Kerala Plus Two Question Paper 2023 Statistics

SECOND YEAR

Kerala Board
Question Paper
2023

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Reg. No. : ......................................
Name : ...........................................
SY-532
SECOND YEAR HIGHER SECONDARY EXAMINATION, MARCH 2023

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-532 1 P.T.O.

Answer any 10 questions from 1 to 12. Each carries 3 scores. (10  3 = 30)
1. Explain different types of correlation.

2. (a) If r = 0, then the regression lines are ________.
(i) coincident (ii) parallel
(iii) perpendicular (iv) intersect
(b) Calculate standard deviation of y if
bxy = 1.5, x = 4 and r = 0.65 (1 + 2)

3. The probability mass function of a discrete random variable X is given. Calculate the
mean and variance of X.

x 0 1 2 3
p(x) 0.1 0.3 0.4 0.2

4. (a) Define distribution function of a continuous random variable.
(b) What are the properties of distribution function of a continuous random variable ?
(1+2)

5. (a) For a standard normal variable z, P(0 < z < ) = ________.
(i) 1 (ii) greater than 0.5
(iii) less than 0.5 (iv) 0.5
(b) If X follows a normal distribution with mean 28 and standard deviation 5. Find
P(25 < X < 30). (1 + 2)

6. (a) The probability density function of a normal random variable X is
– ( x – 20)2
1
f(x) = e 8 , – < x < 
2 2
The standard deviation of X is ________.
(i) 2 (ii) 2
(iii) 4 (iv) 8
(b) Write any four properties of a normal curve. (1 + 2)

SY-532 2

1  12    10  .
3  . (10  3 = 30)
1.    .

2. (a) r = 0     ________ .
(i)   (ii)  
(iii)   (iv)   
(b) bxy = 1.5, x = 4, r = 0.65  y  
 . (1 + 2)

3.        . X 
  .
x 0 1 2 3
p(x) 0.1 0.3 0.4 0.2

4. (a)      .
(b)       
 ? (1+2)

5. (a) ‘z’     .
P(0 < z < ) = ________ .
(i) 1 (ii) 0.5  
(iii) 0.5   (iv) 0.5
(b) X      28  
 5  . P(25 < X < 30) . (1 + 2)

6. (a) X        
– ( x – 20)2
1
f(x) = e 8 , – < x < .
2 2
X    ________ .
(i) 2 (ii) 2
(iii) 4 (iv) 8
(b)       . (1 + 2)

SY-532 3 P.T.O.

7. X1, X2, X3 is a random sample drawn from a population with mean  and standard
deviation .
T1 = 2X1 + 2X2 – 3X3 and T2 = X1 + 2X2 – 2X3 are unbiased estimators of . Obtain
the efficient estimator.

8. (a) If ‘t’ is an estimator of the parameter ‘’, and E(t) = , then ‘t’ is called ________
estimator of .
(i) unbiased (ii) consistent
(iii) efficient (iv) sufficient
(b) A sample drawn from a population is given below :
Obtain the moment estimate for the population mean.
Sample values :14, 12, 13, 17, 19, 20, 13, 22, 19, 21, 15, 16 (1 + 2)

9. (a) Define assignable causes of variations in ANOVA.
(b) What are the assumptions of ANOVA ? (1 + 2)

10. Complete the ANOVA table and interpret the result :
Source df SS MSS F F0.05

Between Samples 8 – 45.2
– 2.95
Within Samples – – 3.5
Total 19 400.1

11. (a) Decrease in the consumption due to some epidemic is associated with ________
component of time series.
(i) Secular trend (ii) Seasonal variation
(iii) Cyclical variation (iv) Irregular variation
(b) Explain cyclical variations in time series analysis. (1 + 2)

12. (a) In Paasche’s Index, the weights used are _______.
(i) Base year price (ii) Base year quantity
(iii) Current year price (iv) Current year quantity
(b) Write any four uses of Index Numbers. (1 + 2)
SY-532 4

7.  ‘’    ‘’     
   X1, X2, X3.
T1 = 2X1 + 2X2 – 3X3 , T2 = X1 + 2X2 – 2X3     
.     .

8. (a) ‘t’  ‘’    . E(t) =    ‘t’
 ‘’  ________ .
(i)  (ii) 
(iii)  (iv) 
(b)      . 
    :
  :14, 12, 13, 17, 19, 20, 13, 22, 19, 21, 15, 16 (1 + 2)

9. (a)    
.
(b)    . (1 + 2)
10.      :
 df SS MSS F F0.05
 8 – 45.2

– 2.95
 – – 3.5

 19 400.1

11. (a)        
 ________  .
(i)   (ii)  
(iii)   (iv)  
(b)      
. (1 + 2)

12. (a)      _______ 
.
(i)    (ii)   
(iii)    (iv)   
(b)     . (1 + 2)

SY-532 5 P.T.O.

