MBOSE Class 12 Question Paper 2025 for Statistics

Meghalaya Board of School Education

QUESTION
PAPERS

Total No. of Printed Pages—11
HS/XII/A. Sc./S/25

2025

STATISTICS

Full Marks : 100

Time : 3 hours

The figures in the margin indicate full marks for the questions

General Instructions :

(i) Write all the answers in the Answer Script.

(ii) Attempt Part—A (Objective Questions) serially.

(iii) Attempt all parts of a question together at one place.

( PART : A—OBJECTIVE )
( Marks : 50 )

SECTION—I
( Marks : 20 )

1. Choose and write the correct answer : 1×10=10

(a) The mean of a binomial distribution is
(i) n
(ii) np
(iii) npq
(iv) None of the above

/222 [ P.T.O.

( 2 )

(b) The skewness of the normal distribution is

(i) 1 (one)

(ii) ¥ (infinity)

(iii) -1 (negative one)

(iv) 0 (zero)

(c) The price index number for the current year
compared to the base year is denoted by

(i) Q 10

(ii) P10

(iii) P 01

(iv) Q 01

(d) The probability of a specified unit being included in
the sample is equal to

(i) N

(ii) n

n
(iii)
N

N
(iv)
n

HS/XII/A. Sc./S/25/222 [ Contd.

( 3 )

(e) The additive model for time series analysis is

(i) Y = T + S

(ii) Y = C + S

(iii) Y = T + S + C + 1

(iv) Y = T + S + C + I

(f) The time reversal test may be expressed as

(i) P 01 = 1

(ii) P 01 ´ P10 = 1

(iii) P 01 ´ P10 = 0

(iv) P10 = 1

(g) A die is thrown. Let X denote the point on the
uppermost face. Then E (X ) is

(i) 1

(ii) 21

(iii) 1
6

(iv) 7
2

HS/XII/A. Sc./S/25/222 [ P.T.O.

( 4 )

(h) The mean and variance of a Poisson distribution are

(i) (0, 0)

(ii) (0, l)

(iii) (l, l)

(iv) (l, 0)

(i) If s 2 is the population variance, then which of the
following is correct in case of SRSWR?

s2
(i) var (x ) >
n

s2
(ii) var (x ) =
n

s2
(iii) var (x ) <
n

s2
(iv) var (x ) ¹
n

(j) The error which arises only in sample survey is
termed as

(i) sampling error

(ii) non-sampling error

(iii) Both (i) and (ii)

(iv) Neither (i) nor (ii)

HS/XII/A. Sc./S/25/222 [ Contd.

( 5 )

2. Fill in the blanks : 1×5=5

(a) If X and Y be two _____ variables, then
E (XY ) = E (X ) × E (Y ).

(b) If the standard deviation of a Poisson variate is 2, the
mean of the Poisson variate is _____.

(c) _____ index is known as ‘ideal’ formula for
constructing index number.

(d) A sample is a study of _____ of the population.

(e) An overall tendency of rise or fall in a time series is
called _____.

3. Write whether the following statements are True or False :
1×5=5

(a) An era of prosperity is a cyclical component of time
series.

(b) Census is superior than sample survey.

(c) Paasche’s index formula does satisfy factor reversal
test.

(d) The mean and standard deviation of standard normal
variate are respectively 0 and 1.

(e) If X is a random variable and c is a constant, then
E (cX ) = cE (X ).

HS/XII/A. Sc./S/25/222 [ P.T.O.

( 6 )

SECTION—II
( Marks : 30 )

4. Answer the following questions : 3×10=30

(a) If a random variable X takes the values 1, 2, 3 with
probability
r
P (X = r ) = ; r = 1, 2, 3
6
find E (X ). 3

(b) The random variable X follows binomial distribution
with mean 6 and variance 4. Find the probability
distribution of X. 3

(c) State the important properties of normal distribution. 3

(d) Write down the formula for the following index
numbers : 1×3=3
(i) Laspeyres’ price index number
(ii) Paasche’s price index number
(iii) Value index number

(e) Mention three uses of index numbers. 1+1+1=3

(f) Which component of time series is mainly applicable
in the following cases? 1×3=3
(i) Fire in a factory
(ii) Recession
(iii) An increase in employment of labour during
harvest time

HS/XII/A. Sc./S/25/222 [ Contd.

