TN 11th Question Paper 2023 Statistics

Tamil Nadu
State Board

2023
QUESTION
PAPER

No. of Printed Pages : 12
6769
!6769IstYearStatistics! £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.

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1. £h[PøÍ, |ßÖ, £µÁõ°Àø», ÷©õ\® GÚ uµªkÁx :
(A) CøhöÁÎ AÍÄ (B) £s¦ AÍÄ
(C) ÂQu AÍÄ (D) Á›ø\ AÍÄ
The rating of movies as good, average and bad is :
(a) Interval scale (b) Nominal scale
(c) Ratio scale (d) Ordinal scale

2. RÌUPshÁØÖÒ G¢u uµÄ ö£Ö® •øÓ, •uÀ{ø» uµÄ •øÓø¯a \õº¢ux
AÀ» ?
(A) A¸Pø©¢u B´ÁõÍøµU öPõsk uµÄ ö£Ö® •øÓ
(B) ÂÚõ£mi¯À öPõsk uµÄ ö£Ö® •øÓ
(C) ©øÓ•P B´Âß ‰»® uµÄPÒ ö£Ö® •øÓ
(D) öÁΰh¨£mh Buõµ[Pμ¸¢x uµÄPÒ ö£Ó¨£k® •øÓ
Which one of the method is not a primary data collection method ?
(a) Local correspondent method
(b) Questionnaire Method
(c) Indirect investigation
(d) Data collected from published sources

3. uµÄPøÍ, |õk, ©õ{»®, |Pµ®, ©õÁmh® ÷£õßÓÁØøÓ Ai¨£øh¯õPU
öPõsk ÁøP¨£kzxÁx __________ BS®.
(A) Ch®\õº ÁøP¨£kzxuÀ (B) Põ»®\õº ÁøP¨£kzxuÀ
(C) AÍÂß ‰»® ÁøP¨£kzxuÀ (D) £s¦\õº ÁøP¨£kzxuÀ
The method of classifying data with reference to location such as countries,
states, cities, districts, etc., is called as __________.
(a) Spatial classification (b) Chronological classification

(c) Quantitative classification (d) Qualitative classification

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4. 5-10, 10-15, 15-20, 20-25, 25-30 GÝ® ¤›Ä CøhöÁÎPøÍU öPõsh
SÊÂÚõÀ Aø©UP¨£k® {PÌöÁs £µÁÀ :
(A) uºzxU PnUQk® •øÓ (B) vÓ¢u ¤›öÁÀø» •øÓ
(C) ÷\ºzxU PnUQk® •øÓ (D) CÁØÖÒ HxªÀø»
The class interval of the type 5-10, 10-15, 15-20, 20-25, 25-30 represents :
(a) exclusive type (b) open-end type
(c) inclusive type (d) none of the above

5. ¤ßÁ¸® ÂÍUP¨£h[PÎÀ Gx uµÄPøÍ E¸Á[PÒ ‰»® ÂÍUSQÓx ?
(A) Ámh ÂÍUP¨£h® (B) E¸Á ÂÍUP¨£h®
(C) £µÁÀ ö\ÆÁP¨£h® (D) ö£›m÷hõ Áøµ£h®
Which one of the following diagrams, use pictures to represent the data ?
(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) Tmka \µõ\›
(C) Cøh{ø» (D) ö£¸US \µõ\›
Intersection of less than Ogive and more than Ogive gives __________.
(a) Mode (b) Arithmetic Mean
(c) Median (d) Geometric Mean

7. •uÀ 11 C¯À GsPÎß ÁºUP[PÎß \µõ\› :
(A) 48 (B) 46 (C) 42 (D) 23
The mean of the squares of first eleven natural numbers is :

(a) 48 (b) 46 (c) 42 (d) 23

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8. \µõ\›US®, •PkUS® EÒÍ Âzv¯õ\® 35 ©ØÖ® vmh »UP® 10 GÛÀ
÷PõmhUöPÊ :
(A) 3.5 (B) 2.5 (C) 6.5 (D) 1.5
If the difference between the mean and the mode is 35 and the standard deviation
is 10, then the coefficient of skewness is :

