Question

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

Age (in years)	0 – 15	15 – 30	30 – 45	45 – 60	60 - 75
No. of patients	5	20	40	50	25

Answer 1

We prepare the cumulative frequency table, as shown below:

Age (in years)	Number of patients `(f_i)`	Cumulative Frequency (cf)
0 – 15	5	5
15 – 30	20	25
30 – 45	40	65
45 – 60	50	115
60 – 75	25	140
Total	`N = Σ f_i` = 140

Now, N = 140 ⇒`N/2 = 70`
The cumulative frequency just greater than 70 is 115 and the corresponding class is 45 –60
Thus, the median class is 45 – 60.
∴ l = 45, h = 15, f = 50, N = 140 and cf = 65.
Now,
Median = l + `((N/2-cf)/f) xx h`

              =`45 + ((140/2-65)/50) xx 15`

             =`45+((70-65)/50) xx 15`

             = 45 + 1.5
            = 46.5

Hence, the median age is 46.5 years.