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

FOR KARNATAKA CLASS 12 PREPARATION

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

Karnataka Class 12 2027 Sample Paper Statistics

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co

m .co s e m
se g l a
` a
GOVERNEMENT OF KARNATAKA
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
6th CROSS, MALLESHWARAM, BENGALURU-560 003
2026-27 II PUC MODEL QUESTION PAPER- 2
Subject: 31 - Statistics Maximum Marks: 80
Time: 3.00 Hours No. of Questions: 38
m
.co
Instructions:
m
.co
1. Statistical tables and graph sheets will be supplied on request.
e m
s
2. Scientific calculators are allowed.
e m
3. All working steps should be clearly shown.
l a
as
4. For ‘Section – A’ questions, only the first written answers will be considered for evaluation.
l ag
ag
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 condition for the time reversal test is
a) P01 x Q01 = V01 b) P01 x P10 = 1 c) P01 x P10 = 0 d) P01 x V01 = Q01
m
.co
em
2) In a binomial distribution, if np = 2, the relation between mean and mode is
a) Mean > Mode b) Mean < Mode
s c) Mean ≠ Mode
la when it is actually true is called
d) Mean = Mode

a g
3) The probability of rejecting the null hypothesis,
a) Size of a test b) Power of a test c) Type – I error d) Type – II error

4) In statistical quality control, if standard is known, then the central line of R-chart is
a) σ′ b) d2σ′ c) D1σ′ d) D2σ′

5) The minimum of the column maximums is known as
a) Strategy b) Saddle point c) Minimax
o m d) Maximin

m
II. Filloin . c
c. the blanks by choosing the appropriate answers given in the brackets: e m (5 X 1 = 5)

e m (Statistic, Cohort, 0, Irregular, 𝛘 (2), Parameter)
𝟐
l as
l as ag
g 6) The life table gives the life history of a __________ as it gradually diminished
a 7) The sudden unexpected variation in the time series is called ____________ variation.
by deaths.

8) If Z1 and Z2 are two standard normal variates, then the distribution of Z11 + Z22 is ___________.

9) A function of the sample values is called a ___________.

10) A game is said to be fair, if the value of the game is ___________.
m .
m .co s e m
s e l a
1g
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. The capacity of a woman to bear children i. Economically stable
b. Base period ii. Shortages are allowed
c. t-distribution curve iii. Shortages are not allowed
d. Likely value of the unknown parameter iv. Fecundity
e. Inventory model - II v. Estimate
vi. Asymptotic to the X-axis

IV. Answer the following questions: (5 X 1 = 5)
12) Write the formula for estimating population between census years.
13) Mention one of the uses of index numbers.
14) For what value of ‘p’ binomial distribution is symmetrical?
15) Define null hypothesis.
16) When do you say that a basic feasible solution of transportation problem is degenerate?

SECTION – B

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

17) Obtain the trend values by the method of semi-averages for the following time series data.
Year 2018 2019 2020 2021 2022 2023 2024
Value 30 52 44 50 40 46 58

18) Write two assumptions of interpolation and extrapolation.
3
19) Write the Bernoulli distribution with parameter p = .
5

20) If the parameter of t-distribution is 6, find the standard deviation.

21) Mention two branches of statistical inference.

22) Write the chi-square test statistic with degrees of freedom in testing of independence of attributes in 2x2
contingency table.

23) Mention two types of causes for variation in a manufacturing process.

24) If R = 100 units/month, C3 = Rs 100, and C1 = Rs 0.50/unit/month, then find Q0.

