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 onward but less than 60 years.
Age in years
Below 20
Below 25
Below 30
Below 35
Below 40
Below 45
Below 50
Below 55
Below 60
Number of policy holders
2
6
24
45
78
89
92
98
100

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is  in the attachment.  

Here, n = 100  

n/2 = 50

Since, the Cumulative frequency just greater than 50 is 78 and the corresponding class is 35 - 40.  Therefore 35 - 40  is the median class.

Here, l = 35 , f = 33, c.f = 43l5,  h = 5

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 35 + [50 - 45)/33] × 5

= 35 + (5 × 5)/33

= 35 + 25/33

= 35 + 0.76

= 35.76

Hence, the Median age is 35.76 years.  

★★ MEDIAN = l + [(n/2 - cf )/f ] ×h

Where,

l = lower limit of the median class

n = number of observations  

cf = cumulative frequency  of class interval preceding the  median class

f = frequency  of median class

h = class  size

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