Question

The following data represents the age-wise distribution of employees in an office.

Age in years	25-30	30-35	35-40	40-45	45-50	50-55	55-60
Number of employees	4	16	19	28	22	8	3

Draw (i) less-than type cumulative frequency curve
(ii) more-than type cumulative frequency curve
on the same graph paper. Find the median age of the employees.

Answer 1

First, we have to draw the less-than type and more-than type cumulative frequency table as shown.

Age in years	Frequency	Upper boundary (ui )	Less-than cumulative frequency (Fi )	Lower boundary (li )	More-than cumulative frequency (Fi' )
-	-	25	0	-	-
25-30	4	30	4	25	100
30-35	16	35	20	30	97
35-40	19	40	39	35	89
40-45	28	45	67	40	67
45-50	22	50	89	45	39
50-55	8	55	97	50	20
55-60	3	60	100	55	4
-	-	-	-	60	0

The less-than type and more-than type cumulative frequency curves are shown below.



The median can be obtained by drawing a perpendicular AB to the X-axis from the point of intersection of the two curves.
The foot of the perpendicular is the median. Here, it is 42 years.
Therefore, median age of the employees 42 years.