TN 11th Question Paper 2024 Statistics

TN PUBLIC EXAM

QUESTION
PAPER
2024

No. of Printed Pages : 12
7669
!7669IstYearStatistics! £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¢öukzx 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.

[ v¸¨¦P / Turn over

7669 2

1. J¸ |õhõЩßÓ ¤µv{v°ß ö£¯øµU SÔ¨¤kÁx __________ AÍÃk.
(A) CøhöÁÎ AÍÄ (B) £s¦ AÍÄ
(C) ÂQu AÍÄ (D) Á›ø\ AÍÄ
The name of the representative in Parliament is in __________ measurement.
(a) Interval Scale (b) Nominal Scale
(c) Ratio Scale (d) Ordinal Scale

2. B´Áõͺ J¸ {ÖÁÚzvß uµÂøÚ¨ £¯ß£kzxQÓõº GÛÀ, AzuµÁõÚx
__________ GÚ AøÇUP¨£kQÓx.
(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. uµÄ ©v¨¦PÐhß AøÁ Ch® ö£Ö® GsoUøPø¯²® ÷\ºzx Aø©UP¨£k®
£mi¯À :
(A) {PÌöÁs ÁøÍÁøµ
(B) AmhÁøn
(C) SÂÄ {PÌöÁs £µÁÀ
(D) {PÌöÁs £µÁÀ
An arrangement of data values together with the number of occurrences forms a :
(a) frequency curve
(b) table
(c) cumulative frequency distribution
(d) frequency distribution

4. uµÄPøÍ AÁØÔß £s¦PÐU÷PØÓ •øÓ°À ÁøP¨£kzx® •øÓ __________
GÚ AøÇUP¨£kQÓx.
(A) £s¦\õº ÁøP¨£kzxuÀ (B) Põ»®\õº ÁøP¨£kzxuÀ
(C) Gs\õº ÁøP¨£kzxuÀ (D) Ch®\õº ÁøP¨£kzxuÀ
The method of classifying statistical data on the basis of descriptive characteristics is called
__________.
(a) Qualitative classification (b) Chronological classification
(c) Quantitative classification (d) Geographical classification

3 7669

5. £À A[P £møh ÂÍUP¨£hzvÀ £møhPÒ __________ C¸UQßÓÚ.
(A) TÖPÍõPÄ®, Akzukzx® (B) TÖPÍõP
(C) TÖPÍõPÄ®, \©©õPÄ® (D) Akzukzx
The bars are __________ in multiple bar diagram.
(a) Placed adjacently and sub-divided (b) Sub-divided
(c) Sub-divided and are of equal height (d) Placed adjacently

6. J¸ {PÌöÁs £µÁ¼À •Pk Gߣx :
(A) ö£¸© {PÌöÁs (B) {PÌöÁs JßÖ
(C) ]Ö© {PÌöÁs (D) CÁØÔÀ HxªÀø»
Mode is that value in a frequency distribution which possesses :
(a) maximum frequency (b) frequency one
(c) minimum frequency (d) none of the above

7. AvP©õÚ ]uÓÀ öPõsh uµÂÀ :
(A) vmh»UP® AvP®
(B) \µõ\› ©ØÖ® Cøh{ø»UQøh÷¯ AvP Âzv¯õ\®
(C) CøhUPõÀ©õÚ Ãa_ SøÓÄ
(D) •Pk ©v¨¦ AvP®
In a more dispersed (spread out) set of data :
(a) Standard deviation is greater
(b) Difference between the mean and the median is greater
(c) Inter-Quartile range is smaller
(d) Value of the mode is greater

8. Cøh{ø»US ÷©À ©ØÖ® RÌ Aø©²® uµÄPÎß GsoUøP __________.
(A) 75% (B) 25% (C) 90% (D) 50%
The number of observations lies above and below the median value is __________.
(a) 75% (b) 25% (c) 90% (d) 50%

