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Question

# Question 3 A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. Age (in years)Number of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100

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Solution

## Here the class width is not same. There is no need to adjust the frequencies according to class intervals. Now, the given frequency table is of less than type represented with upper class limits. As policies were given only to persons having age 18 years onwards but less than 60 years, we can define class intervals with their respective cumulative frequency as below: Age (in years)Number of policy holders(fi)Cumulative frequency (cf)18−202220−256−2=4625−3024−6=182430−3545−24=214535−4078−45=337840−4589−78=118945−5092−89=39250−5598−92=69855−60100−98=2100Total(n) Now from table we observe that n = 100. Cumulative frequency cf just greater than n2(i.e, 1002=50) is 78 belonging to interval 35 - 40. So, median class = 35 - 40 Lower limit l of median class = 35 Class size h = 5 Frequency f of median class = 33 Cumulative frequency cf of class preceding median class = 45 Median=l+(n2−cff)×h=35+(50−4533)×5=35+2533 = 35.76 So, median age is 35.76 years.

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