Kerala Plus Two Question Paper 2025 Statistics

KERALA BOARD

QUESTION
PAPER
2025
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Kerala Board of Public
Examinations

SY-432
Reg. No. : ......................................

Name : ...........................................

SECOND YEAR HIGHER SECONDARY EXAMINATION, MARCH 2025

Part – III Time : 2 Hours
STATISTICS Cool-off time : 15 Minutes
Maximum : 60 Scores

General Instructions to Candidates :
 There is a ‘Cool-off time’ of 15 minutes in addition to the writing time.
 Use the ‘Cool-off time’ to get familiar with questions and to plan your answers.
 Read questions carefully before answering.
 Read the instructions carefully.
 Calculations, figures and graphs should be shown in the answer sheet itself.
 Malayalam version of the questions is also provided.
 Give equations wherever necessary.
 Electronic devices except non-programmable calculators are not allowed in the
Examination Hall.

 
    15  ‘  ’ .
 ‘  ’    
 .
      .
    .
  , , ,   
.
   .
    .
     
    .

SY-432 1 P.T.O.

Answer any 5 questions from 1 to 6. Each question carries 1 score. Choose the
correct answer. (5  1 = 5)
1. Which among the following is an example of +ve correlation ?
(a) Distance and Intensity of light (b) Pressure and volume
(c) Height and distance (d) Income and expenditure

2. Regression analysis is a mathematical measure of the _____ of relationship between
two or more variables.
(a) Size (b) Nature
(c) Degree (d) Colour

3. Any control chart have _____ number of control limits.
(a) 2 (b) 1
(c) 4 (d) 5

4. A good estimator should be _____ .
(a) Consistent (b) Sufficient
(c) Efficient (d) All of the above

x
12
5. dx

x 12 x 11
(a) C (b) C
 12  11
x12 x11
(c) C (d) C
12 11

6. Two statements about binomial distribution are given below :
(i) Binomial distribution is a limiting case of Poisson distribution.
(ii) For binomial distribution, mean is greater than variance.
Choose the correct answer.
(a) (i) is true (b) (ii) is true
(c) Both (i) and (ii) are true (d) None

SY-432 2

1  6    5  .
1  . (5  1 = 5)
1.    positive   .
(a) ,  
(b) , 
(c) , 
(d) , 

2.       
 _____  .
(a)  (b) 
(c)  (d) 

3.    _____    .
(a) 2 (b) 1
(c) 4 (d) 5

4.   estimator _____ 
(a)  (b) 
(c)  (d)   

x
12
5. dx

x 12 x 11
(a) C (b) C
 12  11
x12 x11
(c) C (d) C
12 11

6.      
 :
(i)      
.
(ii)     .
 .
(a) (i)  (b) (ii) 
(c) (i)  (ii)   (d)   .

SY-432 3 P.T.O.

Answer any 5 questions from 7 to 12. Each question carries 2 scores. (5  2 = 10)
7. On a regression analysis in income (X) and expenditure (Y), the following regression
equations are observed :
x+y+3=0
5x – y + 16 = 0
–– ––
Find the values of X and Y.

8. Find the derivative of y = x6 + 48x3 + 24x – 16 with respect to x.

9. The following table shows the probability mass function of a random variable X.

x 0 1 2 3

p(x) 0.2 0.3 k 0.3

Find the value of k.

10. Match the following :

A B

12 /n1
(i) If Z ~ N(0, 1) then Z2 (1)
 22 /n 2

2
(ii) 2 statistic (2) (1)

nS2
(iii) Student ‘t’ statistic (3)
2

X
(iv) F statistic (4) ; X & Y independent
Y
n
X ~ N(0, 1) Y ~ 2(n)

11. Write the important assumptions of ANOVA.

12. A random sample from a population is given below.
35, 45, 40, 42, 39, 55 and 63. Obtain the moment estimator of the population mean.
SY-432 4

7  12    5  .
2  . (5  2 = 10)
7.  (X),  (Y)     
     :
–– ––
X, Y  
x+y+3=0
5x – y + 16 = 0

8. y = x6 + 48x3 + 24x – 16   x   .

