Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode) Exercise Ex. 24(D)

Question 1

Find the mode of the following data:

(i) 7, 9, 8, 7, 7, 6, 8, 10, 7 and 6

(ii) 9, 11, 8, 11, 16, 9, 11, 5, 3, 11, 17 and 8

Solution 1

(i) Mode = 7

Since 7 occurs 4 times

(ii) Mode = 11

Since it occurs 4 times

Question 2

The following table shows the frequency distribution of heights of 50 boys:

Height (cm)	120	121	122	123	124
Frequency	5	8	18	10	9

Find the mode of heights.

Solution 2

Mode is 122 cm because it occur maximum number of times. i.e. frequency is 18.

Question 3

Find the mode of following data, using a histogram:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	12	20	9	4

Solution 3

Mode is in 20-30, because in this class there are 20 frequencies.

Question 4

The following table shows the expenditure of 60 boys on books. Find the mode of their expenditure:

Expenditure (Rs)	No. of students
20-25	4
25-30	7
30-35	23
35-40	18
40-45	6
45-50	2

Solution 4

Mode is in 30-35 because it has the maximum frequency.

Question 5

Find the median and mode for the set of numbers:

2, 2, 3, 5, 5, 5, 6, 8 and 9

Solution 5

 which is 5.

Mode = 5 because it occurs maximum number of times.

Question 6

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

(i) What are his modal marks?

(ii) What are his median marks?

(iii) What are his total marks?

(iv) What are his mean marks?

Solution 6

Arranging the given data in ascending order:

7, 10, 12, 12, 14, 15, 16, 16, 16, 17, 19

(i) Mode = 16 as it occurs maximum number of times.

(ii) 

(iii)Total marks = 7+10+12+12+14+15+16+16+16+17+19 =

154

(iv) 

Question 7

Find the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks.

0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7 and 8.

Solution 7

(i)

(ii) Median = mean of 8^th and 9^th term

(iii) Mode = 5 as it occurs maximum number of times.

Question 8

At a shooting competition the score of a competitor were as given below:

Score	0	1	2	3	4	5
No. of shots	0	3	6	4	7	5

(i) What was his modal score?

(ii) What was his median score?

(iii) What was his total score?

(iv) What was his mean score?

Solution 8

Score x	No. of shots f	fx
0	0	0
1	3	3
2	6	12
3	4	12
4	7	28
5	5	25
Total	25	80

(i) Modal score = 4 as it has maximum frequency 7.

(ii) 

(iii) Total score = 80

(iv)