Question

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.
$\begin{array}{cccccc}\text{Age (in years)}& 0-15& 15-30& 30-45& 45-60& 60-75\\ \text{Numbers of patients}& 5& 20& 40& 50& 25\end{array}$

Answer 1

Sol:

We prepare the cumulative frequency table, as shown:

Age (in years)	Number of patients	Cumulative frequency
0-15	5	5
15-30	20	25
30-45	40	65
45-60	50	115
60-75	25	140
Total	N=Σfi=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.

We know,

Median=l+(N/2−cf/f)×h

And l= 45, h= 15, f= 50, N= 140 and cf= 65

Median=45+((140/2−65) /50)) ×15
Median=45+(70−65/50)×15
Median=45+1.5
Median=46.5

Hence the median age is 46.5 years.