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The given data is an inclusive series.
So, we convert it into exclusive form as below:
Class 5.5 - 15.5 15.5 - 25.5 25.5 - 35.5 35.5 - 45.5 45.5 - 55.5 55.5 - 65.5
Frequency 6 11 21 23 14 5

As the class 35.5 - 45.5 for has maximum frequency, so it is the modal class.
Therefore, = 35.5
h = 10
f1 = 23
f0 = 21
f2 = 14

Mode =

= 35.5 + 1.82
= 37.32
Hence, the average age for which maximum cases occured is 37.32 years.

Example-6:The mode of the following series is 36. Find the missing frequency in
it.
Class Interval 0 - 10 10 – 20 20 – 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency 8 10 X 16 12 6 7

Solution: Since, the mode of the given series is 36 and maximum frequency 16 lies in
the class 30 - 40, so the modal class is 30 - 40.
Therefore, = 30
h = 10
f1 = 16
f0 = x
f2 = 12

Therefore, mode =

160 - 10x = 120 - 6x
4x = 40
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