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Question

Compare the modal ages of two groups of students appearing for an entrance test:
Age (in years)1618 1820 2022 2224 2426
Group A: 50 78 46 28 23
Group B: 54 89 40 25 17

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Solution

We know,

Mode=l+ff12ff1f2×h


l= lower limit of the modal class

h= size of the class intervals

f= frequency of the modal class

f1= frequency of the class preceding the modal class

f2= frequency of the class succeed in the modal class.


For Group A
Here the maximum frequency is 78, then the corresponding class 1820 is modal class.

l=18,h=2018=2,f=78,f1=50,f2=46

Mode=l+ff12ff1f2×h

Mode=18+78502×785046×2

Mode=18+5660

Mode=18+0.93=18.93years

For Group B
Here the maximum frequency is 89, then the corresponding class 1820 is modal class.

l=18,h=2018=2,f=89,f1=54,f2=40

Mode=l+ff12ff1f2×h

Mode=18+89542×895440×2

Mode=18+7084

Mode=18+0.83=18.83years

Hence, Modal age for the group A is higher than that for group B.

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