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Compare the Modal Ages of Two Groups of Students Appearing for an Entrance Test: - CBSE Class 10 - Mathematics

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Question

Compare the modal ages of two groups of students appearing for an entrance test:

Age (in years): 16-18 18-20 20-22 22-24 24-26
Group A: 50 78 46 28 23
Group B: 54 89 40 25 17

Solution

Age (in years) Group ‘A’ Group ‘B’
16–18  50 54
18–20  78 89
20–22  46 40
22–24 28 25
24–25 23 17

For group “A”

The maximum frequency is 78 so the modal class is 18–20.

Therefore,

l = 18

h = 2

f = 78

f1 = 50

f2 = 46

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(78-50)/(156-50-46)xx2`

`=18+28/60xx2`

`=18+14/15`

= 18 + 0.93

= 18.93

For group “B”

The maximum frequency 89 so modal class 18–20.

Therefore,

l = 18

h = 2

f = 89

f1 = 54

f2 = 40

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=18+(89-54)/(178-54-40)xx2`

`=18+35/84xx2`

`=18+35/42`

`=18+5/6`

= 18 + 0.83

= 18.83

Thus, the modal age of group A is 18.93 years whereas the modal age of group B is 18.83 years.

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Solution Compare the Modal Ages of Two Groups of Students Appearing for an Entrance Test: Concept: Mode of Grouped Data.
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