Question

The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day : 

Age (in years)	No. of Patients
10-20	60
20-30	42
30-40	55
40-50	70
50-60	53
60-70	20

Find the median age of the patients.

Answer 1

Age (in years)	No. of Patients	c.f. (less than type)
10-20	60	60
20-30	42	102 → c.f.
30-40 Median class	55 → f	157
40-50	70	227
50-60	53	280
60-70	20	300

Here, N =` 300/2`

N=150

Cumulative frequency just greater than 150 is 157.
∴ Corresponding class (30 – 40) is the median class.
L = 30, f = 55, c.f. = 102, h = 10

`"Median =L"+("N"/2-"c.f")"h"/"f"`

=`30 + (150 - 102) xx(10/55)`

=`30+48 xx (10/55)`

= `30 + 480/55`

=30 + 8.7272

=38.73

Thus, the median age of patients is 38.73 years.