9. X       (pmf)  
 .
x 0 1 2 3
p(x) 0.2 0.3 k 0.3
k   .

10.   :
A B

12 /n1
(i) If Z ~ N(0, 1)  Z2 (1)
 22 /n 2
2
(ii) 2  (2) (1)

nS2
(iii) Student ‘t’ statistic (3)
2

(iv) F  X
(4) ; X & Y independent
Y
n
X ~ N(0, 1) Y ~ 2(n)

11.    .

12. 35, 45, 40, 42, 39, 55, 63      
.     .
SY-432 5 P.T.O.

Answer any 5 questions from 13 to 19. Each question carries 3 scores. (5  3 = 15)
13. Scores obtained by five students in physics and statistics are given below. Find Karl
Pearson’s coefficient of correlation.

Marks in 35 15 25 10 20
Physics

Marks in 29 65 35 26 18
Statistics

14. Define :
(i) Type i error
(ii) Type ii error
(iii) Power of the test

15. An agency studied the rapid increase in the number of drug users in a country. For the
data complete the ANOVA table.

Source of variation d.f. s.s. m.s.s. F F0.01

Between 16 – – – –

Error – – 6.3

Total 30 555

16. For the given table, calculate simple aggregate Index Number.

Commodities Price 2014 Price 2016

Rice 32 36

Oil 110 115

Wheat 25 30

Sugar 41 46

SY-432 6

13  19    5  .
3  . (5  3 = 15)

13. 5       
    .
 35 15 25 10 20

 29 65 35 26 18


14.  :
(i) Type i error
(ii) Type ii error
(iii)    

15.        
  ANOVA   .  
.
Source of variation d.f. s.s. m.s.s. F F0.01

Between 16 – – – –
Error – – 6.3
Total 30 555

16.        
.
Commodities  2014  2016
Rice 32 36
Oil 110 115
Wheat 25 30
Sugar 41 46

SY-432 7 P.T.O.

17. Consider a random variable X which takes the values given below. Find the
distribution function F(x).

x 1 2 3 4 5 6

P(x) 0.1 0.3 0.1 0.2 0.1 0.2

18. If Z ~ N(0, 1), then find the following probabilities :

(i) P(–1.2 < Z < 1.2)

(ii) P(0 < Z < 2.3)

(iii) P(Z < –1.6)

19. A random sample of 100 is taken from a population. The mean and standard deviation
are respectively 76 and 12. Obtain a 99 confidence interval for the mean of the
population.

Answer any 5 questions from 20 to 25. Each question carries 4 scores. (5  4 = 20)

20. The following data refer to the sales of a company from 2005 to 2014. Calculate the
trend value by five yearly moving average method :

Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Sales 2480 1694 3706 1531 2642 3124 1234 3531 2345 3124

21. Find the Rank correlation coefficient using the rankings of ten students in two
examination subjects and comment on the correlation.

Subject I 2 4 1 3 5 7 9 10 6 8

Subject II 1 5 2 7 3 4 6 8 9 10

SY-432 8

17. X       .
   F(x) .

x 1 2 3 4 5 6

P(x) 0.1 0.3 0.1 0.2 0.1 0.2

18. Z ~ N(0, 1)    probabilities   :

(i) P(–1.2 < Z < 1.2)
(ii) P(0 < Z < 2.3)
(iii) P(Z < –1.6)

19.    100     
.   76 ,   12 
.   99 confidence  .

20  25    5  .
4  . (5  4 = 20)

20.   2005  2014     
.   five yearly   
 :

Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Sales 2480 1694 3706 1531 2642 3124 1234 3531 2345 3124

21.        
  .  .

Subject I 2 4 1 3 5 7 9 10 6 8

Subject II 1 5 2 7 3 4 6 8 9 10

SY-432 9 P.T.O.