Answer any 5 questions from 13 to 18. Each carries 4 scores. (5  4 = 20)
13. The two lines of regression are
2x + 3y – 31 = 0 and 5x + 4y – 28 = 0.
(a) Which one is the regression line of Y on X ?
(b) Obtain the correlation between X and Y. (3 + 1)

14. (a) Find the second derivative of the function y = 4x3 – 2x2 + 7x + 9.
2
(b) Find the value of  (x2 – 2) dx. (2 + 2)
0

15. (a) Which distribution is known as the law of improbable events ?
(i) Binomial distribution (ii) Poisson distribution
(iii) Normal distribution (iv) Chi-square distribution
(b) The mean of a Binomial distribution is 4 and its variance is 3. Write the
probability mass function of the distribution. (1 + 3)

16. (a) If Z is a standard normal variable, then distribution of Z2 is _________.
2 2
(i)  (1) (ii)  (n) 

(iii) t(n) (iv) Fn , n
1 2

(b) Draw all possible samples of size 2 from a population consisting of 3, 5, 7, 9, 11
under SRS WOR method. Find E( X ). (1 + 3)

17. (a) To test the independence of attributes which of the following test is used ?
(i) Z-test (ii) t-test
(iii) Chi-square test (iv) F-test
(b) Define :
(i) Level of Significance
(ii) Power of a test
(iii) Critical region (1 + 3)

SY-532 6

13  18    5  .
4  . (5  4 = 20)
13. 2x + 3y – 31 = 0 , 5x + 4y – 28 = 0    .
(a)  X   Y     .
(b) X  Y    . (3 + 1)

14. (a)       .
y = 4x3 – 2x2 + 7x + 9.
2
(b)  (x2 – 2) dx   . (2 + 2)
0

15. (a)       
 ?
(i)   (ii)  
(iii)   (iv) - 
(b)     4   3  . 
   . (1 + 3)

16. (a) ‘Z’       Z2  
_________ .
2 2
(i)  (1) (ii)  (n) 

(iii) t(n) (iv) Fn , n
1 2

(b) 3, 5, 7, 9, 11       
 2    SRSWOR . E( X )
. (1 + 3)

17. (a)     
 .
(i) Z- (ii) t-
(iii) -  (iv) F-
(b)  :
(i)  
(ii)  
(iii)   (1 + 3)
SY-532 7 P.T.O.

18. The following data shows the number of deaths due to smoking for 8 years in a state :
Year 2011 2012 2013 2014 2015 2016 2017 2018
No. of Deaths 175 190 185 195 180 203 197 252
Calculate trend values by 3-yearly moving average method.

Answer any 2 questions from 19 to 21. Each carries 5 scores. (2  5 = 10)
19. Find Karl Pearson’s coefficient of correlation between the variables given below :

X 18 28 12 25 22 15 7 16
Y 12 19 21 34 25 20 15 14

20. The sample mean ( x ) and the range (R) of 12 samples of size 4 each are given below :

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12
x 32 38 33 40 28 36 35 30 42 40 41 39

R 4 7 3 9 2 4 3 5 3 8 5 6
(a) Calculate the control limits for x -chart. (Given A2 = 0.729)
(b) Draw x -chart and comment on the state of control. (2½+2½)

21. Calculate :
(i) Laspeyer’s Index
(ii) Paasche’s Index
(iii) Fisher’s Index
for the following data :

2010 2015
Commodities
Price Quantity Price Quantity
A 30 5 39 5

B 27 8 45 4
C 36 7 38 6
D 42 3 45 4
___________

SY-532 8

18.   8     
  :
 2011 2012 2013 2014 2015 2016 2017 2018
 175 190 185 195 180 203 197 252

3-       .

19  21    2  .
5  . (2  5 = 10)
19.        
 :
X 18 28 12 25 22 15 7 16
Y 12 19 21 34 25 20 15 14

20.   4  12    ( x ) 
(R)  :
 1 2 3 4 5 6 7 8 9 10 11 12

x 32 38 33 40 28 36 35 30 42 40 41 39
R 4 7 3 9 2 4 3 5 3 8 5 6
(a) x -   . (A2 = 0.729)
(b) x - ,    . (2½+2½)

21. (i)  
(ii)  
(iii)  
     :
2010 2015

   
A 30 5 39 5
B 27 8 45 4
C 36 7 38 6
D 42 3 45 4
___________

SY-532 9 P.T.O.

SY-532 10

Statistical Table

SY-532 11 P.T.O.

SY-532 12