Karnataka 2nd PUC Model Question Paper 2025 for Statistics

ACADEMIC YEAR

2025

Karnataka
Board
Model Paper

GOVERNMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD

SUBJECT: STATISTICS (31) BLUE PRINT FOR THE MODEL QUESTION PAPER-1 ( 2024-25) CLASS: II PUC

Section Question type Number of questions Marks Question numbers
I MCQ/ Choose the most appropriate answer 05/05 05/05 01 to 05
A II Fill in the blanks 05/05 05/05 06 to 10
III Match the following 1*/1* 05/05 11*
IV VSA: Very Short Answer 05/05 05/05 12 to 16
B V SA: Short Answer 05/08 10/16 17 to 24
VI LA: Long Answer 04/07 20/35 25 to 31
C
VII LA: Long Answer 02/04 10/20 32 to 35
D VIII ET: Essay Type 02/03 20/30 36 to 38
Total 29/38 80/121

Unit/ Chapter No. of Marks Remember Understand Application HOTS Total
hours OA SA LA ET OA SA LA ET OA SA LA ET OA SA LA ET OA SA LA ET
Revision 05 - (1) (2) (5) (10) (1) (2) (5) (10) (1) (2) (5) (10) (1) (2) (5) (10) (1) (2) (5) (10)
I Vital Statistics 10 13 1+1* - - 1 1 - - - - - - - - - - - 2+1* - - 1
II Index Numbers 15 18 1+1* - 1 - 1 - - 1 - - - - - - - - 2+1* - 1 1
III Time Series 12 13 - 1 - - - - - - 1 - - 1 - - - - 1 1 - 1
IV Interpolation & Extrapolation 08 07 - - 1 - - 1 - - - - - - - - - - - 1 1 -
V Theoretical Distributions 22 23 1 - - - 1+1* 2 2 - 1 - - - - - 1 - 3+1* 2 3 -
VI Statistical Inference 20 18 2+1* - 1 - - 2 - - - - - - 1 - 1 - 3+1* 2 2 -
VII Statistical Quality Control 08 08 - 1 - - 1 - - - - - - - - - 1 - 1 1 1 -
VIII Operations Research 20 21 2+1* - 1 - 1 1 1 - - - - - - - 1 - 3+1* 1 3 -
Total 120 121 7+1* 2 4 1 5+1* 6 3 1 2 0 0 1 1 0 4 0 15+1* 8 11 3
Total Marks 11 4 20 10 6 12 15 10 2 0 0 10 1 0 20 0 20 16 55 30
Grand Total Marks 45 43 12 21 121
Percentage 37% 36% 10% 17% 100

Note: * In the OA, question number 11 has 5 sub questions; each sub question carries 1 mark.

GOVERNMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
II PUC MODEL QUESTION PAPER – 1 (2024-25)
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, only the first written answers will be considered for evaluation.
5. For questions having diagram, graph and map, 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) The births occurring to women of child bearing age is called
a) Fertility b) Fecundity c) Mortality d) Longevity

2) Factor reversal test is satisfied by
a) Laspeyre’s index number b) Marshall- Edgeworth’s index number
c) Fisher’s index number d) Kelly’s index number

3) In a Bernoulli distribution, if q = 0.8, the standard deviation is
a) 0.16 b) 0.8 c) 0.2 d) 0.4

4) Which of the following statements are correct?
i) P(Type – I error ) = α (ii) P(Type – I error ) = 1 – α
iii) P(Type – II error ) = β (iv) P(Type – II error ) = 1 – β

a) i and iv b) i and iii c) ii and iv d) ii and iii

5) The cost associated with the maintenance of inventory until they are sold or used is
a) Holding cost b) Shortage cost c) Setup cost d) Capital cost

II. Fill in the blanks by choosing the appropriate answers given in the brackets: (5 X 1 = 5)
( 0, Strategy, 100, Point, Interval, np)

6) The value of the index number for the base year is __________.

7) The mean of a student’s t - distribution with parameter ‘n’ is _______ .

8) If a single value is proposed as an estimate of the unknown parameter, it is _________ estimation.

9) In statistical quality control, _______ chart is used for number of defectives.

10) In a game, the pre-determined rule by which a player determines his course of action is called ________.

III. Match the following: (5 X 1 = 5)
11) A B
a. Size of the cohort i. Leptokurtic (β2 > 3)
b. Paasche’s index number ii. A function of sample values
c. Chi-square distribution curve iii. Downward bias
d. Statistic iv. Replacement problem
e. Matrix minima method v. Radix
vi. Transportation problem
1

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

12) Mention a method of obtaining vital statistics.
13) Which component of the time series is unpredictable?
14) Under what condition Poisson distribution tends to Normal distribution?
15) Define statistical hypothesis.
16) When is transportation problem said to be balanced?

