Kerala Plus One Question Paper 2023 Statistics

FIRST YEAR

Kerala Board
Question Paper
2023

Download PDF

Reg. No. : ......................................
Name : ...........................................
FY-432
FIRST 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  ‘  ’ .
 ‘  ’    
 .
      .
    .
  , , ,   
.
   .
    .
     
    .

1 P.T.O.

Answer any 5 questions from 1 to 6. Each carries 2 scores. (5  2 = 10)

1. Construct percentage frequency table for the following data :

Age 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35

No. of Students 6 8 18 14 6 3

2. (a) When all the values of a data are equal then the standard deviation would be
________. (1)

(i) 1 (ii) –1

(iii) 0 (iv) 2

(b) In a set of values, highest value is 50 and the range is 24, what is the lowest value ? (1)

(i) 74 (ii) 26

(iii) 72 (iv) 58

3. The heights of students (in inches) is given below. Calculate quartile deviation of the
data :

Heights 55 54 57 67 60 61 58

4. The first four central moments of the distribution are 0, 9.2, –3.6 and 122. Calculate
coefficient of Kurtosis of the distribution and comment on the result.

1 1 1
5. If P(A) = , P(B) = and P(A and B) = . Find P(A  B).
4 2 8

6. Write any two situations where sampling survey is preferable to census.

FY-432 2

1  6    5  .
2  . (5  2 = 10)

1.        :
 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35
 6 8 18 14 6 3


2. (a)        ________
. (1)

(i) 1 (ii) –1
(iii) 0 (iv) 2
(b)       50 ,  24  .
     ? (1)

(i) 74 (ii) 26
(iii) 72 (iv) 58

3.     .   
 :
 55 54 57 67 60 61 58

4.    4   0, 9.2, –3.6, 122 .
   .  
.

1 1 1
5. P(A) =  P(B) =  P(A and B) =   P(A  B) .
4 2 8

6.     2  .

FY-432 3 P.T.O.

Answer any 6 questions from 7 to 13. Each carries 3 scores. (6  3 = 18)

7. (a) Who is known as the father of Indian Statistics ? (1)

(i) R.A. Fisher (ii) P.C. Mahalanobis

(iii) Karl Pearson (iv) Spearman

(b) Writ a short note on any one applied area of Statistics. (2)

8. (a) The pre-test with the questionnaire before conducting a survey is called
________. (1)

(b) Distinguish between primary data and secondary data. Write any 4 points. (2)

9. Prepare a questionnaire regarding the travelling problems faced by school children.

10. In a cycle race competition, the speeds of 5 participants are 12 km/hr, 15 km/hr,
16 km/hr, 18 km/hr and 19 km/hr. Find the average speed.

11. The value of mean and mode of a frequency distribution are 50 and 45 respectively.
Find the median.

12. (a) Explain different types of Skewness. (2)

(b) For a symmetric distribution : (1)

(i) 1 = 0 (ii) 1 < 0

(iii) 1 > 0 (iv) 1  0

13. Name three non-probability sampling methods.

FY-432 4

7  13    6  .
3  . (6  3 = 18)
7. (a)     ? (1)
(i) ..  (ii) .. 
(iii)   (iv) 
(b)      
 . (2)

8. (a)      
 ________  . (1)
(b)       4 
. (2)

9.      
.

10.     5   12
../, 15 ../, 16 ../, 18 ../, 19
../ .  .

11.    ,   50, 45 .
 .

12. (a)    . (2)
(b)    : (1)
(i) 1 = 0 (ii) 1 < 0

(iii) 1 > 0 (iv) 1  0

13.     .

FY-432 5 P.T.O.

Answer any 5 questions from 14 to 19. Each carries 4 scores. (5  4 = 20)

14. There are 3 streams in a Higher Secondary School. Science, Commerce and
Humanities. Boys, girls and transgenders are studying with 3 different second
languages, Malayalam, Hindi and Sanskrit.

(i) Draw classicification sketch.

(ii) Draw the skeleton of the table.

15. Draw suitable diagram for the following data :

Year Sales (000) Income (000) Profit (000)

2000 100 30 10

2001 120 40 15

2002 130 45 25

16. Eleven students were given a test and the scores obtained by them are as follows :

8, 7, 6, 9, 1, 3, 10, 8, 4, 7, 11

Represent the data using a box plot.

17. The number of accidents occurred due to careless driving on a busy road during 7 days
in a week is reported below :

No. of accidents 8 10 6 7 5 4 2

Determine mean deviation about mean.

FY-432 6

14  19    5  .

4  . (5  4 = 20)

14.    ,   
 , ,     
,   .

(i)     .

(ii)   .

15.       :

  (000)  (000)  (000)

2000 100 30 10

2001 120 40 15

2002 130 45 25

16.      8, 7, 6, 9, 1, 3, 10, 8, 4, 7,
11       .

17.      
   :

  8 10 6 7 5 4 2

   .

FY-432 7 P.T.O.

18. One card is drawn at random from a pack of 52 cards. Find the probability that

(i) The card drawn is a king.

(ii) The card drawn is a red card.

(iii) The card drawn is a black ace.

(iv) The card drawn is a club and queen.

19. A coffee shop has 3 coffee machines A, B and C. They produce 25%, 35% and 40% of
the coffee respectively. 3%, 2% and 5% of coffee dispensed by the machines are
defective. Then what is the probability that the coffee supplied to a customer is
defective ?

Answer any 2 questions from 20 to 22. Each carries 6 scores. (2  6 = 12)

20. Given below is the frequency distribution of ages of 70 persons in a colony. Draw a
greater than ogive and a less than ogive for the data :

Age 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

No. of Persons 5 11 27 19 5 3

21. (a) The distribution of sales (in numbers) of brand A toothpaste in a margin free shop
in a town is given below. Find the mode of the distribution. (4)

Sales 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

No. of Days 4 10 20 11 3 2

(b) In a school there are 253 girls whose ages have a mean of 11.8 years. There are
312 boys whose ages have a mean of 12.3 years. Calculate the mean age of all
565 students. (2)

FY-432 8

18. 52        
.     .
(i)    .
(ii)      .
(iii)      .

(iv)      .

19.   A, B, C  3   .  
 25%, 35%, 40%  .   3%, 2%,
5%  .     
   ?

20  22    2  .
6  . (2  6 = 12)

20.    70   
.     
   :
 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
 5 11 27 19 5 3


21. (a)       A 
   .  
. (4)
 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
 4 10 20 11 3 2

(b)    253    11.8 ,
312    12.3  . 
 565    . (2)

FY-432 9 P.T.O.

22. Prices of a particular commodity in 5 years at two different cities in Kerala and
Karnataka are as follows :

Karnataka (in `) 20 25 23 22 24

Kerala (in `) 22 26 25 23 30

Which state has stable price ? Justify your answer.

______________

FY-432 10

22.   2    5
     :

 20 25 23 22 24
()

 22 26 25 23 30
()

    ?  
.

______________

FY-432 11 P.T.O.

FY-432 12