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7669 4

1

∫ x dx Gߣx :
9. 3

0

1 1
(A) 1 (B) 4 (C) 3 (D) 2

1

∫ x dx is :
3

0

1 1
(a) 1 (b) (c) 3 (d)
4 2

10. ex &Cß ÁøPUöPÊ __________.
(A) e−x (B) ex2 (C) xex (D) ex
The derivative of ex is equal to __________.
2
(a) e−x (b) ex (c) xex (d) ex

11. Gs 4 QøhUS® Áøµ J¸ £Pøh E¸mh¨£kQÓx GÛÀ, Auß TÖöÁÎ :
(A) Gsn C¯ßÓ •iÄÓõ Pn® (B) J¸ öÁØÖUPn®
(C) Gsn C¯»õu Pn® (D) Gsn C¯ßÓ •iÄÖ Pn®
In rolling of a die until 4 appears, the sample space is :
(a) a countable infinite set (b) a null set
(c) an uncountable set (d) a countable finite set

10
12. A ©ØÖ® B Gß£Ú C¸ {PÌa]PÒ. ÷©¾® P (A U B) = GÛÀ
15
P(A I B) = __________.

1 2
(A) 1 (B) 3 (C) 0 (D) 3

10
If A and B are two events with P ( A U B ) = then P(A I B) =__________.
15

1 2
(a) 1 (b) (c) 0 (d)
3 3

5 7669

13. J¸ Áõ´¨¦ ©õÔ X &ß {PÌuPÄ £µÁÀ

X 0 1 2 3 4 5

1 1
P(X=x ) 2a 3a 4a 5a
4 4

GÛÀ, P(1£X£4) &Cß ©v¨¦ :
1 10 1 2
(A) 2 (B) 21 (C) 14 (D) 7
A random variable X has the following Probability distribution

X 0 1 2 3 4 5

1 1
P(X=x ) 2a 3a 4a 5a
4 4

Then P(1£X£4) is :
1 10 1 2
(a) (b) (c) (d)
2 21 14 7

14. X ~ U (a, b) GÛÀ, Auß ©õÖ£õk :

( b − a )2 a+ b a + 3b 3a + b
(A) (B) (C) (D)
12 2 4 4
If X ~ U (a, b) then its variance is __________.

( b − a )2 a+ b a + 3b 3a + b
(a) (b) (c) (d)
12 2 4 4

15. J¸ £õ´éõß £µÁ¼À :
(A) \µõ\› > ©õÖ£õk (B) \µõ\› = ©õÖ£õk
(C) \µõ\› ≠ ©õÖ£õk (D) \µõ\› < ©õÖ£õk
In a Poisson distribution :
(a) Mean > Variance (b) Mean = Variance
(c) Mean ≠ Variance (d) Mean < Variance

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7669 6

£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. uµÄPÒ Gߣuß ö£õ¸Ò GßÚ ?
What is the meaning of data ?

17. ©õv›U Po¨¦ ¤øÇø¯ Áøµ¯ÖUPÄ®.
Define Sampling error.

18. ÁøP¨£kzxuø» Áøµ¯ÖUPÄ®.
Define classification of data.

19. Áøµ£h[PÎß öÁÆ÷ÁÖ ÁøPPøÍ GÊxP.
List the various types of graphs.

20. 7 öÁÆ÷ÁÖ |õmPÎÀ J¸ £Ò롧 ¡»Pzv¼¸¢x öPõkUP¨£mh
¦zuP[PÎß GsoUøP 7, 9, 12, 15, 5, 4, 11. ¦zuP[PÎß GsoUøP°ß Tmka
\µõ\› PõsP.
The following data represent the number of books issued in a school library on selected from
7 different days 7, 9, 12, 15, 5, 4, 11. Find the mean number of books.

21. J¸ uµÄzöuõSv°ß ©õÖ£õmkU öPÊ ©ØÖ® vmh»UP® •øÓ÷¯
50, 4 GÛÀ \µõ\› PõsP.
If the coefficient of variation is 50 percent and a standard deviation is 4, find the mean.