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

17) Mention two uses of time series.

18) Write two conditions for applying binomial expansion method of interpolation and extrapolation.

19) Find the mean of a hyper-geometric distribution whose parameters are a = 3, b = 9 and n = 4.

20) If X ~ N(μ, σ2), then write the distribution of and .

21) A random sample of size 36 is drawn from a population whose standard deviation is 3. Compute standard
error of the sample mean.

22) Given: n = 10, s2 = 14.4 and σ2 = 16, compute the chi – square test statistic.

23) In statistical quality control, if = 4, determine the upper control limit for the c - chart.

24) If R = 3000 units/year, C1 = Rs 4/unit/year and C3 = Rs 60/order, then calculate the minimum average
inventory cost.

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

25) Calculate the consumer price index number by using family budget method for the following data.
Price (in Rs)
Group Weight
Base year Current year
Food 3000 4200 30
Fuel 2500 3280 20
Clothing 2000 2160 10
Housing 3200 4000 30
Entertainment 1600 2000 10
Other 3000 3600 20

26) Interpolate the value of Y when X = 26 by using Newton’s advancing difference method.
X 20 30 40 50
Y 72 202 557 1137

27) The probability that a team winning the game is 2/5. If this team plays in 6 games, then find the
probability that it wins in i) all the games ii) one or more games.

28) Obtain the theoretical frequencies by fitting Poisson distribution for the number of mistakes per page
from the following distribution.
Number of mistakes per page 0 1 2 3 4
Number of pages 92 79 50 15 4
2

29) From a random sample of 64 students of PUC, 16 students were found wearing spectacles. Can we
conclude at 5% level of significance that the proportion of students wearing spectacles is 20%?

30) Solve the following game by using dominance principle. Is the game fair?
Player – B
B1 B2 B3
A1 -1 5 6
Player – A A2 0 4 3
A3 -4 2 7
A4 -5 0 8

31) The purchase price of a machine is Rs 5000. Its maintenance costs and resale values are as follows:
Years 1 2 3 4 5
Maintenance cost (in Rs) 100 200 330 510 860
Resale value (in Rs) 3000 2500 2000 1500 1000
What would be the optimum replacement period for the machine?

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

32) In an institution, the weights of students follow normal distribution with mean 60 kg. and standard
deviation 4.5 kg. If committee decides to consider the students with minimum weight of 62 kg., show that
only 33% of the students got selected.

33) The following data represents the blood pressure of 5 persons before and after performing dhyana.
B.P. before dhyana 100 97 92 94 95
B.P. after dhyana 96 98 90 91 93
Can we conclude at 5% level of significance that dhyana reduces blood pressure?

34) Given D3 = 0 and D4 = 2.115, write the control limits for R – chart.
Sub-group number 1 2 3 4 5 6
Range 2 5 2 4 2 3

35) Solve the following linear programming problem graphically:
Maximize Z = 6x + 10y
Subject to constraints: x + y ≤ 8
x + 3y ≤ 18
and x, y ≥ 0

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

36) Calculate gross reproduction rate and net reproduction rate for the following data and comment on the
result.
Age group Female Female Survival
(in years) population births ratio
15 – 19 16000 480 0.91
20 – 24 14500 899 0.90
25 – 29 13000 650 0.90
30 – 34 11500 460 0.88
35 – 39 10000 300 0.87
40 – 44 8700 87 0.86
45 – 49 7500 30 0.85

3

37) Calculate the Marshall-Edgeworth’s and Dorbish-Bowley’s price index numbers from the following data.
Items Base year Current year
Price (in Rs) Quantity Price (in Rs) Quantity
A 17 10 25 14
B 22 12 29 17
C 30 13 24 22
D 41 12 47 15

38) a) Estimate the trend values by four yearly moving averages for the following time series data.
Year 2015 2016 2017 2018 2019 2020 2021 2022 2023
Value 16 18 16 24 20 30 26 34 40

b) Fit a straight line trend equation of the form y = a + bx to the data given below.
Year 2010 2012 2014 2016 2018 2020 2022
Production (in ‘000 quintals) 80 90 92 83 94 99 92

SECTION - E
(For Visually challenged students only)

35) A tailor gets a profit of Rs.100 from a shirt and Rs. 170 from a pant. In a week from available 56 hours,
he uses 36 hours for cutting and 20 hours for stitching. For cutting he requires 2 hours for a shirt and 3
hours for a pant. He requires 1 hour for stitching a shirt and 2 hours for stitching a pant. Formulate an
L.P.P.

*******

4

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