Karnataka 2nd PUC Model Question Paper 2027 for Statistics

FOR KARNATAKA 2ND PUC EXAM PREPARATION

Karnataka 2nd PUC
2027
Sample Paper ·
Statistics
EXAM YEAR TYPE SUBJECT

Karnataka 2nd PUC 2027 Sample Paper Statistics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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GOVERNEMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
6th CROSS, MALLESHWARAM, BENGALURU-560 003
2026-27 II PUC MODEL QUESTION PAPER- 1
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.
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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 life expectancy of a new born baby
a) Radix b) Longevity c) Fertility d) Fecundity

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2) The prices of items decreased by 10% in 2024 as compared to 2020. The index number for the year 2024

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a) 10 b) 90 c) 100
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3) In a Poisson distribution, if λ = 2, the values
a) 0, 3 b) 0, 4 c) 3, 4 d) 1, 2

4) Type – I error is
a) Rejecting H0 when it is true b) Rejecting H0 when it is not true
c) Accepting H0 when it is true d) Accepting H0 when it is not true

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5) In inventory theory, shortage cost per unit good per unit time is denoted by
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a) P b) C1 c) C2 d) C3
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II. (5 X 1 = 5)
l a (Chance, Parameter, Σa = Σb , Retail, 1, 0) a g
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7) The value of variance and standard deviation of a standard normal distribution is ________.

8) A statistical constant of the population is called a __________.

9) A small amount of variation for which no specific cause can be attributed is termed as ______ variation.

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10) A transportation problem is said to be balanced if and only if __________.

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g la MODEL QUESTION PAPER FROM KSEAB
2026-27 II PU STATISTICS (31) Pagea of 4
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 4

III. Match the following: (5 X 1 = 5)
11) A B
a. 15 – 49 years i. Leptokurtic
b. Laspeyre’s price index ii. Left tailed test
c. Chi-square distribution curve iii. Child bearing age of females
d. H1: P < P0 iv. Transportation problem
e. Least cost entry method v. Upward bias
vi. Downward bias

IV. Answer the following questions: (5 X 1 = 5)
12) Mention one of the uses of vital statistics.
13) Define time series.
14) Write the mean of a Bernoulli distribution.
15) Write the formula of S.E.(p).
16) Mention a need for replacement of equipment.

SECTION – B

V. Answer any FIVE of the following questions: (5 X 2 = 10)
17) Mention a factor causing following variations in a time series:
(i) Seasonal variation (ii) Cyclical variation
18) Write two conditions for applying binomial expansion method of interpolation and extrapolation.
19) In a Poisson distribution, if P(X = 0) = 0.1225, write the probability mass function.
20) Mention two features of student’s t-distribution.
21) Define: ‘Point estimation’ and ‘interval estimation’.
22) In a paired t-test, if n = 5, d̅ = 3, and Sd = 2, then what would be the value of the test statistic?
̅ ′ = 65, σ′ = 5, and n =5, then write the upper control limit of X
23) In statistical quality control, if X ̅-chart.
24) For an equipment the fourth year depreciation cost is Rs 6,000 and the cumulative maintenance cost is
Rs 6,200. Find the average annual cost.

SECTION – C

VI. Answer any FOUR of the following questions: (4 X 5 = 20)
25) Calculate simple geometric mean price index number for the following data.
Item Price (in Rs)
Base year Current year
A 14 21
B 12 09
C 20 27
D 28 25

2026-27 II PU STATISTICS (31) MODEL QUESTION PAPER FROM KSEAB Page 2 of 4
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 4

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X 20 40 60 80 100
Y 20 32 54 90 144

27) Four fair coins are tossed 96 times. Find the expected frequencies of number of heads obtained.

28) Find the mean and variance of a hyper-geometric distribution with parameters a =4, b = 8, and n = 6.

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29) A sample of 64 students taken from a school. The mean and standard deviation of their heights are
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151 cm and 4 cm respectively. Test at 1% level of significance that average height of students is 150 cm.

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30) Solve the following game by using maximin-minimax principle. Is the game fair?

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a B1 B2 B3
A1 1 -1 3
Player – A A2 2 -1 2
A3 -1 0 0
A4 2 0 4

31) There is a demand for 10,000 items per year. The replenishment cost is Rs 200 and the maintenance cost

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is Rs 10 per year. Replenishment is instantaneous and shortages are not allowed. Find:
(i) Economic order quantity
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(ii) Re-order time.
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VII. Answer any TWO of the following questions: (2 X 5 = 10)
32) The weight of persons is normally distributed with mean 70 kg and standard deviation 4 kg. Find the
probability that a randomly selected person whose weight is:
(i) more than 62 kg
(ii) less than 74 kg.

33) In 60 throws of a single die, the following distribution of faces are obtained:
Face 1 2 3 4 5 6 Total
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Frequency 15 8 14 12 6 5 60
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Test at 5% level of significance that the die is unbiased.
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1
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6
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2 1
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3

35) Solve the following linear programming problem graphically:
Minimize Z = 10x + 8y
Subject to constraints: 4x + y ≥ 40
2x + 3y ≥ 60
and x, y ≥ 0
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3g
g la MODEL QUESTION PAPER FROM KSEAB
2026-27 II PU STATISTICS (31) Pagea of 4
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 4

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 2000 24 0.9
20 – 24 3000 204 0.9
25 – 29 5000 400 0.9
30 – 34 6000 336 0.8
35 – 39 4000 120 0.8
40 – 44 3500 70 0.7
45 – 49 2500 15 0.7

37) Show that Fisher’s index number satisfies time reversal test and factor reversal test for the following
data.
Items 2019 2024
Price (in Rs) Quantity Price (in Rs) Quantity
A 10 15 14 25
B 14 20 20 30
C 17 30 15 45
D 20 25 30 32

38) a) Find the trend values by five yearly moving averages for the following time series data. (05)
Year 2016 2017 2018 2019 2020 2021 2022 2023 2024
Value 40 44 41 47 43 55 54 56 62

b) Fit a straight line trend equation of the form y = a + bx to the time series data given below. (05)
Year 2014 2016 2018 2020 2022 2024
Profit (Lakh Rs) 12 10 20 25 30 41

SECTION - E
(For Visually challenged students only)

35) A tailor gets a profit of Rs.200 from a shirt and Rs. 300 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 the
linear programming problem.

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