Question

In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients:

Age (In years)	Number of patients
10 – 20	60
20 – 30	42
30 – 40	55
40 – 50	70
50 – 60	53
60 – 70	20

Answer 1

Class (Age in years)	Frequency (Number of patients) fi	Cumulative frequency (Less than upper limit type)
10 – 20	60	60
20 – 30	42	102 → cf
30 – 40 Median class	55 → f	157
40 – 50	70	227
50 – 60	53	280
60 – 70	20	300
	N = Σfi = 300

Here, total of frequencies N = Σf_i = 300.

`N/2 = 300/2 = 150`.

Cumulative frequency which is just greater than 150 is 157.

∴ The corresponding class 30 – 40 is the median class.

L = 30, f = 55, cf = 102, h = 10.

Median = `L + [(N/2 - cf)/f] xx h`

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

= `30 + 48/55 xx 10`

= 30 + 8.73

= 38.73

The median age of the patients is 38.73 years.