Kerala Plus One Question Paper 2025 Statistics

KERALA BOARD

QUESTION
PAPER
2025
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Kerala Board of Public
Examinations

FY-332
Reg. No. : ......................................

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

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

FY-332 1 P.T.O.

Answer any 5 questions from 1 to 6. Each carries 1 score. (5  1 = 5)

1. Which organization publishes the journal ‘SANKHYA’ ?

(a) CSO (b) NSSO

(c) ISI (d) KSA

2. Consider the following statements about the requisites of a questionnaire :

I : Questions should be capable of generating all required information.

II : No logical arrangement of questions is needed.

Choose the correct answer.

(a) I and II are correct (b) I is correct and II is not correct

(c) I is not correct and II is correct (d) I and II are not correct

3. Arranging the sample values in ascending or descending order is essential to calculate
this :

(a) Mean (b) Median

(c) Mode (d) Standard deviation

4. To compare two data sets with different units, we use measures that are free from units.
Which of the following is a unit free measure ?

(1) Mean Deviation

(2) Standard Deviation

(3) Coefficient of variation

Select the correct answer from the options given below :

(a) (1) only (b) (2) only

(c) (2) and (3) (d) (3) only

FY-332 2

1  6    5  .

1  . (5  1 = 5)

1.   ‘SANKHYA’    ?
(a) CSO (b) NSSO
(c) ISI (d) KSA

2.      
.
I :     
.
II :    .
   :
(a) I  II  . (b) I , II 
(c) I , II . (d) I  II  

3.       
  .
(a)  (b) 
(c)  (d)  

4.        
    . 
    .
(1)  
(2)  
(3)  
      .
(a) (1)  (b) (2) 
(c) (2)  (3) (d) (3) 

FY-332 3 P.T.O.

5. For a distribution Q1 + Q3 > 2Q2, then the distribution is :

(a) Positively skewed (b) Negatively skewed

(c) Symmetric (d) None of these

6. As compared to census survey, sample survey helps in reducing :

(a) Cost of the study (b) Time require for the study

(c) Both cost and time (d) Neither cost nor time

Answer any 4 questions from 7 to 12. Each carries 2 scores. (4  2 = 8)

7. Give a brief description about NSSO.

8. Write FOUR methods of collecting primary data.

9. Prepare a percentage frequency table :

Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

Frequency 3 7 10 2 3

10. Name two graphs that can be used to measure the central tendency of a data.

11. For a distribution 2 = 4 and 4 = 48. Determine the nature of kurtosis.

12. Name two non-probability sampling methods.

FY-332 4

5.   Q1 + Q3 > 2Q2    :

(a)   (b)  

(c)  (d) 

6.    ,   
 :

(a)  (b)   

(c)   (d)  

7  12    4  .
2  . (4  2 = 8)

7. NSSO     .

8.      .

9.     :
 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
 3 7 10 2 3

10.        
 .

11.   2 = 4  4 = 48 .  
.

12.     .

FY-332 5 P.T.O.

Answer any 5 questions from 13 to 18. Each carries 3 scores. (5  3 = 15)

13. In a school, 620 parents applied for their child’s admission, out of which 130 children
are boys. In the parents of girl children, 180 are self-employed, 40 are government
employees and rests are private sector employees. In the parents of boys, 94 parents are
government employees. The total parents work in private sector is 300. Give this
information in a tabular form.

14. (a) Consider the following statements about mean. Which of them is correct ?

(1) Some data set do not have mean.

(2) The value of mean depends on all the observations.

Choose the correct answer :

(i) (1) only (ii) (2) only

(iii) (1) and (2) (iv) neither (1) nor (2)

(b) The average weight of 100 boys was 52 kgs. Later it was found that the weight of
one boy was misread as 15 kgs instead of 50 kgs. Calculate the correct average. (1+2)

15. (a) Which of the following measures of dispersion can attain a negative value ?

(i) Mean deviation (ii) Range

(iii) Standard deviation (iv) None of these

(b) In a class test, 25% students got a score less than 15 and 25% students got score
more than 50. Calculate the Quartile Deviation of the scores. (1+2)

16. In a distribution, the difference of upper and lower quartiles is 15, their sum is 35 and
median is 20. Find the Bowley’s coefficient of skewness.

FY-332 6

13  18    5  .
3  . (5  3 = 15)
13.  , 620    
.  130  . 
 180    40  
   .
  94   . 
      300 . 
    .

14. (a)    . 
  ?
(1)    .
(2)     .
   :
(i) (1)  (ii) (2) 
(iii) (1)  (2)  (iv) (1)  (2)  

(b) 100    52  . 
  50   15   
  .   . (1+2)

15. (a)     
  ?
(i)   (ii) 
(iii)   (iv) 

(b)   , 25%  15-   , 25%
 50-   . 
 (QD) . (1+2)

16.       15 , 
  35 ,  20 .   
.
FY-332 7 P.T.O.

17. (a) Which of the following is an axiom of probability ?

(1) P(AC) = 1 – P(A)

(2) P(S) = 1

Choose the correct answer :

(i) (1) only (ii) (1) and (2)

(iii) (2) only (iv) Neither (1) nor (2)

(b) Define the following :

(i) Equally likely events

(ii) Mutually exclusive events (1+2)

18. Explain simple random sampling. What are the methods of collecting simple random
samples ?

Answer any 5 questions from 19 to 24. Each carries 4 scores. (5  4 = 20)

19. (a) The persons who were deputed by the investigator to collect data from the field
are called :

(i) Enumerator (ii) Researcher

(iii) Informant (iv) Witness

(b) Give any three differences between questionnaire and schedule. (1+3)

20. The daily earnings of 100 workers are given in the following table :

Daily earnings (`) 300 – 400 400 – 500 500 – 600 600 – 700 700 – 800 800 – 900 900 – 1000

No. of workers 5 12 18 25 20 12 8

Draw a Histogram.