(a) 3.5 (b) 2.5 (c) 6.5 (d) 1.5

9. “DATE” GßÓ ö\õÀ¼¾ÒÍ GÊzxUPøÍU öPõsk E¸ÁõUP¨£k® öÁÆ÷ÁÓõÚ
|õßöPÊzx ö\õØPÎß GsoUøP :
(A) 24 (B) 4 (C) 48 (D) 8
The number of different four letter words that can be formed with the word
“DATE” is :

(a) 24 (b) 4 (c) 48 (d) 8

10. J¸ £Pøh Ã_®÷£õx 3 QøhUPõ©À C¸UP {PÌuPÄ :

(A) 1 (B) 1 (C) 1 (D) 5
6 3 4 6

Probability of not getting 3 when a dice is thrown is :

1 1 1 5
(a) (b) (c) (d)
6 3 4 6

11. F(x ) Gߣx J¸ £µÁÀ \õº£õÚõÀ, F(−∞) Gߣx __________.

(A) 1 (B) 1 (C) 0 (D) 1
4 2

If F(x ) is a distribution function, then F(−∞) is __________.

1 1

(a) (b) 1 (c) 0 (d)
4 2

5 6769

12. J¸ ö£ºöÚͼ £µÁ¼À •¯Ø]PÎß GsoUøP __________.

(A) 4 (B) 2 (C) 3 (D) 1
Number of trials in a Bernoulli distribution is __________.

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

13. N (µ, σ2) ß ÷PõmhÍÄ ©ØÖ® umøh¯ÍÄPÒ :

(A) 0, 2 (B) 0, 1 (C) 0, 0 (D) 0, 3
Skewness and Kurtosis of N (µ, σ2) are :

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

1
∫x
10
14. dx &Cß ©v¨¦ ___________.
0

(A) 1 (B) 1 (C) 10 (D) 11
9 11

1
The value of ∫ x
10
dx is :
0

1 1
(a) (b) (c) 10 (d) 11
9 11

15. φ Gߣx |hUP C¯»õu {PÌa] GÛÀ, p(φ) &ß ©v¨¦ __________.

(A) 0.1 (B) 1 (C) 0 (D) 0.5
If φ is an impossible event then p(φ)= __________.

(a) 0.1 (b) 1 (c) 0 (d) 0.5

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6769 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. ¦Òΰ¯À Gߣøu Áøµ¯ÖUPÄ®.
Define Statistics.

17. ©õv›ø¯ Áøµ¯ÖUPÄ®.
Define Sample.

18. Ámh ÂÍUP¨£hzvß TÖPÎß ÷Põn[PÒ Põs£uØPõÚ `zvµzøu GÊxP.
Write down the formula used for computing the angles of the components in Pie
diagram.

19. {øÓ°mh Tmk \µõ\›ø¯ £ØÔ _¸UP©õP GÊxP.
Express Weighted Arithmetic Mean in brief.

20. Pmh ÂÍUP¨£hzvÀ £¯ß£k® AÍøÁPÒ ¯õøÁ ?
Write the measures used in box plot.

21. ©v¨¤kP
4x−1
lim
x→1 x+2

Evaluate the following limits.

4x−1
lim
x→1 x+2

22. \õº£ØÓ {PÌa]PÐUPõÚ ö£¸UPÀ ÷uØÓzøu GÊxP.

State the Multiplication theorem of probability for independent events.

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23. Kº D¸Ö¨¦ £µÁ¾UPõÚ {£¢uøÚPøÍU TÖP.
State the conditions of a Binomial Distribution.

24. X &ß {PÌuPÄ £µÁÀ ¤ßÁ¸©õÖ :

X 0 1 2 3 4 5
P (X = x ) k 2k 5k 7k 3k 4k

‘k’ &Cß ©v¨ø£U PõsP.
If a random variable X has the following probability distribution.

X 0 1 2 3 4 5
P (X = x ) k 2k 5k 7k 3k 4k

Find the value of ‘k’.

£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. •uÀ {ø» ©ØÖ® Cµshõ® {ø» uµÄPÎß ÷ÁÖ£õmøhU TÖP.
Distinguish between Primary data and Secondary data.

