Kerala Plus Two Question Paper 2024 Statistics

Kerala Board

Question Paper
2024

Reg. No. : ......................................
SY-532 Name : ...........................................

SECOND YEAR HIGHER SECONDARY EXAMINATION, MARCH – 2024

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 6 questions from 1 to 7. Each carries 1 score. (6  1 = 6)
1. The maximum value of coefficient of correlation is
(a) 0 (b) 1
(c) –1 (d) 2

2. The time taken by a student to reach the school is an example of ______ variable.
(a) qualitative (b) discrete
(c) continuous (d) normal

3. The ratio of two independent chi-square variables is ______.
(a) Normal (b) t-statistic
(c) Chi-square statistic (d) F-statistic

4. An estimator, t is said to be an unbiased estimator for the parameter ‘’ if E(t) = _____.
(a)  (b) 0
(c) 1 (d) t

5. 1 – p (type II Error) = _____.
(a)  (b) 
(c) Power of a test (d) Level of significance

6. The test statistic used in ANOVA is _____.
(a) z (b) t
(c) 2 (d) F

7. The sale of cotton clothes in summer is associated with _____ component of time
series.
(a) Secular trend (b) Seasonal variation
(c) Cyclical variation (d) Irregular variation

Answer any 10 questions from 8 to 19. Each carries 2 scores. (10  2 = 20)
8. Write a short note on positive correlation and negative correlation between variables.

9. In a regression analysis the following results are obtained :
byx = 0.23, r = 0.45, x = 10
Find the standard deviation of y.

10. Find the derivative of the following function :
y = x2 + 3x + 4
SY-532 2

1  7    6  .
1  . (6  1 = 6)
1.      _________ .
(a) 0 (b) 1
(c) –1 (d) 2
2.       ______  
.
(a)  (b) 
(c)  (d) 

3.       ______  .
(a)  (b) t-
(c) -  (d) F-

4. t        
 E(t) = _________ .
(a)  (b) 0
(c) 1 (d) t
5. 1 – p ( II ) = _________.
(a)  (b) 
(c)   (d) 
6.     _________ .
(a) z (b) t
(c) 2 (d) F
7.     ________
 .
(a)   (b)  
(c)   (d) 

8  19    10  .
2  . (10  2 = 20)
8.      
 .
9.       .
byx = 0.23, r = 0.45, x = 10
‘y’   .

10.    .
y = x2 + 3x + 4

SY-532 3 P.T.O.

11. Evaluate the following definite integral :
1
. 2
 x dx.
.
0

12. A fair coin is tossed 16 times. Find the mean and variance of the number of heads
obtained.

13. Write down any 4 properties of normal curve.

14. If a sample of size 2 is taken from the population 2, 3, 5 without replacement, find the
mean of the sample means.

15. Name the four properties of a good estimator.

16. Distinguish between assignable causes and chance causes of variation in ANOVA.

–
17. Control charts for X and R charts are maintained on the tensile strength in kg of a
–
certain yarn. The subgroup size is 5. The values of X and R are computed for each
–
subgroup. Sum of Average of 25 subgroup is X = 514.8, R = 120. Compute control
–
limits for X chart. [Hint : A2 = 0.577]

18. What are the components of a time series ?

19. From the following data construct Simple Aggregate index number for 2014 taking
2011 as the base :
Commodities Price in 2014 Price in 2011
Rice 32 28
Oil 88 75
Sugar 40 35
Wheat 22 18
SY-532 4

11.   .
1
. 2
 x dx.
.
0

12.   16  .    
 .

13.    4  .

14. 2, 3, 5       
  .   .

15.    4  .

16.   ,    
 .

17.       .
–
  5 . X   R    
– –
. 25  X = 514.8, R = 120. X  
 . [ : A2 = 0.577]

18.    ?

19.     2011   2014  
 .
 2014   2011  
 32 28
 88 75
 40 35
 22 18

SY-532 5 P.T.O.

