Tamil Nadu 11th Std Model Question Paper 2026 Statistics

Tamil Nadu Board Model Question Paper

No. of Printed Pages : 11
8469
!8469IstYearStatistics! £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.

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1. C¢v¯¨ ¦Òΰ¯À {ÖÁÚzøu (ISI) ÷uõØÖÂzuÁº __________.
(A) _Põz÷© (B) P.C. ©íõ»÷Úõ¤ì
(C) ÂÀ¼¯® ¤÷ÍL÷£º (D) PõºÀ ¤¯ºéß
The founder of Indian Statistical Institute (ISI) is __________.
(a) Sukhatme (b) P.C. Mahalanobis
(c) William Playfair (d) Karl Pearson

2. RÌPshÁØÖÒ 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 methods is not a primary data collection method ?
(a) Local correspondent method
(b) Questionnaire method
(c) Indirect investigation
(d) Data collected from Published sources

3. ÂÚõ¨£mi¯À öPõsk uµÄPÒ ÷\P›US® •øÓ°À, RÌUPshÁØÖÒ Gx
uÁÓõÚx ?
(A) uPÁÀ ö£Ö® ÂQu® ªP SøÓÁõP C¸UP»õ®
(B) SøÓ¢u ÷|µzvÀ ö£¸® £Sv°À uµÄ ö£ÖuÀ
(C) uPÁÀ AΨ£Á›ß ÂÁµ® µP]¯©õP £õxPõUP¨£k®
(D) C®•øÓ°øÚ G¢uöÁõ¸ uPÁÀ AΨ£Á›hzv¾® £¯ß£kzu •i²®
Which one is false in the questionnaire method ?
(a) Response rate may be low
(b) Vast coverage in less time
(c) It offers greater anonymity
(d) This method can be adopted to any respondent

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

5. Ámh ÁiÁ Áøµ£h® Gߣx __________ GÚ AøÇUP¨£kQÓx.
(A) Ámh ÂÍUP¨£h®
(B) E¸Á ÂÍUP¨£h®
(C) ö£›m÷hõ Áøµ£h®
(D) £µÁÀ ö\ÆÁP¨£h®
Circular diagram is known as __________.
(a) Pie diagram
(b) Pictogram
(c) Pareto diagram
(d) Histogram

6. RÈÚ SÂÄ {PÌöÁs ÁøÍ÷Põk®, ÷©¼Ú SÂÄ {PÌöÁs ÁøÍ÷Põk®
öÁmiU öPõÒЮ ¦ÒÎ __________ BS®.
(A) \µõ\› (B) •Pk (C) ©õÖ£õk (D) Cøh{ø»
Intersection of less than Ogive and more than Ogive gives __________.
(a) Mean (b) Mode (c) Variance (d) Median

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7. uµÄPÒ AøÚzx® \©©õP C¸US®÷£õx A.M., G.M., ©ØÖ® H.M.
CÁØÔØQøh÷¯¯õÚ EÓÄ :
(A) A.M. < G.M. < H.M.
(B) A.M.=G.M.=H.M.
(C) A.M. > G.M. > H.M.
(D) A.M. < H.M. < G.M.
When all the observations are same, then the relation between A.M., G.M., and H.M., is :
(a) A.M. < G.M. < H.M.
(b) A.M.=G.M.=H.M.
(c) A.M. > G.M. > H.M.
(d) A.M. < H.M. < G.M.

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. vmh »UPzvØS \µõ\›°ß \uÃu® __________.
(A) CøhUPõÀ©õÚ Ãa_
(B) PõÀ©õÚ Â»UP®
(C) ÷PõmhU öPÊ
(D) ©õÖ£õmkU öPÊ
The expression of the Standard Deviation as a percentage of the Mean is the _________.
(a) Inter Quartile range
(b) Quartile deviation
(c) Skewness Coefficient
(d) Coefficient of Variation

5 8469

10. 20C18 &ß ©v¨¦ :
(A) 360 (B) 190 (C) 95 (D) 180
The value of 20C18 is :
(a) 360 (b) 190 (c) 95 (d) 180

11. x6 &ß ÁøPUöPÊ :

x7
(A) 6x 5 (B) 5x 5 (C) (D) 6x 6
7
Derivative of x6 is :

x7
(a) 6x 5 (b) 5x 5 (c) (d) 6x 6
7

12. J¸ ÁõµzvÀ v[PÒQÇø© Á¸ÁuØPõÚ {PÌuPÄ __________.
1 3 4 2
(A) 7 (B) 7 (C) 7 (D) 7
Probability of getting a Monday in a week is __________.
1 3 4 2
(a) (b) (c) (d)
7 7 7 7

