Class 9 RD Sharma Solutions – Chapter 24 Measures of Central Tendency – Exercise 24.4

Question 1. Find out the mode of the following marks obtained by 15 students in a class:
Marks : 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7.

Solution:

The mode is the most common number that occurs frequently in the given data.
Marks
4
5
6
7
8
9
10
Number of students
2
2
2
4
2
2
1
Here, we can see that 7 occurred most frequently.
Hence, Mode = 7

Question 2. Find out the mode from the following data :
125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

Solution:

The frequency of given set of observations:
Values
125 175 225 325 375
Frequency
4
2
3
1
1
Here the maximum frequency is 4 which is 125.
Hence, Mode = 125

Question 3. Find the mode for the following series:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2

Solution:

Frequency of the given set of observations:
Values
7.2
7.3 7.4 7.5 7.6 7.7
Frequency
4
2
1
2
1
2
Here the maximum frequency is 4 which is 7.2.
Hence, mode = 7.2

Question 4. Find the mode of the following data in each case:
(i) 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Solution:

First arrange the data in the ascending order:
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here we can clearly see that 14 occurs 4 times, hence it has the highest frequency.
So, mode = 14

(ii) 7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7

Solution:

Frequency of the given set of observations:
Values
7
9
12
13
15 18 25
Frequency
5
1
3
1
1
1
1
Here the maximum frequency is 5 which is 7.
Hence, mode = 7.

Question 5. The demand of different shirt size, as obtained by a survey, is given below:

Size:	38	39	40	41	42	43	44	Total
Number of persons (wearing it)	26	39	20	15	13	7	5	125

Find the modal shirt sizes, as observed from the survey.

Solution:

Frequency of the given set of observations:
Size:
38 39 40 41 42 43 44 Total
Number of persons (wearing it) 26 39 20 15 13
7
5
125
Here the maximum frequency is 39 which is 39.
Hence, mode = 39.