Karnataka 2nd PUC Model Question Paper 2027 for Statistics (Paper 5)

FOR KARNATAKA CLASS 12 PREPARATION

Karnataka 2nd PUC
Model Question Paper
2027 for Statistics
(Paper 5)
EXAM YEAR TYPE SUBJECT

Karnataka Class 12 2027 Sample Paper Statistics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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GOVERNEMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSEMENT BOARD
6th CROSS, MALLESHWARAM, BENGALURU-560 003
2026-27 II PUC MODEL QUESTION PAPER- 5
Subject: 31 - Statistics Maximum Marks: 80
Time: 3.00 Hours No. of Questions: 38
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Instructions:
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1. Statistical tables and graph sheets will be supplied on request.
2. Scientific calculators are allowed.
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3. All working steps should be clearly shown.
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4. For ‘Section – A’ questions, only the first written answers will be considered for evaluation.
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5. For the question having graph, alternative question is 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 probability of a person of age x years, will die before reaching age (x+1) years is
a) Longevity b) Mortality ratio c) Survival ratio d) Expectation of life
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2) The weights used in the construction of Marshall-Edgeworth’s
ec) q
price index number
a)
𝑞0 +𝑞1
b) q
as d) q
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0 1
2

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3) The variance of a Bernoulli distribution with parameter ‘p’ is
a) q b) npq c) np d) pq

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 iii b) i and iv c) ii and iii d) ii and iv
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5) Theocost c
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. Capital cost m
e cost
e ma) b) Set-up cost c) Holding cost
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d) Shortage
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la II. Fill in the blanks by choosing the appropriate answers given in theabrackets:
ag (Standard normal, Defective, Ratios, An upper, Saddle, Poisson)
(5 X 1 = 5)

6) Index numbers are expressed in __________ but for comparison purpose they are expressed in
percentages.
7) In ___________ distribution, variance and standard deviation are equal.
8) Chi-square test for goodness of fit is always _______________ tailed test.

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9) An item having one or more defects is a ______________ item.
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10) The position of the pay-off matrix where maximin and minimax coincide is the __________ point.
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III. Match the following: (5 X 1 = 5)
11) A B
a. Maternal mortality i. Free of bias
b. Fisher’s index number ii. 1 – P(Type – I error)
c. Chi-square distribution iii. Puerperal deaths
d. Power of a test iv. Mean equals to its parameter
e. North-west corner rule method v. P(Type – I error)
vi. Transportation problem

IV. Answer the following questions: (5 X 1 = 5)
12) Which birth rate is used to compare fertility rates of different populations?
13) What do you mean by historigram?
14) Under what condition Poisson distribution tends to normal distribution?
15) What is the best estimator of the population mean?
16) Write one of the disadvantages of inventory.
SECTION – B

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

17) Define random variation in a time series and give an example.
18) State two conditions for applying binomial expansion method of interpolation and extrapolation.
19) In a Poisson distribution, if standard deviation is 2, then find its mean.
20) Find the variance of chi-square distribution with 6 degrees of freedom.
21) If σ = 4 and n = 64, then find the standard error of sample mean.
22) Write two applications of t-test.
23) Name the control charts for variables.
24) Verify whether the following solution to a transportation problem is non-degenerate?
20 10
3 6
15 5
4 5
5
2
SECTION – C

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

25) Calculate cost of living index number for the following data by using family budget method.
Group Weight Price (in Rs)
Base year Current year
Food 30 2500 3125
Housing 20 2200 2420
Clothing 10 1800 2160
Fuel 15 2000 2600
Miscellaneous 25 2800 3920
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c.26)o Interpolate the value of ‘Y’ when X = 26 by using Newton’s advancingsedifference
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X 20 30 40 50
Y 72 202 557 1137

27) Team A has probability 0.4 of winning a game. If it plays 5 games, find the probability that it wins –
(i) 4 games (ii) at least 2 games.

28) A box contains 7 pink and 5 blue marbles. From this box four marbles are drawn at random. Using hyper-
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geometric distribution, find the probability that the sample contains 2 pink marbles. Also find the expected
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number of pink marbles.
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29) From a random sampleem of 100 students of PUC, 16 students were found wearing spectacles.glCan as we
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conclude at 5%l alevel of significance that population proportion of students wearing spectacles
a is more
than 10%?a

30) Solve the following game by using dominance principle. Is the game fair?
Player – B
B1 B2 B3 B4
A1 2 1 -3 0
Player – A A2 6 4 5 0
A3 -1 3 0 -2
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. cost and resale value at different years are given
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31) The cost of a machine is Rs 30,000 and its maintenance
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1 gl 2
below:
Year
Maintenance cost (in Rs) 1000
a 2000
3
3100
4
4500
5
6000
Resale value (in Rs) 20000 16000 13000 10000 8000
Determine the optimal period for the replacement of the machine.

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

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32) Daily wages of 100 workers are normally distributed with mean Rs 600 and standard deviation Rs 50.

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Find the number of workers getting wages between Rs 500 and Rs 650.

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33) Test
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whether means differ significantly from the following data at 1% level of
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significance.
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Sample – I Sample – II
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10
62
12
55
Variance 16 25

34) If n = 100 and P ′ = 0.02, then find the control limits for np-chart.

35) Solve the following linear programming problem graphically:
Maximize Z = 20x + 14y
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Subject to constraints: 3x + 2y ≤ 18
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4x + 3y ≥ 12
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and x, y ≥ 0
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SECTION – D

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

36) Calculate standardized death rates for the following data and state which village is more healthier.
Age group Village – A Village – B Standard
(in years) Population Deaths Population Deaths population
0 – 16 6000 60 4000 48 5000
16 – 40 16000 96 12000 48 15000
40 – 60 8000 80 7000 63 6000
60 and above 5000 200 3000 117 4000

37) Compute Laspeyre’s, Paasche’s and Dorbish-Bowley’s price index numbers for the following data.
Items 2020 2025
Price (in Rs) Quantity Price (in Rs) Quantity
A 10 06 20 15
B 15 10 10 20
C 38 09 50 16
D 30 08 40 28

38) a) Find the trend values for the following time series data by using three yearly moving averages. (05)
Year 2019 2020 2021 2022 2023 2024 2025
Value 69 61 68 54 49 56 48

b) Fit a straight line trend equation of the form y = a + bx to the time series data given below. (05)
Year 2018 2019 2020 2021 2022 2023 2024
Production (in ‘000 tons) 79 83 90 94 90 95 99

SECTION - E
(For Visually challenged students only)

35) Write the procedure of solving linear programming problem graphically.

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