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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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