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Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age in years0-1010-2020-3030-4040-50
No. of persons525?187

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Solution

Let the missing frequency be x.

Age in years
(x)
No. of persons
(f)
C.F.
0-1055
10-202530
20-30x30 +x
30-401848 +x
40-50755 +x
N=55+x
As, N=55+x N2=55+x2
Median=l+N2+Cf×h
As median is given 24, therefore median class is 2030.

Therefore,
l=lower limit of median class =20
C=C.F. of the class preceding the median class =30
h= higher limit - lower limit =4030=10
f=frequency of median class =x

median=20+55+x230x×10

24=20+x52x×10

4=x5x×5

4x=5x25

x=25

Hence, the missing frequency is 25.

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