A life insurance agent found the following data for distribution of ages of 100 policy holders. Age in years Blow 20, Blow 25, Blow 30, Blow 35

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.

Answer 1

: Here class width is not same. There is no need to adjust the frequencies according to class intervals. Now 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 frequencies as below:

Now from the table we may observe that N = 100

Cumulative frequency just greater than \(\frac{N}{2}\) (N = 50) is 78belonging to interval 35-40.

So, 

Median Class = 35 – 40 

Lower limit (l) = 35 

Class size (h) = 5 

Frequency (f) = 33 and F = 45

Median = l + \(\frac{\frac{N}{2}-F}{f}\times h\)

\(=35+(\frac{50-45}{33})\times 5\)

\(=35+\frac{5}{33}\times 5\)

= 35 + 0.76 

= 35.76 

So, Median age is 35.76 years.