26. AmhÁøn°ß £¯ßPÒ ¯õøÁ ?
What are the advantages of tables ?

27. ÂÍUP¨£h® ©ØÖ® Áøµ£h® ÁøµÁuØPõÚ •UQ¯zxÁzøu GÊxP.
Write down the significance of Diagrams and Graphs.

28. \©a^µØÓ £µÁ¼ß •Pk ©ØÖ® \µõ\› •øÓ÷¯ 32.1 ©ØÖ® 35.4 GÛÀ
Cøh{ø» AÍÄ PõsP.

In a moderately asymmetrical distribution the values of mode and mean are 32.1
and 35.4 respectively. Find the median value.

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6769 8

29. ]Ó¢u ]uÓÀ AÍøÁ°ß £s¦PÒ ¯õøÁ ?
What are the requisites of a good measure of Dispersion ?

30. 10Pr=720 GÛÀ r &ß ©v¨¦ GßÚ ?
If 10Pr=720, find the value of r.

 
31. P(A) =
1 4
, P (B) = ©ØÖ® P (A ∪ B) =
2
GÛÀ P  A  &ø¯U PõsP.
7 7 7 B

1 4 2 A
If P(A) = , P (B) = and P (A ∪ B) = , then find the value of P   .
7 7 7 B

32. J¸ ^mkUPmiÀ EÒÍ 52 ^mkPÎÀ 4 ^mkPÒ JßÓß¤ß JßÓõP v¸®£
øÁUS® •øÓ°À GkUP¨£kQÓx GÛÀ, CµõáõUPÎß GsoUøP°ß \µõ\›
©ØÖ® ©õÖ£õkPøÍU PõsP.
From the pack of 52 cards, 4 cards are drawn one after another with replacement.
Find the Mean and Variance of the distribution of the number of Kings.

33. RÌPsh ÂÁµ[PÐUS usk&Cø»¨ £vøÁ Aø©UPÄ®.
267, 269, 283, 295, 254, 251, 250, 287, 273.
Construct a Stem and Leaf plot for the given data.
267, 269, 283, 295, 254, 251, 250, 287, 273.

£Sv & IV / PART – IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 5x5=25
Note : Answer all the questions.
34. (A) ¦Òΰ¯¼ß £oPøͨ £ØÔ ÂÍUPÄ®.
AÀ»x
(B) ÂÚõ£mi¯À u¯õ›zu¼À EÒÍ ÁÈPõmkuÀ GßÚ ? ÷©¾® AÁØøÓ¨
£ØÔ ÂÁ›UPÄ®.
(a) Explain the functions of Statistics.
OR

(b) What are the guiding considerations in the construction of questionnaire ?
Explain.

9 6769

35. (A) ÁøP¨£kzxu¼ß £À÷ÁÖ ÁøPPøÍ ÂÍUPÄ®.

AÀ»x

(B) J¸ £ÒΰÀ 11 &B® ÁS¨¦ £iUS® ©õnÁºPÒ ö£ØÓ ©v¨ö£sPÒ
AmhÁøn°À öPõkUP¨£mkÒÍÚ. CzuµÄPÐUS ÷©¼Ú SÂÄ
{PÌöÁs ÁøÍ÷Põk ÁøµP.

©v¨ö£sPÒ 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

©õnÁºPÎß
2 4 9 10 8 5 3 2
GsoUøP

(i) 33 ©v¨ö£sPÐUS ÷©À ö£ØÓ ©õnÁºPÎß GsoUøPø¯
©v¨¤kP.

(ii) uµÄUS Cøh{ø» AÍÄ Psk¤iUPÄ®.

(a) Explain various types of classification.

OR

(b) Draw more than Ogive Curve for the following data showing the marks secured
by the students of class XI in a School.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of Students 2 4 9 10 8 5 3 2

(i) Estimate the total number of students who secured marks more than
33.

(ii) Find the median of the data.

