©õv›U Po¨¤ØS® EÒÍ ÷ÁÖ£õkPøÍ GÊxP.
Distinguish between sample and sampling.

26. uÛzu {PÌöÁs £µ-ÁÀ GßÓõÀ GßÚ ?
What is discrete frequency distribution ?

27. J¸ ø\UQÒ Kmk£Áº •uÀ 3 Q.«. yµzøu 8 Q.«./©o ÷ÁPzv¾®, Akzu
2 Q.«. yµzøu 3 Q.«./©o GßÓ ÷ÁPzv¾®, Pøh] 2 Q.«. yµzøu
2 Q.«./©o GßÓ ÷ÁPzv¾® PhUQÓõº GÛÀ, AÁµx ö©õzu £¯nzvß \µõ\›
÷ÁPzøuU PõsP.
A cyclist covers his first three kms at an average speed of 8 kmph. Another
two kms at 3 kmph and the last two kms at 2 kmph. Find the average speed for
the entire journey.

28. J¸ ]Ô¯ ¯õ£õµ {ÖÁÚzvÀ, A ©ØÖ® B GßÓ Cµsk umha\ºPÒ
{¯ªUP¨£mi-¸UQßÓÚº. umha\º A \µõ\›¯õP J¸ |õøÍUS 30 £UP[PøÍ
vmh »UP® 6 BP EÒÍÁõÖ umha_ ö\´QÓõº, umha\º B \µõ\›¯õP J¸
|õøÍUS 45 £UP[PøÍ, vmh »UP® 10 BP EÒÍÁõÖ umha_ ö\´QÓõº
GÛÀ, G¢u umha\º {ø»z ußø© Eøh¯Áº ?
In a small business firm, two typists are employed - typist A and typist B.
Typist A types out, on an average 30 pages per day with a standard deviation
of 6. Typist B on an average types out 45 pages with a standard deviation of 10.
Which typist shows greater consistency in his output ?

3
29. ©v¨¤kP ∫ x 3 dx .
1

3
3
Evaluate
∫ x dx .
1

7 6069

30. J¸ ½¨ Bsk AÀ»õu \õuõµn Bsk \©Áõ´¨¦ •øÓ°À ÷uº¢öukUS®
÷£õx 53 bõ°ØÖ QÇø©PÒ AÀ»x 53 v[PÒ QÇø©PÒ Á¸ÁuØPõÚ
{PÌuPøÁU PõsP.
What is the chance that a non-leap year selected at random will contain 53
Sundays or 53 Mondays ?

31. J¸ |£º C¸ |õn¯[PøÍ J÷µ ÷|µzvÀ _skQÓõº. C¸ uø»PÒ ÂÊ¢uõÀ
AÁ¸US ` 4 &E®, J¸ uø» ÂÊ¢uõÀ ` 2 &® QøhUQÓx. BÚõÀ Cµsk÷© §
ÂÊ¢uõÀ AÁ¸US ` 3 CǨ£õQÓx, AÁ›ß Gvº£õºUP¨£k® C»õ£® PõsP.
A player tosses two coins, if two head appear he wins ` 4, if one head appears he
wins ` 2, but if two tails appear he loses ` 3. Find the expected sum of money he
wins.

32. X ~ U(200, 250) GÛÀ {PÌuPÄ Ahºzva \õº¦ (p.d.f.) ©ØÖ® P(X > 230) PõsP.
If X ~ U(200, 250) find its p.d.f. and P(X > 230).

33. RÌPsh AmhÁøn, J¸ ÁS¨¤À EÒÍ ©õnÁºPÒ J¸ £õhzvÀ ö£ØÓ
©v¨ö£s £µÁø» SÔUQÓx GßP.

©v¨ö£s 0-10 10-20 20-30 30-40 40-50

©õnÁºPÎß
5 15 22 10 8
GsoUøP

(i) GzuøÚ ©õnÁºPÒ 30 &US® RÌ ©v¨ö£sPøÍ ö£ØÔ¸UQÓõºPÒ ?
(ii) GzuøÚ ©õnÁºPÒ 40 AÀ»x 40 &US AvP©õÚ ©v¨ö£sPøÍ
ö£ØÔ¸UQÓõºPÒ ?
(iii) GzuøÚ \uÃu ©õnÁºPÎß ©v¨ö£sPÒ 10 - 20 GßÓ ¤›ÂÀ EÒÍx.
The following table is the distribution of marks of students of a class in a subject.