22. (i) A sample is known as small sample if its size is _____ .
(a) less than 50
(b) greater than 50
(c) less than 30
(d) greater than 30 (1)
(ii) Equations of two lines of regression are 2x – 5y + 33 = 0 and 30x – 9y – 108 = 0.
Which one is regression line of y on x ? (3)

23. You are given the sample mean and range of five samples of size four
––
each. Construct X chart and state whether the process is under statistical control or
not. (A2 = 0.729)

Sample 1 2 3 4 5

Average X
–– 2.6 3.2 4.3 2.4 2.3

Range R 0.3 0.3 0.2 0.5 0.1

24. 1000 Employees in a company were graded according to their performance and age
groups. Examine whether there is any association between age groups and their
performance.

Age group

< 50 > 50 Total
Performance

Low 100 300 400

High 350 250 600

Total 450 550 1000

12 for  = 0.05 is 3.84

25. In a distribution exactly normal, 7 of the items are under 35 and 89 are under 63.
Find the mean and standard deviation of the distribution.
SY-432 10

22. (i)        
_____ .
(a) 50  
(b) 50  
(c) 30  
(d) 30   (1)
(ii)    .
2x – 5y + 33 = 0
30x – 9y – 108 = 0
    y on x  . (3)

23.         
––
. X chart      
. (A2 = 0.729)
Sample 1 2 3 4 5

Average X
–– 2.6 3.2 4.3 2.4 2.3

Range R 0.3 0.3 0.2 0.5 0.1

24.   1000   ,
   .  
   .
Age group
< 50 > 50 Total
Performance

Low 100 300 400

High 350 250 600

Total 450 550 1000

12 for  = 0.05 is 3.84

25.     7  35   89
 63   . ,   
.

SY-432 11 P.T.O.

Answer any 2 questions from 26 to 28. Each question carries 5 scores. (2  5 = 10)
26. Calculate the following Index Numbers using the data given below :
(i) Laspeyre’s Index Number
(ii) Paasche’s Index Number
(iii) Fisher’s Index Numbers
2017 2018
Commodities
Price (`) Qty (kg) Price (`) Qty (kg)
A 25 8 30 9
B 28 7 29 8
C 40 4 42 6
D 48 6 50 8

27. (i) The sale of umbrellas during rain is associated with _____ component of time
series.
(a) Secular trend
(b) Seasonal variation
(c) Cyclical variation
(d) Irregular variation (1)
(ii) Index Numbers are called Economic Barometers. Is it True or False ? (1)
(iii) Draw all possible samples of size two in SRSWOR from a population consisting
––
of values 3, 4, 5, 6 and 9. Also find E(X). Check whether sample mean is an
unbiased estimator of population mean ? (3)

28. (i) For the following probability distribution :
Evaluate
(a) E(X) (b) E(X2) (c) V(X)
X 5 6 0 1 2
3 2 7 2 1
P(x)
15 15 15 15 15 (3)
(ii) The mean of a binomial distribution is 9 and variance is 6. Write the probability
mass function and hence evaluate P(X = 2). (2)

____________

SY-432 12

26  28    2  .
5  . (2  5 = 10)
26.       
 :
(i)   
(ii)   
(iii)   
2017 2018
Commodities
Price (`) Qty (kg) Price (`) Qty (kg)
A 25 8 30 9
B 28 7 29 8
C 40 4 42 6
D 48 6 50 8

27. (i)      
.
(a)  
(b)  
(c)  
(d)   (1)
(ii)      . 
,  ? (1)
(iii) 3, 4, 5, 6, 9    SRSWOR   
––
     E(X) .  
      ? (3)

28. (i)     
 :
(a) E(X) (b) E(X2) (c) V(X)
X 5 6 0 1 2
3 2 7 2 1
P(x)
15 15 15 15 15 (3)
(ii)     9 ,  6  .
   .   P(X = 2)
. (2)
____________

SY-432 13 P.T.O.

SY-432 14

SY-432 15 P.T.O.

SY-432 16