13. A ©ØÖ® B Gß£Ú JßøÓö¯õßÖ Â»US® {PÌa]PÒ GÛÀ P(A∪B) Gߣx :
(A) P(A)+P(B)−P(A∩B) (B) P(A)+P(B)
(C) P(A) P(B) (D) P(A)−P(B)
If A and B are mutually exclusive events, then P(A∪B) is equal to :
(a) P(A)+P(B)−P(A∩B) (b) P(A)+P(B)
(c) P(A) P(B) (d) P(A)−P(B)

14. E(X+C)=8 ©ØÖ® E(X−C)=12 GÛÀ C &Cß ©v¨¦ :
(A) −4 (B) −2 (C) 2 (D) 4
Given E(X+C)=8 and E(X−C)=12 then C is equal to :
(a) −4 (b) −2 (c) 2 (d) 4

15. B(n, p) &ß \µõ\› ©ØÖ® ©õÖ£õk •øÓ÷¯ :

(A) np, npq (B) npq, np (C) npq , np (D) np, npq
The Mean and Variance of B(n, p) are :
(a) np, npq (b) npq, np (c) npq , np (d) np, npq

8469 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. {¦nzxÁ ©v¨¥mk AÔ¯¼À ¦Òΰ¯¼ß £¯ß£õkPøÍU TÖP.
Explain the role of Statistics in Actuarial Science.

17. ©õv›ø¯ Áøµ¯ÖUPÄ®.
Define Sample.

18. ÁøP¨£kzxu¼ß ÁøPPøÍ £mi¯¼kP.
List out various types of classification.

19. ÂÍUP¨£h® GßÓõÀ GßÚ ?
What is a diagram ?

20. Q1=30 Q2=45 Q3=50 GÚU öPõsk ö£Í¼°ß ÷PõmhU öPÊ Põs.
If Q1=30 Q2=45 Q3=50 find Bowley’s coefficient of Skewness.

21. J¸ ÷£õmi°À 10 ÷£º öPõsh SÊÂÀ GzuøÚ ÁÈPÎÀ •uÀ ©ØÖ®
Cµshõ® Ch® ÁÇ[P •i²® ?
In a competition, in how many ways can first and second place be awarded to 10 people ?

22. P(A1B)=0.3, P(B)=0.7 GÛÀ P(A/B) &ß ©v¨¦ PõsP.
If P(A1B)=0.3, P(B)=0.7 find the value of P(A/B).

23. f(x)=5x4, 0 < x < 1 Gߣx {PÌuPÄ Ahºzva \õº£õS©õ ?
Verify whether the following is a probability density function
f(x)=5x4, 0 < x < 1.

24. öPõkUP¨£mh uµÄPÐUS Cøh{ø» PõsP.
10, 12, 14, 18, 22, 26, 28, 29, 30
Find the Median for the given data.
10, 12, 14, 18, 22, 26, 28, 29, 30

7 8469

£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. ¦Òΰ¯¼ß Sn[Pøͨ £mi¯¼kP.
List the characteristics of Statistics.

26. ©õv›US®, ©õv›U Po¨¤ØS® EÒÍ ÷ÁÖ£õkPøͨ £mi¯¼kP.
Distinguish between Sample and Sampling.

27. AmhÁøn uµÄPøÍ, ÂÍUP¨£h® ©ØÖ® Áøµ£hzv¼¸¢x ÷ÁÖ£kzvU
Põmk® Cµsk ]Ó¨£õÚ ÷ÁÖ£õkPøÍ GÊxP.
Mention any two features of Tabulated Data distinguishing it from Diagrams and Graphs.

28. J¸ ÁS¨¤À 4 ©õnÁºPЮ, 3 ©õnÂPЮ EÒÍÚº. ©õnÁºPÒ ©ØÖ®
©õnÂPÎß \µõ\› ©v¨ö£sPÒ •øÓ÷¯ 20 ©ØÖ® 30 GÛÀ A¢u ÁS¨¤ß
\µõ\›ø¯U PõsP.
A class consists of 4 boys and 3 girls. The average marks obtained by the boys and girls are
20 and 30 respectively. Find the class average.

29. RÌPõq® ÂÁµ[PÐUS β2 Põs.
µ1=0 µ2=4 µ3=0 µ4=37.6

Find the value of β2 for the following data.
µ1=0 µ2=4 µ3=0 µ4=37.6

30. I¢x £UP[PøÍU öPõsh I[÷Põnzvß •øÚ¨ ¦ÒÎPøÍU öPõsk £À÷ÁÖ
ÁÈPÎÀ ÷\º¨£uõÀ GzuøÚ •U÷Põn[PÒ Aø©UP»õ® ?
How many triangles can be formed by joining the vertices of a pentagon of five sides ?

