In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.[CBSE 2014]

Age (in years)	0 - 15	15 - 30	30 - 45	45 - 60	60 - 75
Number of patients	5	20	40	50	25

To find median,

Assume Σf_i = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and C_f = cumulative frequency

Lets form a table.

So, N = 140

⇒ N/2 = 140/2 = 70

The cumulative frequency just greater than (N/2 = ) 70 is 115, so the corresponding median class is 45 - 60 and accordingly we get C_f = 65(cumulative frequency before the median class).

Now, since median class is 45 - 60.

∴ l = 45, h = 15, f = 50, N/2 = 70 and C_f = 65

Median is given by,

⇒

= 45 + 1.5

= 46.5

Thus, median age is 46.5 years.