Answer any 6 questions from 20 to 27. Each carries 4 scores. (6  4 = 24)
20. The following data relate to time spent for exercising daily in minutes (X) and blood
pressure (Y) of a group of patients :
X Y
Mean 60 100
Standard deviation 20 15
r = –0.81
(a) Find the regression line of Y on X.
(b) Calculate the blood pressure of a person who exercised 70 minutes daily. (3 + 1)

21. A random variable X has the following probability distribution :
X –1 0 1
P(X) 0.4 0.3 0.3
Determine (a) E(X)
(b) V(X) (1 + 3)

22. For a variable X following Poisson distribution with  = 0.1, calculate
(1) P(X = 2)
(2) P(X is atleast 2) (1 + 3)

23. In an examination, 600 students have appeared for a paper in Economics. Their average
mark is normally distributed with Mean = 40 and Standard Deviation = 10. Find the
approximate number of students who get marks between 30 and 50.

24. Explain the concept of statistic and parameter with an example each.

25. The mean weight of a sample of 100 students is 52 kgs. with standard deviation 3 kgs.
Can it be considered as a sample taken from a normal population having mean greater
than 50 kgs. at 1% level of significance. (Z = 2.33)

26. The incomplete ANOVA table of a study is given below, complete the fields and
interpret the result.
Source df Sum of squares Mean sum of squares F
Between samples 5 – 12 –
Within samples – 76 –
Total 24 –
F0.01 = 4.17

SY-532 6

20  27    6  .
4  . (6  4 = 24)
20.      (X) (), 
(Y)    .
X Y
 60 100
  20 15
r = –0.81
(a) Y  X  .
(b)  70     
 . (3 + 1)
21. X      .
X –1 0 1
P(X) 0.4 0.3 0.3
(a) E(X)
(b) V(X)
 . (1 + 3)
22.   X     = 0.1 .
(1) P(X = 2)
(2) P(X  2 )  . (1 + 3)
23.    600  . 
   .   = 40,
 = 10 . 30  50   
  .
24. ,     .
25. 100      52  
 3 .  .    50 .  
     1%  
  . (Z = 2.33)
26.        
.     .
 df   F
  
 5 – 12 –
  – 76 –
 24 –
F0.01 = 4.17
SY-532 7 P.T.O.

27. The following data shows the values of range (R) for ten samples of size 5 each.
Calculate the values for central line and control limits for range chart. Also draw the
control chart and determine whether the process is under control. [D3 = 0, D4 = 2.115]
Sample No. Range (R)
1 7
2 4
3 8
4 5
5 7
6 4
7 8
8 4
9 7
10 9

Answer any 2 questions from 28 to 30. Each carries 5 scores. (2  5 = 10)
28. Calculate the Karl Pearson’s coefficient of correlation for the following :
X 5 10 5 11 12 4 3 2 7 1
Y 1 6 2 8 5 1 4 6 5 2
Also comment on the result.

29. (a) A time series is a set of data recorded ______.
(i) Geographically
(ii) Chronologically
(iii) Both geographically and chronologically
(iv) None of these
(b) The following data relate to the sale of mobile phones from a shop in the city
from 2005 to 2012. Calculate the trend values by 4 yearly moving average.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Sales 128 265 341 412 485 531 578 620 (1 + 4)

30. Using the following data calculate :
(a) Laspeyre’s Index Number
(b) Paasche’s Index Number
(c) Fisher’s Index Number
Commodities Base Year Current Year
Price Quantity Price Quantity
A 9.25 5 15 5
B 8 10 12 11
C 4 6 5 6
D 1 4 1.25 8
____________

SY-532 8

27. 5   10     
.    .
      .
[D3 = 0, D4 = 2.115]
  
1 7
2 4
3 8
4 5
5 7
6 4
7 8
8 4
9 7
10 9
28  30    2  .
5  . (2  5 = 10)
28.       
.   .
X 5 10 5 11 12 4 3 2 7 1
Y 1 6 2 8 5 1 4 6 5 2
29. (a)   _________   .
(i) 
(ii) 
(iii)   
(iv) 
(b)    2005  2012   
    . 4   
  .
Year 2005 2006 2007 2008 2009 2010 2011 2012
Sales 128 265 341 412 485 531 578 620 (1 + 4)
30.    
(a)   
(b)   
(c)   
 .
Commodities Base Year Current Year
Price Quantity Price Quantity
A 9.25 5 15 5
B 8 10 12 11
C 4 6 5 6
D 1 4 1.25 8
_____________
SY-532 9 P.T.O.

SY-532 10

SY-532 11 P.T.O.

SY-532 12

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