8469 8

31. Tmk {PÌuPÄ ÷uØÓzøu GÊxP.
State the Theorem on Total Probability.

32. ÁÇUP©õÚ SÔ±kPÎߣi, p J¸ D¸Ö¨¦ £µÁÀ ©õÔ X, n=6 ©ØÖ®
9P(x=4)=P(x=2) GÛÀ p &ß ©v¨¦ PõsP.

With usual notation find p for Binomial random Variable X if n=6 and 9P(x=4)=P(x=2).

1
33. J¸ D¸Ö¨¦¨ £µÁ¼À n=10 ©ØÖ® P = 5 GÛÀ A¨£µÁ¼ß \µõ\› ©ØÖ®
©õÖ£õk Põs.
1
In a Binomial distribution if n=10 and P = , find the Mean and Variance of the distribution.
5

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

34. (A) ¦Òΰ¯¼ß £oPøͨ £ØÔ ÂÍUSP.
AÀ»x
(B) 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® ?
(a) Explain the functions of Statistics.

OR

(b) 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 at least one from each section. In how many ways can the student
answer the exam ?

9 8469

35. (A) {PÌuPÄ \õµõ ©õv›U Po¨¦ GßÓõÀ GßÚ ? JÆöÁõßøÓ²® uUP
GkzxUPõmkhß ÂÍUSP.

AÀ»x

(B) R÷Ç öPõkUP¨£mkÒÍ ÂÁµ[PÐUS Pmh&ÂìPº £h® ÁøµP.

3, 5, 10, 11, 12, 16, 17, 17, 19, 20, 22

(a) What is Non-Probability Sampling ? Explain each one with the help of examples.

OR

(b) Draw Box-Whisker plot for the following.

3, 5, 10, 11, 12, 16, 17, 17, 19, 20, 22

36. (A) öPõkUP¨£mh uµÄPÐUS usk&Cø»¨ £vøÁ Aø©UP.

2.12, 2.14, 2.15, 2.17, 2.21, 2.23, 2.24, 2.31, 2.37, 2.40, 2.45, 2.57

AÀ»x

(B) öPõkUP¨£mkÒÍ J÷µ ©õv›¯õÚ ‰ßÖ I, II ©ØÖ® III ö£miPÎÀ
JÆöÁõ¸ ö£mi°¾® Cµsk |õn¯[PÒ EÒÍÚ. ö£mi I CÀ, Cµsk
u[P |õn¯[PЮ ö£mi II &À Cµsk öÁÒÎ |õn¯[PЮ, ö£mi III &À
J¸ u[P |õn¯•®, 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) Construct a stem and leaf plot for the given data :

2.12, 2.14, 2.15, 2.17, 2.21, 2.23, 2.24, 2.31, 2.37, 2.40, 2.45, 2.57

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 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.

8469 10

37. (A) RÌPsh uµÄPÐUS (¹&¡ÔÀ) Ámh ÂÍUP¨£h® ÁøµP.
CÚ[PÒ EnÄ ÷£õUS ÁõhøP ªß Cuµ PÀÂ
Áµzx Pmhn® ö\»Ä
ö\»Ä 15 3 10 2 10 20

AÀ»x

(B) X &ß {PÌuPÄ £µÁÀ R÷Ç öPõkUP¨£mkÒÍx.

X −2 3 1
1 1 1
P(x)
3 2 6

E (2X+5) Cß ©v¨¦ PõsP.

(a) Draw a Pie diagram for the following data (Rupees in hundreds).

Items Food Transport Rent Electricity Miscellaneous Education
Charge
Expenditure 15 3 10 2 10 20

OR

(b) A probability distribution of a random variable X is given by :

X −2 3 1
1 1 1
P(x)
3 2 6

Find E (2X+5).

11 8469

38. (A) J¸ ÷uºÂÀ Gmk ©õnÁºPÒ RÌUSÔ¨¤mkÒÍÁõÖ ©v¨ö£sPÒ
ö£ØÖÒÍÚº. 25, 48, 32, 52, 21, 64, 29, 57 GßÓ ©v¨ö£sPÒ ÂÁµzvØS
•uÀ PõÀ©õÚ® (Q1) ‰ßÓõ® PõÀ©õÚ® (Q3) BQ¯ÁØøÓU PõsP.

AÀ»x

(B) Põ¨¦ F] u¯õ›US® {ÖÁÚzvÀ SøÓ£õkÒÍ J¸ Põ¨¦ F]
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 GzuøÚ ö£miPÎÀ SøÓ£õhØÓ Põ¨¦
F]PÒ EÒÍÚ ?
(a) Compute (First Quartile) Q1 and (Third Quartile) Q3 for the data relating to the marks
of 8 students in an examination is given below.

25, 48, 32, 52, 21, 64, 29, 57

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 ?

-oOo-