22. {£¢uøÚ {PÌuPøÁ Áøµ¯ÖUPÄ®.
Define Conditional Probability.

23. uÛzu Áõ´¨¦ ©õÔ°ß Pou Gvº£õºzuø» Áøµ¯ÖUPÄ®.
Define Mathematical Expectation of a discrete random variable.

24. ©v¨¤kP :& 5C3, 100C99.
Find 5C3, 100C99.

7 7669

£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. •ß ÷\õuøÚ – Áøµ¯ÖUPÄ®. Auß ]Ó¨¦PøÍU TÖP.
Define Pre-test and state its advantages.

26. öuõhº¦ SÂÄ {PÌöÁs £µÁÀ GßÓõÀ GßÚ ?
What is relative-cumulative Frequency Distribution ?

27. Ámh ÂÍUP¨£h® ÁøµÁuØPõÚ ÁÈ•øÓPøÍ GÊxP.
Write down the method of constructing Pie diagram.

28. 25, 48, 32, 52, 21, 64, 29, 57 GßÓ 8 ©õnÁºPÒ J¸ ÷uºÂÀ ö£ØÓ ©v¨ö£s
ÂÁµzvØS •uÀ PõÀ©õÚ®, ‰ßÓõ® PõÀ©õÚ® BQ¯ÁØøÓU PõsP.
Compute Q1 and Q3 for the data relating to the marks of 8 students in an examination given
below 25, 48, 32, 52, 21, 64, 29, 57

29. ]uÓø» ÂÁ›zx Auß £¯ß£õkPøÍ GÊxP.
Explain Dispersion and write their uses.

30. Kº AÖ[÷PõnzvÀ EÒÍ •øÚ¨¦ÒÎPøÍU öPõsk GzuøÚ
•U÷Põn[PøÍ E¸ÁõUP»õ® ?
How many triangles can be formed by joining the vertices of a hexagon ?

31. P(A)=0.35, P(B)=0.73 ©ØÖ® P(A∩B)=0.14 GÛÀ P(A U B) PõsP.

Given that P(A)=0.35, P(B)=0.73 and P(A∩B)=0.14, find P(A U B) .

32. J¸ £õ´éõß £µÁ¼À 3P(X=2)=P(X=4). λ &ß ©v¨¦ PõsP.
In a Poisson distribution 3P(X=2)=P(X=4). Find its parameter λ.

[ v¸¨¦P / Turn over

7669 8

Kx 4 , 0 < x < 1,
33. J¸ öuõhº \©Áõ´¨¦ ©õÔ X Gߣx f ( x ) =  GßÓ ÂvUSm£mk

 0 , ©ØÓ£i
{PÌuPÄ Ahºzv \õº¦ GÛÀ, K &ß ©v¨¦ PõsP.

A continuous random variable X has probability density function given by
Kx 4 , 0 < x < 1,
f (x) =  Find K.
 0 , otherwise

£Sv & IV / PART – IV

SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 5x5=25

Note : Answer all the questions.

34. (A) ÂÁ\õ¯® ©ØÖ® öuõÈÀxøÓ°À ¦Òΰ¯¼ß £¯ß£õkPøͨ £ØÔ
ÂÍUSP.

AÀ»x

(B) J¸ {ÖÁÚzvÀ u¯õ›UP¨£mh ÂÍUSPÎÀ 2% SøÓ£õkÒÍøÁ.
200 ÂÍUSPÒ öPõsh TÔÀ

(i) 2 ÂÍUSPÐUS® SøÓÁõP

(ii) 2 ÂÍUSPÐUS® ÷©»õP,

SøÓ£õkPÒ C¸¨£uØPõÚ {PÌuPÄPøÍU PõsP. [e−4=0.0183]

(a) State the applications of statistics in Agriculture and Industry.

OR

(b) If 2% of electric bulbs manufactured by a certain company are defective, find the
probability that in a sample of 200 bulbs.