Marks 0-10 10-20 20-30 30-40 40-50
No. of students 5 15 22 10 8

(i) How many students have scored less than 30 ?
(ii) How many students have scored 40 or more than 40 ?
(iii) What is the percentage of students whose marks are in the class 10-20 ?

6069 8

£Sv & IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõÂØS® Âøh¯ÎUPÄ®. 5x5=25
Note : Answer all the questions.

34. (A) P.C. ©í»÷Úõ¤ì AÁºPÎß £[PΨø£¨ £ØÔ J¸ SÔ¨¦ ÁøµP.
AÀ»x
(B) £[Rmk (£køP) Áõ´¨¦ ©õv›U Po¨¦ •øÓ G¢u `Ì{ø»US EP¢u
•øÓ GÚU TÖP. Ax÷£õßÓ ©õv›ø¯ GÆÁõÖ ÷uº¢öuk¨£õ´ ? J¸
GkzxUPõmkhß ÂÁ›UPÄ®.
(a) Write a brief note on the contributions by P.C. Mahalanobis.
OR
(b) Under what circumstances stratified random sampling procedure is
considered appropriate ? How would you select such a sample ? Explain by
means of an example.

35. (A) Tøh¨£¢x ÷£õmi°À ö£ØÓ ö©õzu ¦ÒÎPÎß ÂÁµzvØS usk &
Cø»¨£vÄ JßøÓ Aø©UPÄ®.
216, 223, 183, 219, 228, 200, 217, 208, 195, 172, 210, 213, 208, 192, 197,
185, 213, 219.
AÀ»x
(B) R÷Ç öPõkUP¨£mh uµÄPÒ (` ¡ÔÀ) J¸ Sk®£zvß ö\»ÂÚ[PøÍU
SÔ¨¤kQÓx. CuØS Ámh ÂÍUP¨£h® ÁøµP.

CÚ[PÒ ö\»Ä (` ¡ÔÀ)
EnÄ 87

Eøh 24

ö£õÊx÷£õUS 11

PÀÂ 13

ÁõhøP 25

Cuµ ö\»ÄPÒ 20

÷©¾®
(i) PÀ ö\»ÂØPõÚ ÁmhU ÷Põn¨ £Sv°À ÷Põn® PõsP.
(ii) ÁõhøPUS® ö£õÊx ÷£õUQØS® Cøh÷¯ EÒÍ ÷Põn ÷ÁÖ£õmøh
PõsP.

9 6069

(a) The total scores in a series of basketball matches were 216, 223, 183, 219,
228, 200, 217, 208, 195, 172, 210, 213, 208, 192, 197, 185, 213, 219. Construct
a stem and leaf plot for the given data.
OR
(b) Draw a pie diagram for the following data (in hundreds) of house hold
expenditure of a family.

Items Expenditure ( ` 100)
Food 87
Clothing 24
Recreation 11
Education 13
Rent 25
Miscellaneous 20

Also find
(i) The central angle of the sector corresponding to the expenditure
incurred on education.
(ii) Find the angle difference between rent and recreation cost.

36. (A) J¸ £Sv°À Á]US® ©UPÎß Á¯x £ØÔ¯ uµÄPÒ RÌUPsh
AmhÁøn°À uµ¨£mkÒÍÚ. Av¼¸¢x Cøh{ø» PõsP.

Á¯x (BskPÎÀ) GsoUøP (B°µzvÀ)
10&US RÌ 2

20&US RÌ 5

30&US RÌ 9

40&US RÌ 12

50&US RÌ 14

60&US RÌ 15

70&US RÌ 15.5

80&US RÌ 15.6

AÀ»x

6069 10

(B) PõÀ©õÚ Â»UP® ©ØÖ® PõÀ©õÚ Â»UPU öPÊ PõsP.
¤›Ä CøhöÁÎ 10-15 15-20 20-25 25-30 30-35

¤›Ä CøhöÁÎ
8 12 14 10 6
{PÌöÁs
(a) The following table shows age distribution of persons in a particular region.