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36. (A) J¸ ÷uºÂÀ •uÀ ¤›ÂÀ 3 ÂÚõUPЮ, Cµshõ® ¤›ÂÀ 3 ÂÚõUPЮ,
‰ßÓõ® ¤›ÂÀ 2 ÂÚõUPЮ ÷PmP¨£kQßÓÚ. JÆöÁõ¸ ¤›Â¾®

SøÓ¢u£m\® J¸ ÂÚõøÁz öu›Ä ö\´x ö©õzu® 5 ÂÚõUPÐUS Âøh
uµ ÷Ásk®. AÆÁõöÓÛÀ ÷uºÄ GÊx® ©õnÁº GzuøÚ ÁÈPÎÀ
ÂÚõUPøÍz öu›Ä ö\´¯»õ® ?

AÀ»x

(B) öPõkUP¨£mkÒÍ J÷µ ©õv›¯õÚ I, II ©ØÖ® III BQ¯ ‰ßÖ ö£miPÎÀ
JÆöÁõ¸ ö£mi°¾® Cµsk |õn¯[PÒ EÒÍÚ. ö£mi I &CÀ, Cµsk

u[P |õn¯[PЮ, ö£mi & II &CÀ Cµsk öÁÒÎ |õn¯[PЮ, ö£mi
III &CÀ J¸ u[P |õn¯® ©ØÖ® J¸ öÁÒÎ |õn¯•® EÒÍÚ. J¸

ö£miø¯ \©Áõ´¨¦ •øÓ°À ÷uºÄ ö\´x J¸ |õn¯® GkUP¨£kQÓx.

Ax u[P |õn¯©õP C¸¢x ö£mi°À EÒÍ ©ØöÓõ¸ |õn¯•® u[P
|õn¯©õP C¸UP {PÌuPÄ PõsP.

(a) There are 3 questions in the first section, 3 questions in the second section

and 2 questions in the third section in a question paper of an exam. The
student has to answer any 5 questions, choosing atleast one from each
section. In how many ways can the student answer the exam ?

OR

(b) Given three identical boxes I, II and III each containing two coins. In box I,
both coins are gold coins. In box II, both are silver coins and in the box III,
there is one gold and one silver coin. A person chooses a box at random and

takes out a coin. If the coin is of gold, what is the probability that the other

coin in the box is also of gold.

11 6769

37. (A) x GßÓ öuõhº Áõ´¨¦ ©õÔUPõÚ {PÌuPÄ Ahºzva \õº¦ :

x
 , 0<x <2
f ( x )=  2
0, ©ØöÓ[S®


GÛÀ, \µõ\›²®, ©õÖ£õk® PõsP.

AÀ»x

(B) Põ¨¦ F] (safety pin) u¯õ›US® {ÖÁÚzvÀ SøÓ£õkÒÍ J¸ Põ¨¦
F]ø¯ Põs£uØPõÚ {PÌuPÄ 0.04 GÛÀ.

(i) 100 Põ¨¦ F] EÒÍ J¸ ö£mi°À 1 SøÓ£õkÒÍ Põ¨¦ F]
C¸¨£uØPõÚ {PÌuPÄ.

(ii) Cx÷£õßÓ 200 ö£miPÎÀ GÆÁÍÄ ö£miPÎÀ SøÓ£õhØÓ Põ¨¦
F]PÒ EÒÍÚ. [e−4=0.0183]

(a) The p.d.f. of a continuous random variable x is given by :

x
 , 0<x <2
f (x )=  2
0, elsewhere

Find its Mean and Variance.

OR

(b) The probability of safety pin manufactured by a firm to be defective is 0.04.

(i) Find the probability that a box containing 100 such pins has one defective
pin.

(ii) Among 200 such boxes, how many boxes will have no defective pin.

[e−4=0.0183].

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38. (A) ¤ßÁ¸® ÂÁµ[Pμ¸¢x P70 &ß ©v¨¦ PõsP.

¤›Ä CøhöÁÎ 10-20 20-30 30-40 40-50 50-60
{PÌöÁs 18 25 31 42 20

AÀ»x
(B) vmh»UP® PõsP : 43, 52, 70, 38, 62.
(a) Calculate P70 for the following data.

Class Interval 10-20 20-30 30-40 40-50 50-60
Frequency 18 25 31 42 20

OR
(b) Calculate Standard Deviation for the following data : 43, 52, 70, 38, 62.

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