devarshi-dt-logo

Question:

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onward but less than 60 years. Age (in years) Number of policy holders Below 20 2 Below 25 6 Below 30 24 Below 35 45 Below 40 78 Below 45 89 Below 50 92 Below 55 98 Below 60 100

Solution:

We first construct a frequency table from the given cumulative frequency distribution:

Age (in years) Number of policy holders Frequency Cumulative Frequency
18-20 2-0=2 2 2
20-25 6-2=4 4 6
25-30 24-6=18 18 24
30-35 45-24=21 21 45
35-40 78-45=33 33 78
40-45 89-78=11 11 89
45-50 92-89=3 3 92
50-55 98-92=6 6 98
55-60 100-98=2 2 100

We have, n=100
n/2=50

The cumulative frequency just greater than n/2 is 78 and the corresponding class is 35-40.
Thus, 35-40 is the median class such that n/2=50, l=35, f=33, cf=45, and h=5

Substituting these values in the formula
Median, M = l + \frac{\frac{n}{2} - cf}{f} \times h
M = 35 + (\frac{50 - 45}{33}) \times 5
M = 35 + \frac{5}{33} \times 5 = 35 + 0.76 = 35.76

Hence, the median age = 35.76 years.