Kerala Plus Two Question Paper 2022 Statistics

Reg. No. : .....................................
Name : ..........................................
SY-32
SECOND YEAR HIGHER SECONDARY EXAMINATION, MARCH 2022

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.
 Statistical tables can be used in the examination hall.

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

SY-32 1 P.T.O.

PART – I

A. Answer any 5 questions from 1 to 9. Each carries 1 score. (5  1 = 5)
Choose the correct answer for the following questions :
1. If F(x) is a c.d.f. of a random variable X then F[–] = ________.
(a) 0 (b) 1
(c) –1 (d) –

2. Consider the following bivariate data :
X 2 4 6 8
Y 1 3 5 7
Correlation coefficient between X and Y is ________.
(a) 0 (b) 1
(c) –1 (d) 0.5

3. Who is known as the father of Quality Control Analysis ?
(a) R.A. Fisher (b) P.C. Mahalanobis
(c) Francis Galton (d) Walter A. Schewhart

e –4 4 x
4. Random variable X has p.m.f. f(x) = ; x = 0, 1, 2, ..... . Which of the
x!
following is true ?
(a) E(X) = 0 and V(X) = 0 (b) E(X) = 2 and V(X) = 2
(c) E(X) = 4 and V(X) = 4 (d) E(X) = 4 and V(X) = 2

5. If Cov(x, y) = xy then correlation coefficient is ________.
(a) 1 (b) 0
(c) –1 (d) 2

6. Probability distribution of a statistic is called _______ distribution.
(a) Binomial (b) Poisson
(c) Normal (d) Sampling

SY-32 2

PART – I

A. 1  9    5  .
1  . (5  1 = 5)
     :
1.    c.d.f. F(x)   F[–] = ________

(a) 0 (b) 1
(c) –1 (d) –

2.      :
X 2 4 6 8
Y 1 3 5 7
X  Y     ________ .
(a) 0 (b) 1
(c) –1 (d) 0.5

3.        ?
(a) R.A.  (b) P.C. 
(c)   (d) .. 

e –4 4 x
4. X    p.m.f. f(x) = ; x = 0, 1, 2, ..... 
x!
   ?
(a) E(X) = 0; V(X) = 0 (b) E(X) = 2; V(X) = 2
(c) E(X) = 4; V(X) = 4 (d) E(X) = 4; V(X) = 2

5. Cov(x, y) = xy     ________
.
(a) 1 (b) 0
(c) –1 (d) 2

6.     _______
  .
(a)  (b) 
(c)  (d) 

SY-32 3 P.T.O.

7. Year 2016 2017 2018 2019 2020 2021

Earnings (in lakhs) 15 14 16 17 15 13
Semi average trend values for the above data is
(a) 14, 15 (b) 15, 15
(c) 15, 13 (d) 16, 17

8. If Laspeyer’s index number = 120 and Paasche’s index number = 130 then Fisher
index number is ________.
(a) 120 (b) 130
(c) 128 (d) 124.9

9. Correlation coefficient between X and Y is 0.7. Standard deviation of X = 2 and
Standard deviation of Y = 5. Regression coefficient of Y on X is ________.
(a) 0.19 (b) 14.3
(c) 1.75 (d) 0.28

B. Answer all questions from 10 to 13. Each carries 1 score. (4  1 = 4)
10. Find the derivative of x3 + x + 1.

11. Choose the correct answer :
X is a continuous random variable with variance 4. The values of V(2X + 1) is
________.
(a) 8 (b) 4
(c) 9 (d) 16

12. Choose the correct answer :
Sample values taken from a population are 10, 12, 13, 14, 13, 10 moment estimate
of population mean is ________.
(a) 13 (b) 12
(c) 11.5 (d) 72

13. If P[0 < Z < Z1] = 0.4251 then find the value of Z1, where Z ~ N(0, 1).

SY-32 4

7.  2016 2017 2018 2019 2020 2021
() 15 14 16 17 15 13
        ?
(a) 14, 15 (b) 15, 15
(c) 15, 13 (d) 16, 17

8.    = 120    = 130
     ________ .
(a) 120 (b) 130
(c) 128 (d) 124.9

9. X  Y     0.7 . X 
  2  Y    5 
   Y on X ________ .
(a) 0.19 (b) 14.3
(c) 1.75 (d) 0.28

B. 10  13    . 1  .
(4  1 = 4)
10. x3 + x + 1   .

11.   :
X     4 . V(2X + 1) 
 ________ .
(a) 8 (b) 4
(c) 9 (d) 16

12.   :
      10, 12, 13, 14, 13, 10
.     ________ .
(a) 13 (b) 12
(c) 11.5 (d) 72

13. P[0 < Z < Z1] = 0.4251  Z1   .  Z ~ N(0, 1)
.

SY-32 5 P.T.O.

