MBOSE Class 11 Question Paper 2020 for Statistics

( 10 ) Total No. of Printed Pages ––10

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10. (a) Explain the term “classification” and “tabulation”
and point out the importance in a statistical 2020
investigation. 6
STATISTICS
(b) Compute the median of the following data. 6 12
Full Marks : 100
Size of Item Fequency
Time : 3 hours
0-5 20
The figures in the margin indicate full marks for the questions
5-10 24
General Instructions :
10-15 32
(i) Write all the answers in the Answer Script.
15-20 28
(ii) Attempt Part –––A Objective Questions serially.
20-25 20
(iii) Attempt all parts of a question together at one place.
25-30 16

30-35 34 ( PART : A –– OBJECTIVE )

35-40 10 ( Marks : 50 )

40-45 8 SECTION – I

( Marks : 20 )

1. Choose and write the correct answer : 1  10  10
a. The number of combinations of ‘n’ different things
taken ‘r’ at a time in which two particular things
never occur is

(i) n2
Cr
n2
(ii) Cr  2

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(8) (3)

(c) Prove that n Pr  r . n Pr 1 n 1Pr where 0  r  n. 5 e. The value of 2x , taking interval of difference to
be unity is

6. (a) Write down Newton’s forward interpolation
(i) 3.2x
formula. Find the value of f (1) from the following (ii) 2x 1
data 2 12  5  7 12
(iii) 2x
x : 0 2 4 6
(iv) none of the above.
f (x) : 8 11 20 41

f. If P(E) is the probability of an event, then

(b) Define  and E. State the properties of  and E. 5 (i) P(E)  0

(ii) 0  P( E )  1

GROUP –– B
(iii) 1  P( E)  1
7. (a) State and prove the addition Law of Probability.
(iv) P(E)  1 .
2+4=6

(b) A couple has 2 children. Find the probability that
g. If A and B are two events associated with a random
both are boys if it is known that 2+2=4
experiment such that P(B) = 0.35, P( A  B ) = 0.85
(i) One of the children is a boy and P(A  B)  0.15 then P(A) is

(i) 0.65
(ii) the elder child is a boy.
(ii) 0.40

(iii) 0.50
(c) If A and B are independent events such that
P(A) = 0.3 and P(B) = 0.4. Find P( A and B ). 2 12 (iv) none of the above.

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(5) (6)

2. Fill in the blanks : 1 5  5 (e) If A denotes the arithmetic mean and G denotes
the geometric mean between two positive
(a) If nC16 n C14, then n C 28 is . numbers then A  G.

(b) If m and n are positive integers, we can define
Δm [Δn f(x) ] as .
SECTION –– II
(c) If A and B are two mutually exclusive events then ( Marks : 30 )
P (A  B )  P(A)  P(B) = .

(d) The median of the values 11, 7, 6, 9, 12, 15,19 is 4. Answer the following questions : 3  10  30
.

(e) The relationship between variance and standard (a) If n Pr  840, nCr  35, find r .
deviation of a variable x is .
(b) Find the term independent of x in the expansion
15
 2 
3. Write whether the following statements are True or of  3x  2 
 x 
False. 1 5  5

(a) If n and r are positive integers and (c) If f ( x)  (1  x)(1  2 x)(1  3x) , then find the value of
r  n , then n Cr n Cr 1 n 1Cr 3 f (x ).

(b) The expression E 2 f 2(x) and [Ef(x)] 2 are identical. 2x 3
(d) Evaluate .
E 2x 3
(c) If A and B are independent events, then A and B
are also independent. 5
(e) Let A and B be events such that 2 P ( A)  P ( B ) 
13
(d) For comparing the health conditions of two towns,
A 2
we have to calculate standardised death rate. and P    Find P ( A  B ) .
B  5

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(4) (7)

h. For the set of observations, given that median = 8 (f) A can solve 90% of the problems given in a book
and mode = 4, then mean is and B can solve 70%. What is the probability that
(i) 10 atleast one of them will solve a problem selected
at random from the book.
(ii) 20
(g) Calculate the variance of
(iii) 32
3, 6, 8, 12, 8, 6, 15, 8, 9, 7.
(iv) none of the above.
(h) What are the various methods of collecting
statistical data?
i. Gross reproduction rate is defined as
(i) Mention three uses of vital statistics.
Total fertility  Female births
(i) (j) What are the characteristics for an ideal measure
Total births
of central tendency?
Total births
(ii)
Female Population
( PART : B –– DESCRIPTIVE )

Total fertility  Total births ( Marks : 50 )
(iii)
Female Births
Answer four questions, taking atleast one from each
(iv) none of the above.
Group.

GROUP –– A
j. Standardised death rates are particularly useful
for 5. (a) Find the number of different words that can be
formed from the letters of the word ‘TRIANGLE’
(i) comparing death rates in male and female
so that the vowels are together. 4 12
(ii) comparing death rates in two regions. 18
 2 2
(iii) both (i) and (ii) (b) Determine whether the expansion of  x  
 x
(iv) neither (i) and (ii). will have a term containing x18.? 3

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(2) (9)

(iii) n
Cr2 8. (a) A factory has 100 workers, 60 of them work in
the morning section and 40 in the evening
(iv) 2! n2Cr2 section. The mean wage of all the workers is
Rs. 38. The mean wage of the workers in the
morning section is Rs. 40. What is the mean wage
of the workers in the evening section? 4
b. The middle term(s) in the expansion of (a  b)10 is
the (b) For any event E, prove that 3
(i) 5th term P( E )  1  P (E ).

(ii) 6th term
(c) A and B throw a die alternately till one of them
(iii) 5 term and 6 term
th th gets a 6 and wins the game. Find their respective
probabilities of winning if A starts first. 5 12
(iv) 4th term and 5th term.

GROUP –– C
c. Newton’s backward formula is used when the
9. (a) Define crude death rate and point out its
interpolating value lies
limitations. Explain clearly the standardized
(i) at the beginning of the series. death rate including the method of computation.
Why is a standardized death rate needed?
(ii) in the middle of the series. 1 + 1 12 + 2 + 2 = 6 12
(iii) in the end of the series. (b) Which of the two localities A and B is healthier.
(iv) none of the above. 3+3=6
Age Locality A Locality B
Group Popula- Deaths Popula- Deaths
tion per 100 tion per 100
d. The relation between E and  is
0-10 600 30 400 40
(i) E  1 
10-20 1000 5 1500 4
(ii)   1 E
(iii) 2  1  E 20-60 3000 8 2400 10
60 and 400
(iv) none of the above. above 50 700 30

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