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 $60$ year.

Age (in years)	Number of policy holders
Below $20$ Below $25$ Below $30$ Below $35$ Below $40$ Below $45$ Below $50$ Below $55$ Below $60$	$2$ $6$ $24$ $45$ $78$ $89$ $92$ $98$ $100$

Answer 1

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

We have, $n=100$

$\frac{n}{2}=50$

The cumulative frequency just greater than $\frac{n}{2}$ is $78$ and the corresponding class is $35-40$.

Thus, $35–40$ is the median class such that

$\frac{n}{2}=50,l=35,f=33,cf=45,$ and $h=5$

Substituting these values in the formula

Median, $M=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

$M=35+\left(\frac{50-45}{33}\right)\times 5$

$M=35+\frac{5}{33}\times 5=35+0.76=35.76$

Hence, the median weight $=35.76$ years .