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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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