(i) less than 2 bulbs are defective

(ii) more than 2 bulbs are defective [e−4=0.0183]

9 7669

35. (A) RÌPsh usk & Cø»¨ £v¼¸¢x \µõ\›, Cøh{ø» AÍÄ, •Pk, Ãa_
BQ¯ÁØøÓU PõsP.

usk Cø»
25 2 5
26 0 2
27 6 6 6
28 3 9
29 8

AÀ»x
(B) ‰ßÖ PÀ¿›PÎÀ £À÷ÁÖ CÍ[Pø» £mh¨£i¨¦ £iUS® ©õnÁºPÎß
GsoUøP°ß AmhÁøn R÷Ç öPõkUP¨£mkÒÍx.

£°¾® PÀ¿›
Bsk A B C

•u»õ® Bsk 450 350 400

Cµshõ® Bsk 250 250 350

‰ßÓõ® Bsk 225 200 300

öPõkUP¨£mh uµÄPÐUS TÖ£møh ÂÍUP¨£h® ÁøµP.
(a) Determine the mean, median, mode and the range on the stem and leaf plot given
below.

Stem Leaf
25 2 5
26 0 2
27 6 6 6
28 3 9
29 8

OR

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7669 10

(b) The number of students studying various undergraduate degree programmes in three
colleges are given in the following table :

College
Year of Study
A B C

First Year 450 350 400

Second Year 250 250 350

Third Year 225 200 300

Draw sub-divided bar diagram.

36. (A) RÌUPsh ÂÁµ[PÐUSU PõÀ©õÚ[PÒ Q1 ©ØÖ® Q3 PõsP.

SÊUPÒ 30 - 32 32 - 34 34 - 36 36 - 38 38 - 40 40 - 42 42 - 44

{PÌöÁs 12 18 16 14 12 8 6

AÀ»x
(B) R÷Ç öPõkUP¨£mh ÂÁµ[PÐUS vmh»UP® PõsP.

x 1 2 3 4 5 6 7
{PÌöÁs 10 20 30 35 14 10 2

(a) Calculate the Quartiles Q1 and Q3 for the data given below.

Group 30 - 32 32 - 34 34 - 36 36 - 38 38 - 40 40 - 42 42 - 44
Frequency 12 18 16 14 12 8 6

OR

(b) Find the standard deviation for the distribution given below :

x 1 2 3 4 5 6 7
Frequency 10 20 30 35 14 10 2

11 7669

37. (A) x &I¨ ö£õÖzx öuõøP°kP.
1
(i) x7 (ii)
x6

(iii) x (iv) x 5−4x 2+3x+2

AÀ»x
(B) 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¨£kÁuØPõÚ 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] {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
(a) Integrate the following with respect to x.

1
(i) x7 (ii)
x6

(iii) x (iv) x 5−4x 2+3x+2

OR
(b) Mr. Arivazhagan, Mr. Ilavarasan and Mr. Anbarasan attended an interview conducted
for appointing a Physical Education 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 Programme in the 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.

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7669 12

38. (A) J¸ Áõ´¨¦ ©õÔ ¤ßÁ¸® {PÌuPĨ £µÁø»¨ ö£ØÔ¸UQÓx.

X 0 1 2 3 4 5 6 7 8
P(x ) a 3a 5a 7a 9a 11a 13a 15a 17a

(i) ‘a’ &ß ©v¨¦ PõsP.

(ii) ©v¨¥k PõsP :
(A) P(X < 3)
(B) P(X/5)
(C) P(3£X£7)

AÀ»x
(B) ©õv›U Po¨¦ \õµõ ¤øÇPøÍ ÂÁ›zx GÊxP.
(a) A random variable has the following distribution function.

X 0 1 2 3 4 5 6 7 8
P(x ) a 3a 5a 7a 9a 11a 13a 15a 17a

(i) Find the value of ‘a’.
(ii) Evaluate :
(A) P(X < 3)
(B) P(X/5)
(C) P(3£X£7)
OR
(b) Write an essay about non sampling errors.

-o0o-

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