PART – II

A. Answer any 2 questions from 14 to 17. Each carries 2 scores. (2  2 = 4)

14. Match the following :

(A) (B)

(i) (a) Cyclical Variation

(ii) (b) Irregular Variation

(iii) (c) Seasonal Variation

(iv) (d) Secular Trend

SY-32 6

PART – II

A. 14  17    2  .

2  . (2  2 = 4)

14.   :

(A) (B)

(i) (a) 



(ii) (b) 



(iii) (c) 



(iv) (d) 



SY-32 7 P.T.O.

15. Find control limits for X -chart. X = 16.2 and R = 7.4 are given for 10 samples
of size 5 each.

16. Define (a) Type-I error (b) Type-II error in testing of hypothesis.

17. In a bivariate data following results were obtained :
Mean value of x = 53, Mean value of y = 27, Regression Co-efficients
byx = –1.5, bxy = –0.2.

Find the most likely value of y when X = 60.

B. Answer any 2 questions from 18 to 20. Each carries 2 scores. (2  2 = 4)
18. Distinguish between Point estimation and Interval estimation of a parameter.

19. If X ~ N (68, 2) and P[X > 72] = 0.1587. Find the value of .

20. If the two regression lines are X + 2Y = 5 and 2X + 3Y = 8 then calculate
Arithmetic means of X and Y.

PART – III

A. Answer any 3 questions from 21 to 24. Each carries 3 scores. (3  3 = 9)
21. (a) Find integral of 8 with respect to x.
1
(b) Evaluate :  (x + 1) dx (1 + 2)
0

22. X be a normal variable with mean 50 and standard deviation 10. Find P[X < 70].

23. A population consists of the values 8, 9, 13, 15 and 16. Take all possible samples
of size 2 by SRSWOR.
(a) Find mean of the population.
(b) Check whether E (Sample Mean) = Population Mean.

SY-32 8

15. 5  10  X = 16.2  R = 7.4   X -
  .

16.   (a) -I  (b) -II  
.

17.    x    = 53, y    = 27,
  byx = –1.5, bxy = –0.2.
X   60  y     .

B. 18  20    2  .
2  . (2  2 = 4)
18.  ,    
.

19. X ~ N (68, 2)  P[X > 72] = 0.1587     
.

20. X + 2Y = 5, 2X + 3Y = 8     . X 
 Y    .

PART – III

A. 21  24    3  .
3  . (3  3 = 9)
21. (a) x  8   .
1
(b)  (x + 1) dx . (1 + 2)
0
22. X    . X   50  
 10  . P[X < 70] .

23. 8, 9, 13, 15, 16   . SRSWOR  2
  .
(a)   .
(b) E ( ) =    .

SY-32 9 P.T.O.

24. Sales of statistics books in a School from 2015 to 2020 as follows :

Year 2015 2016 2017 2018 2019 2020

Number of books 15 28 30 28 26 32

Calculate 3 year moving average values.

B. Answer any 2 questions from 25 to 27. Each carries 3 scores. (2  3 = 6)
25. From the following data, calculate the rank correlation coefficient between X and
Y:

X 36 56 20 65 56

Y 50 35 70 25 58

26. A continuous random variable X has the p.d.f., f(x) = 2x ; 0  x  1
= otherwise
Obtain distribution function of X.

27. Total revenue of a firm is given by R(X) = 22X – X2. Where ‘X’ is the number of
units sold. Find the optimum (Maximum or Minimum) revenue that the company
can take.
PART – IV

A. Answer any 3 questions from 28 to 31. Each carries 4 scores. (3  4 = 12)
28. Let x = 6.14, y = 4, xy = 209, y2 = 146, n = 7. Write the regression equation
x on y.

29. A discrete random variable X has the p.m.f. :

X 1 2 3

1 2 3
P(x)
6 6 6
Find
(a) P[1  X  2]
(b) E(X)
(c) V(X) (1 + 1 + 2)
SY-32 10

24. 2015  2020      
    :
 2015 2016 2017 2018 2019 2020
  15 28 30 28 26 32
3     .

