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Question

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.
Age in yearsNumber of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100


Solution

Class interval Frequency Cumulative frequency
15-20 2 2
20-25 4 6
25-30 18 24
30-35 21 45
35-40 33 78
40-45 11 89
45-50 3 92
50-55 6 98
55-60 2 100

Where, n = 100 and n over 2 = 50

Median class = 35-45

Then, l = 35, cf = 45, f = 33 & h = 5

Median= l +( fraction numerator begin display style n over 2 minus c f end style over denominator f end fraction) h

= 35 + (fraction numerator 50 minus 45 over denominator 33 end fraction)5 
= 35 + (25 over 33)

=35.75

Hence the median age is 35.75 yrs

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