Age (years) No. of persons (in thousands)
Below 10 2
Below 20 5
Below 30 9
Below 40 12
Below 50 14
Below 60 15
Below 70 15.5
Below 80 15.6
Find the median age.
OR
(b) Calculate the quartile deviation and its coefficient from the following
data :
Class interval 10-15 15-20 20-25 25-30 30-35
Frequency 8 12 14 10 6

37. (A) J¸ £ÒΰÀ EhØPÀ B]›¯º £o°hzvØPõÚ ÷|º•Pz ÷uºÄUS
v¸. AÔÁÇPß, v¸. CÍÁµ\ß, v¸. Aߣµ\ß BQ÷¯õº P»¢x
öPõshÚº. v¸. AÔÁÇPß ÷uº¢öukUP¨£- k - Á uØPõÚ Áõ´¨¦ 45% .
v¸. CÍÁµ\ß ÷uº¢öukUP¨£kÁuØPõÚ Áõ´¨¦ 28% ©ØÖ®
v¸. Aߣµ\ß ÷uº¢öukUP¨£kÁuØPõÚ Áõ´¨¦ 27% BS®.
v¸. AÔÁÇPß ÷uº¢öukUP¨£mhõÀ Tmk EhØ £°Ø] (Mass-Drill-MD)
{PÌa]ø¯ ö\¯À£kzu Áõ´¨¦ 42% . C÷u÷£õßÖ CÍÁµ\ÝUS 40%
©ØÖ® Aߣµ\ÝUS 48% Áõ´¨¦ EÒÍx GÛÀ ¤ßÁ¸ÁÚÁØÔØS
{PÌuPÄ PõsP.
(i) v¸. AÔÁÇPß EhØPÀ B]›¯µõP {¯ªUP¨£h
(ii) v¸. CÍÁµ\ß EhØPÀ B]›¯µõP {¯ªUP¨£h
(iii) v¸. Aߣµ\ß EhØPÀ B]›¯µõP {¯ªUP¨£h
AÀ»x

11 6069

(B) J¸ ö£mi°À 8 ö£õ¸mPÎÀ Cµsk SøÓ£õkÒÍ ö£õ¸mPЮ EÒÍÚ.
Cv¼¸¢x ‰ßÖ ö£õ¸mPÒ Áõ´¨¦ •øÓ°À v¸®£ øÁUPõ©À
GkUP¨£kQßÓÚ GÛÀ SøÓ£õkÒÍ ö£õ¸mPÎß GsoUøP°ß \µõ\›
PõsP.
(a) Mr. Arivazhagan, Mr. Ilavarasan and Mr. Anbarasan attended an interview
conducted for appointing a physical teacher in a school. Mr. Arivazhagan
has 45% chance for selection, Mr. Ilavarasan has 28% chance and
Mr. Anbarasan has 27% chance. Also, the chance for implementing monthly
Mass Drill (MD) programme in school is 42% if Mr. Arivazhagan is appointed;
40% if Mr. Ilavarasan is appointed; and 48% if Mr. Anbarasan is appointed.
Find the probability that the mass drill is implemented by if :
(i) Mr. Arivazhagan is appointed as the Physical Education Teacher.
(ii) Mr. Ilavarasan is appointed as the Physical Education Teacher.
(iii) Mr. Anbarasan is appointed as the Physical Education Teacher.
OR
(b) A box contains 8 items of which 2 are defective. A man select 3 items at
random without putting it back in the box. Find the average of the expected
number of defective items he has drawn.

38. (A) X Gߣx \µõ\› 2 ©ØÖ® vmh»UP® 3 Eøh¯ J¸ C¯À{ø» £µÁø»U
öPõsh ©õÔ GßP. \µõ\›°¼¸¢x X &ß J¸ ©v¨¦ x 1 Áøµ²ÒÍ
CøhöÁÎUPõÚ {PÌuPÄ 0.4115 GÛÀ, A®©v¨¦ x1 &IU PõsP.
AÀ»x
(B) Kº D¸Ö¨¦¨ £µÁ¼ß ÷PõmhAÍÄ ©ØÖ® umøh¯ÍÄ •øÓ÷¯
1/6 ©ØÖ® −11/36 GÛÀ A¢u D¸Ö¨¦¨ £µÁø»U PõsP.
(a) X has normal distribution with mean 2 and standard deviation 3. Find the
value of the variable x, such that the probability of the interval from the
mean to that value is 0.4115.
OR
(b) The skewness and kurtosis of a binomial distribution are 1/6 and −11/36
respectively. Find the Binomial distribution.

-o0o-