MBOSE Class 12 Question Paper 2020 for Statistics

Total No. of Printed Pages—8
HS/XII/A.Sc/S/20

2020

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) If the mean of a binomial distribution having n = 8 is
4, then the value of p is
(i) 32

1
(ii)
3
1
(iii)
2
(iv) 16

/33 [ P.T.O.

( 2 )

(b) In sampling distribution, a finite population of
12 units, samples of size 7 can be selected in
(i) 792 ways
(ii) 704 ways
(iii) 84 ways
(iv) 868 ways

(c) The equality of mean and variance of a discrete
distribution indicates that the distribution is
(i) Poisson
(ii) binomial
(iii) normal
(iv) hypergeometric

(d) The variance of the binomial distribution is
(i) np
(ii) npq

(iii) npq
(iv) nq

(e) The bias which has its origin in sampling only is
(i) bias due to substitution
(ii) response bias
(iii) observational bias
(iv) None of the above

HS/XII/A.Sc/S/20/33 [ Contd.

( 3 )

(f) Changes that take place as a result of natural
calamities are classified under the head
(i) secular movement
(ii) seasonal variations
(iii) cyclical variations
(iv) irregular variations

(g) Index number must satisfy
(i) only time reversal test
(ii) only factor reversal test
(iii) Both test in (i) and (ii)
(iv) Both test in (i) and (ii) are not necessary

(h) If Z  2  3X  5Y and E ( X )  1 , E (Y)  2 then the
value of E (Z ) is
(i) 10
(ii) 15
(iii) 13
(iv) 12

(i) The following is not a method for measuring trend :
(i) Graphic method
(ii) Moving average method
(iii) Harmonic analysis method
(iv) Least squares method

HS/XII/A.Sc/S/20/33 [ P.T.O.

( 4 )

(j) The term parameter is used to denote the
characteristic of the
(i) population
(ii) size of population
(iii) sample size
(iv) None of the above

2. Fill in the blanks : 1×5=5

(a) If  is the expected value of x, then E (x   )  _____.

(b) If x j is a random variable with the probability of
f (x j ) , then its expectation is _____.

(c) The sum of probabilities in a Poisson distribution is
_____.
(d) If the trend is absent in the data, then the seasonal
indices are computed by the method of _____
averages.
(e) Simple random sampling is not suitable if the
population is _____.

3. State whether the following statements are
True or False : 1×5=5
(a) Simple random sampling requires smaller sample
size than stratified random sampling for a fixed level
of precision.
(b) Fisher’s index number is the geometric mean of
Laspeyres’ and Paasche’s indices.

HS/XII/A.Sc/S/20/33 [ Contd.

( 5 )

(c) The total number of samples when sampling is
done without replacement from a population of size
n is n Cn .

(d) In time-series analysis, the free-hand method can
represent both linear and non-linear trends.
(e) The number of parameters of a normal distribution
is one.

SECTION—II
( Marks : 30 )

4. Answer the following questions : 3×10=30
(a) In a binomial distribution, prove that
mean > variance.
(b) If X follows a binomial distribution with mean 4 and
variance 2, find P ( X  5) .

(c) If X and Y are independent random variables, then
show that E [{ X  E ( X )}{Y  E (Y )}]  0 .

(d) The number of mistakes counted in 100 typed pages
of a typist revealed that he made 2·8 mistakes on an
average per page. Find the probability that in a page
typed by him there are two or more mistakes. (Given
that e 28  0  061 ).

(e) “Index numbers are very useful for studying the
economic and business activity, but they have their
own limitations.” Mention any three of these
limitaitons.

HS/XII/A.Sc/S/20/33 [ P.T.O.

( 6 )

(f) Explain briefly how Fisher’s ideal index number is
constructed. Justify it being called ‘ideal’.

(g) For a basket of commodities the price of each
commodity in the year 2016 is three times the price
in the base year. What is Paasche’s price index for
the year 2016?

(h) Write down the properties of normal distribution.

(i) State some of the important factors responsible for
non-sampling errors in any survey (census on
sample).

(j) Distinguish between seasonal variation and cyclical
variation.

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

Answer four questions, taking at least one from each Group

GROUP—A

5. (a) (i) Define random variable and probability
distribution. 1+1=2
(ii) Three coins are tossed. Find the probability
distribution of the number of heads. 2½
(b) Find the mean and variance of a Poisson
distribution. 4
(c) The mean and variance of a binomial distribution
are 4 and 4/3. Find P ( X  1) . 4

HS/XII/A.Sc/S/20/33 [ Contd.

( 7 )

6. (a) State the distinctive features of the binomial,
Poisson and normal probability distributions. When
does a binomial or a Poisson distribution tend to a
normal distribution? 6½
(b) Find the mean of binomial distribution. 3
(c) For a binomial distribution, the mean is 6 and the
standard deviation is 2 . Find the values of n, p, q
with usual notations. 3

GROUP—B

7. (a) What is time series? What is the need to analyse a
time series? 1+3=4
(b) What are the different types of index numbers?
Discuss the mains steps followed in the construction
of cost of living index number (CLIN)? 2+3=5
(c) Calculate the cost of living index number (CLIN)
from the following table : 3½
Items Price Weight
Base Year Current Year
Food 39 47 4
Fuel 8 12 1
Clothing 14 18 3
House Rent 12 15 2
Miscellaneous 25 30 1

8. (a) Discuss the differences between seasonal and
cyclical variations. 6½
(b) Show that Fisher’s index number satisfies both time
and factor reversal tests. 6

HS/XII/A.Sc/S/20/33 [ P.T.O.

( 8 )

GROUP—C
9. (a) Write short notes on the following : 2½×4=10
(i) Sampling error
(ii) SRSWOR
(iii) SRSWR
(iv) Judgement sampling
(b) What are the principles of sample survey? 2½

10. (a) Prove that in simple random sampling, sample mean
is an unbiased estimate of the population. 6½
(b) Show that

2 N  n
V (x ) SRSWOR = 
n N
where x and  have usual meanings. 6

  

HS/XII/A.Sc/S/20/33 20K