Karnataka 1st PUC Model Question Paper for Statistics

SAMPLE PAPER

Karnataka
Board
Model Paper

Model Question Paper

STATISTICS (31)
Time: 3 Hours (Total number of questions: 38) Max. Marks: 80
Instructions:
1. Statistical table and graph sheets will be supplied on request.
2. Scientific calculators are allowed.
3. All working steps should be clearly shown.
4. For Section – A questions, only the first written answers will be considered for evaluation.
5. For questions having diagram, graph, alternative questions are given at the end of the question paper in a separate
section for visually challenged students.
SECTION – A
I. Choose the most appropriate answer from the choices given: (5 X 1 = 5)

1) Who is the father of statistics?
a) R. A. Fisher b) A. L. Bowley c) Horace Secrist d) Boddington

2) Classification on the basis of attribute is
a) Chronological b) Geographical c) Qualitative d) Quantitative

3) The geometric mean of 1 and 4 is
a) 1 b) 2 c) 3 d) 4

4) If A and B are two mutually exclusive and exhaustive events, P(A) = 0.6, then P(B) is
a) 0 b) 1 c) 0.5 d) 0.4

5) If E(X) = 6, the value of E(2X) is
a) 2 b) 3 c) 6 d) 12

II. Fill in the blanks by choosing the appropriate answers given in the brackets: (5 X 1 = 5)
(0.3, 3, 0, Quartiles, Cumulative, Deciles )

6) The added up frequencies are called ________________ frequencies.

7) Measures which divide the data into four equal parts are known as ____________.

8) For a mesokurtic distribution, the value of β2 is _______.

9) If P(A) = 0.7, then the value of P(A′ ) is __________.

10) The value of V(3) is ________.

III. Match the following: (5 X 1 = 5)

11) A B
a. Absolute error i. Two dimensional diagram
b. Pie-chart ii. Q3 - Q1
c. Mode iii. 1
d. Inter-quartile range iv. 0
e. The probability of sure event v. Actual value – estimated value
vi. 3Median - 2mean

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IV. Answer the following questions: (5 X 1 = 5)

12) Which graph is used to locate median?
13) For a data, if D5 = 40, write the value of P50.
14) If variance = 25, find the standard deviation.
15) What is meant by interpolation?
16) Define continuous random variable.

SECTION – B
V. Answer any FIVE of the following questions: (5 X 2 = 10)

17) Write two branches of statistics.
18) Mention two methods of sampling.
19) Given: n1=10, n2 = 20, x̅1 = 34 and x̅2 = 37. Find the combined arithmetic mean.
20) Find the range from X: 6, 15, 10, 30, 20.
21) If Σd2 = 21 and n = 8, find Spearman’s co-efficient of rank correlation.
22) What is the difference between correlation and association of attributes?
1 2
23) If P(A∩B) = 2 and P(B) = 3 , find P(A|B).
24) If E(X) = 18 and E(Y) = 10, calculate E(X+Y).

SECTION – C
VI. Answer any FOUR of the following questions: (4 X 5 = 20)

25) Write three functions and two limitations of statistics.

26) Define primary data and mention the methods of collection of primary data.

27) Prepare a frequency distribution table for the following data by taking class intervals: 0 – 20, 20 – 40,
40 – 60, …..
16 92 60 54 57 39 95 24 99 62
21 67 28 04 42 86 15 58 81 40
60 12 85 77 34 73 52 79 48 43

28) Draft a blank table to show the information of students:
(i) Class: I PUC, II PUC
(ii) Sex: Boys, Girls
(iii) Faculty: Arts, Commerce, Science.

29) Represent the following data by multiple bar diagram.
Food grain Production (in tons)
2021 2022 2023
Rice 90 100 150
Ragi 150 140 120
Wheat 250 280 200

30) Find the Yule’s co-efficient of association for the following data.
Boys Girls Total
Pass 120 40 160
Fail 30 10 40
Total 150 50 200

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31) Interpolate the value of index number for the year 2017 by using binomial expansion method.
Year 2015 2016 2017 2018 2019
Index Number 100 107 - 157 212

VII. Answer any TWO of the following questions: (2 X 5 = 10)

32) Draw histogram for the following data and locate mode from the graph.
C.I. 0–5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30
Frequency 21 32 44 26 20 10

33) Compute the harmonic mean for the following distribution.
X 10 30 50 70 90
Frequency 12 15 40 35 18

34) Estimate the value of ‘x’ when y = 40 using the following data.
x y
Mean 25 30
Standard deviation 5 4
Co-efficient of correlation, γ = 0.8

35) A, B and C hit a target with probability 0.4, 0.5 and 0.6 respectively. If they fire at the target
independently, find the probability that: (i) all of them hit, (ii) at least one of them hit the target.

SECTION – D
VIII. Answer any TWO of the following questions: (2 X 10 = 20)

36) Following are the runs scored by two cricketers in 5 matches.
Cricketer – A 40 60 80 25 45
Cricketer – B 20 42 68 36 34
Find (i) Who is better run scorer? (ii) Who is more consistent in run scoring?

37) For the following data, calculate the relation between two variables X and Y by using Karl-Pearson’s
method.
X↓ Y→ 0-10 10-20 20-30 30-40
0 8 7 3 -
1 - 6 4 -
2 - 3 5 6
3 - - 1 7

38) a) A bag contains 3 green and 4 blue marbles. Two marbles are randomly drawn. Find the probability that
they are of (i) same colour (ii) different colours.

b) Find mean and variance of the following distribution.
x 20 40 60 80
p(x) 0.1 0.4 0.3 0.2

SECTION – E
(For visually challenged students only)

29) Write the general rules for constructing diagram.

32) Write the procedure of constructing histogram.

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