MBOSE Class 11 Question Paper 2023 for Statistics

Total No. of Printed Pages ––9 (2)

HS/XI/A.Sc./S/23
b. Frequencies are necessary for drawing
2023
(i) Ogive
STATISTICS
(ii) Histogram
Full Marks : 100
(iii) Bar-diagram
Time : 3 hours
(iv) Pie-Chart
The figures in the margin indicate full marks for the questions

General Instructions :
c. The vertical axis in case of a less than ogive shows
(i) Write all the answers in the Answer Script.
(ii) Attempt Part –––A Objective Questions serially. (i) Mid points

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

(iii) Upper limits
( PART : A –– OBJECTIVE )
(iv) Cumulative frequency.
( Marks : 50 )

SECTION – I

( Marks : 20 ) d. The expression for the event ‘neither A nor B’ is

(i) AB
1. Choose and write the correct answer : 1  10  10
a. Specific Death Rate is calculated on the basis of (ii) (A  B)c
(i) standard population
(ii) specified section of the population (iii) A  Bc
(iii) the population as a whole
(iv) None of these. (iv) None of the above.

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(3) (4)

e. Standard deviation of 6 numbers 5, 5, 5, 7, 7,7 is h. If P(A/B) = P(A) then the events A and B are

(i) 1 (i) Complementary

(ii) 2 (ii) Independent

(iii) 6 (iii) Mutually exclusive

(iv) 5.5 (iv) None of the above.

f. If log 4 (x  3)  2 , then the value of x is i. If the occurrence of one event prevents the
occurrence of the other event, then the events
(i) 13 are said to be

(ii) 12 (i) exhaustive

(iii) 16 (ii) equally likely
(iv) 4 (iii) mutually exclusive

(iv) independent

g. If f (x )  x(x  1)(x  2) and h=1 then the value of
f (x ) is
j. The value of nC1 is
(i) (x  1) x (x  1)
(i) 0
(ii) x ( x  2) (ii) n

(iii) 3x (x  1) (iii) 1

(iv) x (x  1) (iv) None of the above.

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(5) (6)

2. Fill in the blanks : 1 5  5 SECTION –– II

(a) The probability of an impossible event is ______. ( Marks : 30 )

(b) The geometric mean of 8 and 50 is ______.
4. Answer the following questions : 3  10  30
(c) In finite differences, if C is a constant then
E(C)= _______. (a) Differentiate between questionaires and
schedules.
(d) Crude death rate is a _______ death rate.
(b) What are raw data?
(e) A questionaire is filled up by _______.
(c) If f ( x )  ( 4 x  3) find 2 f ( x) .

(d) Define Crude Death rate.
3. State whether the following statements are True or
False. 1 5  5
(e) Name different types of averages used for
measures of central tendency.
(a) The sum of cumulative frequencies of ‘less-than
type’ and ‘more-than type’ of a class interval is
equal to the total frequency. (f) Show that n Cr n C n r .

(b) Variance is always positive. (g) Write down the sample space if one dice is
thrown twice .
(c) If P(A) = P(A–B), then A and B are mutually
exclusive. (h) Distinguish between entry and argument.

(d) In Newton’s forward interpolation formula, values (i) Differentiate with example between
of the argument may not be equidistant. population and sample.

(e) The Binomial expansion of (a + b) n has (n + 1) (j) Distinguish between sample point and
terms. sample space.

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(7) (8)

( PART : B –– DESCRIPTIVE ) GROUP –– B
( Marks : 50 ) 7. (a) Define with example: 6

Answer any four questions, taking atleast one from Elementary event, certain event, sample space,
each Group. mutually exclusive events, exhaustive events and
independent events.
GROUP –– A
(b) Two unbiased dice are thrown. Write down the
5. (a) In how many ways can the letters of the word
sample space. Find the probability that the sum
PERMUTATION be arranged if the vowels remain
of the numbers indicated by the number on the
together? 6
topmost faces of the dice is 6 12
4
 2 3
(b) Expand  x   , x  0 . 2 12 (i) a prime number
 x
(ii) divisible by 5
(c) Compute (98)5. 4 (iii) at least 5
(iv) a perfect square.
6. (a) Define the operators  and E. 4
Show that E  1   8. (a) State the theorem of compound probability. In a
group of 20 males and 5 females. 10 males and 3
 2  2 females are service holders. What is the
(b) Find the value of  x , interval of differencing probability that a person selected at random, is a
E 
service holder, given that the selected is a male. 6
being unity. 2 12
(b) Two newspapers X and Y are published in a certain
(c) State Lagrange’s interpolation formula. Find the city. It is estimated from a survey that 16% read
value of f(45), by Newton’s forward interpolation X, 14% read Y and 5% read both the papers. Find
formula from the following table: the probability that a randomly selected person 6
6
x : 40 50 60 70 80 (i) does not read any newspaper

f(x) : 31 73 124 159 190 (ii) reads only Y.

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(9)

GROUP –– C

9. (a) Define statistics in two different senses. Mention
the important uses and limitations of statistics.
2 12  4  6 12

(b) Show that 6

(i) AM  GM  HM

(ii) AM  HM  GM 2

10. (a) Define Vital Statistics. Describe the different
sources of vital statistics. 2 12  4  6 12

(b) Write short notes on 6

(i) Age-Specific Death Rate

(ii) Standardised Death Rate

(iii) Demographic Statistics.



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