B. 25  27    2  .
3  . (2  3 = 6)
25.     X  Y   
   :
X 36 56 20 65 56
Y 50 35 70 25 58

26. f(x) = 2x ; 0  x  1
= .
 X     p.d.f. . X 
  .

27.     R(X) = 22X – X2 . ‘X’ 
  .   
   .
PART – IV

A. 28  31    3  .
4  . (3  4 = 12)
28. x = 6.14, y = 4, xy = 209, y2 = 146, n = 7  . 
 x on y .

29. X     p.m.f.   :
X 1 2 3
1 2 3
P(x)
6 6 6
(a) P[1  X  2]
(b) E(X)
(c) V(X)
 . (1 + 1 + 2)

SY-32 11 P.T.O.

30. (a) Write the conditions required for binomial experiments.

(b) X follows binomial distribution with mean = 6 and variance = 3.6.

Find probability of ‘Success’. (2 + 2)

31. (a) What you mean by assignable factors in ANOVA ?

(b) Complete the ANOVA table given below and make a conclusion :

Source d.f. SS M.S.S. F F0.05

Between — 18 — 1.2 4.07

Within 8 — 5

Total 11 — (1 + 3)

B. Answer any 1 question from 32 and 33. Carries 4 scores. (1  4 = 4)

32. Two lines of regression are y – x = 5 and 16x = 9y – 94.

(a) Identify the given lines as regression line of y on x and regression line of
x on y.

(b) Find regression coefficients.

(c) Compute correlation coefficient. (2 + 1 + 1)

33. The result of a test can be summarised as :

Result
Gender Total
Pass Fail

Male 28 12 40

Female 34 26 60

Calculate Chi-square statistics value.
SY-32 12

30. (a)     .
(b)     X   = 6 
 = 3.6  . ‘’  . (2 + 2)

31. (a) ANOVA     
 ?
(b)   ANOVA  
  :

Source d.f. SS M.S.S. F F0.05

Between — 18 — 1.2 4.07

Within 8 — 5

Total 11 — (1 + 3)

B. 32  33     . 4 

(1  4 = 4)
32. y – x = 5, 16x = 9y – 94    .
(a)    y on x, x on y 
.
(b)   .
(c)   . (2 + 1 + 1)

33.     :


 
 

 28 12 40

 34 26 60

Chi-square   .

SY-32 13 P.T.O.

PART – V
Answer any 2 questions from 34 to 36. Each carries 6 scores. (2  6 = 12)
34. Scores obtained (out of 15) for 5 students in a class test as follows :

English 8 6 10 7 15

Statistics 10 7 8 4 6

Calculate Karl Pearson’s correlation coefficient.

35. (a) Find Simple A.M. Price Index for the following data :

Price in 2020 44 38 48

Price in 2021 48 40 54

(b) Calculate Laspeyer’s index for the following data :

Base Year Current Year

Price Quantity Price Quantity

2 20 5 15

4 4 8 5

1 10 2 12

5 5 10 6 (2 + 4)

36. (a) X1, X2, X3 is a random sample taken from a population with Mean  and
Standard Deviation . Let T1 = 2X1 – 2X2 + X3 and T2 = 3X1 – X2 – X3 are
two unbiased estimators of . Find which one is more efficient.
(b) A sample of 144 observations is taken from a population with Mean 50.
The Sample Mean = 55 with S.D. = 20. Test the hypothesis that
population Mean is equal to the Sample Mean at 5% level of significance.
(Given Z/2 = 1.96) (3 + 3)

___________

SY-32 14

PART – V
34  36    2  .
6  . (2  6 = 12)
34.    5    (15 ) 
 :
 8 6 10 7 15
 10 7 8 4 6
    .

35. (a)     A.M.  
 :
2020   44 38 48

2021   48 40 54

(b)       :
   
   
2 20 5 15
4 4 8 5
1 10 2 12
5 5 10 6 (2 + 4)

36. (a)   ,       
   X1, X2, X3 . T1 = 2X1 – 2X2 + X3,
T2 = 3X1 – X2 – X3    2   .
    ?
(b)  50     144 
.   = 55    = 20
 .     5%
   . (Z/2 = 1.96 
) (3 + 3)
___________

SY-32 15 P.T.O.

SY-32 16