( 7 )

(g) Enumerate the objective of analysis of time series. 3

(h) A simple random sample of 10 households was drawn
from a town of 1200 households. The numbers of
persons in the selected houses were :
2, 2, 3, 3, 4, 5, 6, 3, 3, 4
Estimate the number of persons in the town. 3

(i) Discuss briefly the basic principles of a sample
survey. 3

(j) Explain clearly the following with suitable examples :
1×3=3

(i) Population

(ii) Sample

(iii) Sampling frame

HS/XII/A. Sc./S/25/222 [ P.T.O.

( 8 )

( PART : B—DESCRIPTIVE )
( Marks : 50 )

Answer four questions, taking at least one from each Group

GROUP—A

5. (a) Define a discrete random variable. Give one example. 2

(b) A random variable X has the following distribution :

X 0 1 2 3 4 5
P (X ) 0·1 0·2 0·3 0·1 — 0·1

Find P (4) and E (X ). 1+3=4

(c) Write down three properties of expectation. ½+½+½=1½

(d) Find the mean and variance of binomial distribution. 5

6. (a) If X follows normal distribution with mean 66 and
standard deviation 5, find—

(i) P (65 < X < 70) ;

(ii) P (X ³ 72).

Given that
P (Z £ 0 × 8) = 0 × 7881 and P (Z £ 0 × 2) = 0 × 5793 5

HS/XII/A. Sc./S/25/222 [ Contd.

( 9 )

1
(b) If X has a Poisson distribution and P (X = 0) = , what
2
is E (X )? 2½

(c) The random variable X has the p.m.f.

X =x 0 1 2 3
1 1 1 1
p(x )
3 2 24 8

Find the expected value of Y = (X - 1)2 . 5

GROUP—B

7. (a) Define time series. What are its components? Explain
any one of them. 2+2+2=6

(b) Using least squares of method, find the trend values
from the following data : 5

Year 1990 1991 1992 1993 1994 1995 1996
Production 83 60 54 21 22 13 23

(c) Define moving average method. 1½

8. (a) Explain briefly the method of computing index
number—
(i) by weighted aggregative method;
(ii) by simple aggregative method;
(iii) by simple average of price relative method. 2×3=6

HS/XII/A. Sc./S/25/222 [ P.T.O.

( 10 )

(b) Construct price index numbers from the following
data, using—

(i) Laspeyres’ and

(ii) Marshall-Edgeworth : 2+3=5

1990 1993
Commodity
Price Quantity Price Quantity
A 6 50 10 56
B 2 100 2 120
C 4 60 6 60
D 10 30 12 24

(c) Why is Fisher’s index number formula called an ideal
index number formula? 1½

GROUP—C

9. (a) What is a simple random sample? Mention the
various methods of drawing a random sample.
1½+3=4½

(b) Define simple random sampling with and without
replacement. 3

(c) Prove that in simple random sampling without
replacement, sample mean is an unbiased estimate of
population mean. 5

HS/XII/A. Sc./S/25/222 [ Contd.

( 11 )

10. (a) What are the errors in a sample survey? Show how
non-sampling errors differ from sampling errors.
1+3=4

(b) What do you mean by stratified random sampling?
Describe how you will draw a stratified random
sample. Write down the formulae for estimating the
population total and population mean by a stratified
sample. 2+3+2=7

(c) What is the total number of samples, when sampling
is done without replacement from a population of
size N ? 1½

HHH

HS/XII/A. Sc./S/25/222 K25—100

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