FY-332 8

17. (a)       ?
(1) P(AC) = 1 – P(A)
(2) P(S) = 1
   :
(i) (1)  (ii) (1)  (2) 

(iii) (2)  (iv) (1)  (2)  

(b)    :
(i)   
(ii)    (1+2)

18.    (SRS) .    
   ?

19  24    5  .
4  . (5  4 = 20)

19. (a)        :
(i)  (ii) 
(iii)  (iv) 

(b)       .
(1 + 3)

20. 100       :
  300 – 400 400 – 500 500 – 600 600 – 700 700 – 800 800 – 900 900 – 1000
(`)
 5 12 18 25 20 12 8

  .

FY-332 9 P.T.O.

21. A box contains 2 white and 4 black balls. Another box contains 5 white and 7 black
balls. A ball is transferred from first box to second box. Then a ball is drawn from the
second box. It is a white ball. What is the probability that the transferred ball was black ?

22. Two students, A and B, conduct an experiment to measure the acceleration due to
gravity using a simple pendulum. Given below is the information gathered from their
trails :

Student A Student B

No. of trials 5 6

Mean (m/s2) 9.8 9.822

S.D. (m/s2) 0.0134 0.0592

By the help of coefficient of variation, determine which student is more stable in
measurements.

23. (a) The GM of two positive numbers is the __________ of the AM and HM of the
values.

(i) AM (ii) GM

(iii) HM (iv) SD

(b) A cyclist travels a distance of 100 kilometers, for the first 50 kilometers at a speed
of 20 km/h and for the remaining 50 kilometers at a speed of 40 km/h. What is the
average speed for the entire journey ? (1+3)

24. The distribution of daily wages of worker in a SEZ is given below :

Wages (`) Below 250 250 – 500 500 – 750 750 – 1000 1000 – 1250 1250 – 1500

No. of workers 10 30 40 25 20 15

Find median wage.

FY-332 10

21.   2   4   .
  5  7   .  
     . 
     .   .
       ?

22. A, B       
     .  
    .
 A  B
  5 6

 (m/s2) 9.8 9.822

SD (m/s2) 0.0134 0.0592
     
  .

23. (a)    GM   AM, HM 
__________ .
(i) AM (ii) GM
(iii) HM (iv) SD

(b)   100   .  50 
20 ./   50  40 ./
 .    
 ? (1+3)

24.  SEZ-       :
  (`) 250  250 – 500 500 – 750 750 – 1000 1000 – 1250 1250 – 1500

 10 30 40 25 20 15

   .

FY-332 11 P.T.O.

Answer any 2 questions from 25 to 27. Each carries 6 scores. (2  6 = 12)

25. (a) The probability of getting a black king when a card is selected from a well
shuffled pack of 52 cards is :

1 1
(i) (ii)
13 26

1 1
(iii) (iv)
52 2

(b) For events A and B it is known that P(A) = P(B) and P(A  B) = 0.1 and
P(A  B) = 0.7. Find P(A).

(c) A bag contains 8 red, 3 white and 7 blue balls. Three balls are drawn at random
from the bag. Find the probability that :

(i) All are blue

(ii) All balls are of different colours

(iii) 2 red and 1 white balls (1+2+3)

26. (a) A medical researcher is studying the systolic blood pressure of patients in two
different age groups. Group 1 consists of 25 patients aged 30 – 40 years and
Group 2 consists of 30 patients aged 50 – 60 years. The average systolic blood
pressure of Group 1 is 120 mm Hg, and the average systolic blood pressure of
Group 2 is 135 mm Hg. What is the average systolic blood pressure for all the
patients in both age groups ?

(b) The daily production of a firm is given in the following table. Determine the
mode of the production :

Production per day (tons) 20 – 22 22 – 24 24 – 26 26 – 28 28 – 30

No. of days 7 13 22 10 4 (3+3)

FY-332 12

25  27   2  . 6 
. (2  6 = 12)

25. (a) 52       
      :
1 1
(i) (ii)
13 26
1 1
(iii) (iv)
52 2

(b) A, B   P(A) = P(B), P(A  B) = 0.1, P(A  B) = 0.7
  P(A) .

(c)   8 , 3 , 7   . 
     .
   :
(i)  
(ii)    
(iii) 2  1  (1+2+3)

26. (a)       
  .  1- 30 – 40   25
  2- 50 – 60   30  .
 1     120 mm Hg ,  2 
   135 mm Hg .  
     
 ?

(b)       .
   :
  20 – 22 22 – 24 24 – 26 26 – 28 28 – 30
()
  7 13 22 10 4 (3+3)

FY-332 13 P.T.O.

27. (a) The standard deviation of a set of 50 observations is 24. If the value of each
observation is decreased by 5, then the new standard deviation of these
observations would be :

(i) 24 (ii) 29

(iii) 19 (iv) None of these

(b) A company manufactures a product and the distribution of the daily sales
(in units) for the product over a month is as follows :

Sales (Units) 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

No. of days 5 8 12 9 6

Calculate the standard deviation of the daily sales for the product. (1+5)

______________

FY-332 14

27. (a) 50      24 .

    5 ,  

    :

(i) 24 (ii) 29

(iii) 19 (iv) 

(b)       

  ()    :

 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
()
 5 8 12 9 6

    

. (1+5)

______________

FY-332 15 P.T.O.

FY-332 16