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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:

Marks 4 5 6 7 8 9 10
No. of Students 2 2 2 4 2 2 1

Since maximum frequency corresponds to the value 7 then mode = 7 marks.

 

Question: 2

Find out the mode from the following data:

125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125

Solution:

Values 125 175 225 325 375
Frequency 4 2 3 1 1

Since maximum frequency 4 corresponds to the value 125 then 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:

Values 7.2 7.3 7.4 7.5 7.6 7.7
Frequency 4 2 1 2 1 2

Since maximum frequency 4 corresponds to the value 7. 2 then 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

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

Solution:

(i) Arranging the numbers in ascending order:

14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28

Here the observation 14 is having the highest frequency i. e, 4 in given data, so mode = 14.

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

Values 7 9 12 13 15 18 25
Frequency 5 1 3 1 1 1 1

Since maximum frequency 5 corresponds to the value 7 then mode = 7

 

Question: 5

The demand of different shirt sizes, as obtained by a survey, is given below:

Size: 38 39 40 41 42 43 44 Total
No. of persons (wearing it) 26 39 20 15 13 7 5 125

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

Solution:

Size: 38 39 40 41 42 43 44 Total
No. of persons(wearing it) 26 39 20 15 13 7 5 125

Since, maximum frequency 39 corresponds to the value 39 then mode = 39


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