Question

The following table shows the age of patients admitted in a hospital during a particular week:

Age (in years):	5 - 15	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65
Number of patients:	5	12	20	24	15	4

Find the mean age of patients.

Answer 1

Given

Class	`(x_i)`	`(f_i)`	`(u_i = \frac{x_i - 30}{10})`	`(f_i u_i)`
5-15	10	5	-2	-10
15-25	20	12	-1	-12
25-35	30	20	0	0
35-45	40	24	1	24
45-55	50	15	2	30
55-65	60	4	3	12
		`N = 80`		`\sum f_i u_i = 44`

Formula

\[ \overline{X} = A + h\left(\frac{\sum f_i u_i}{N}\right) \]

Substitution

\[ \overline{X} = 30 + 10 \times \frac{44}{80} \]

\[ \overline{X} = 30 + 5.5 \]

Final answer

\[ \overline{X} = 35.5 \text{ years} \]