SECTION – C

VI. Answer any FOUR of the following questions: (4 X 5 = 20)
25) Calculate the consumer price index number by aggregative expenditure method for the following data.
Commodity Quantity Price per unit (in Rs)
2019 2019 2024
A 15 07 09
B 20 14 18
C 10 21 17
D 25 16 19
E 30 21 27
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

m
m .co

c.26)o Interpolate and extrapolate the sales for the years 2021 and 2025 fromstheemfollowing data.
m la 2024 2025
se Year
Sales (in Crore Rs)
2019
20
2020
24
2021
-
2022
30 g
2023
a 36 50 -

27) Fit a Poisson distribution to the following data and obtain the theoretical frequencies for the number of
printing mistakes per page.
Number of printing mistakes 0 1 2 3 4 & more
Number of pages 61 21 15 3 0

28) There are 15 lecturers in a college. Out of them, 8 belong to the science faculty. The college
m
.co
management builds 5 residential quarters and allots them to 5 randomly selected lecturers. By using
m
hyper-geometric distribution, find the probability that
.co
(i) all the quarters are allotted to science lecturers
s e m
em a
(ii) three quarters are allotted to science lecturers.

a s l
gdiameter
l a
g a standard deviation of 0.15 inches. Test whether the machine is functioning properly at
29) A machine makes screws with diameter 0.3 inches. A random sample of 10 screws show mean
0.32 inchesawith
5% level of significance.

30) Find an initial basic feasible solution for the following transportation problem by North-West corner rule
method and compute the total transportation cost.
Ware house
Supply
P Q R S
A 25 17 25 14 300
m
.co
B 15 10 18 24 500
Factory
C 16 20 8 13 600
Demand 75 325
s em 500 500 1400

g la Its maintenance cost and resale value at different years
31) The purchase price of a machine is Rs 25,000.
are as follows: a
Year 1 2 3 4 5
Maintenance cost (Rs) 600 1300 2020 3000 4100
Resale value (Rs) 19000 17000 15000 12000 10000
What would be the optimum replacement period for the machine?

VII. Answer any TWO of the following questions: (2 X 5 = 10)
32) Height of group of 1000 candidates, who attended the army selection camp is normally distributed with
m
.co
mean 154 cm and standard deviation 3 cm. Minimum eligible height for army selection is 157 cm. How

o m
many candidates from above group are eligible?
m
. c s e
emwho took PUC examination, 240 passed. At 1% level of significance, canglitabe concluded that SSLC
33) In an institution, out of 200 students who took SSLC examination, 180 passed and out of 300 students
s
la students have performed better than the PUC students? a
g
a 34) Ten samples each of size 5 were inspected and number of defectives in each of them are as follows:
Sample number 1 2 3 4 5 6 7 8 9 10
Number of defectives 0 1 2 3 3 2 1 0 1 2
Obtain the control limits for np-chart..

35) Solve the following linear programming problem graphically:
Maximize Z = 2x + 3y
Subject to constraints: x + y ≥ 350
m .
m
and x, y ≥ 0 .co
2x + y ≤ 600
s e m
s e l a
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) a) Compute the ‘total fertility rate’ from the following data. (05)
Age group Female Live
(in years) population births
15 – 19 20000 500
20 – 24 18000 1800
25 – 29 15000 1800
30 – 34 13000 1430
35 – 39 11000 550
40 – 44 10000 294
45 – 49 8000 80

b) Calculate the ‘standardized death rate’ for the following data. (05)
Age group Population Deaths Standard
(in years) population
0 – 20 8000 80 7000
20 – 40 10000 90 9000
40 – 60 7000 105 5000
60 & above 5000 155 4000

37) Calculate Marshall – Edgeworth’s and Fisher’s price index numbers from the following data.
2019 2024
Item
Price (in Rs) Quantity Price (in Rs) Quantity
A 10 12 19 15
B 14 15 22 19
C 21 25 19 37
D 27 20 36 25

38) Fit a quadratic trend equation of the form y = a + bx + cx2 by the method of least squares to the
following time series data. Estimate the value for 2024.
Year 2019 2020 2021 2022 2023
Value 40 20 30 15 25

SECTION - E
(For Visually challenged students only)

35) A manufacturer produces 2 products, A and b which need two machines P and Q. Product A requires 6
hours on machine P and 2 hours on machine Q. Product b requires 4 hours on machine P and 4 hours on
machine Q. There are 60 hours of time available on machine P and 80 hours on machine Q. Profit earned
by the manufacturer on selling one unit of product A is Rs 20 and one unit of product B is Rs 12.
Formulate the linear programming problem.

***

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