Question

Find the mean of the following frequency distribution:

Classes:	25 - 30	30 - 35	35 - 40	40 - 45	45 - 50	50 - 55	55 - 60
Frequency:	14	22	16	6	5	3	4

Answer 1

Given

Class	`(x_i)`	`(f_i)`	`(u_i = \frac{x_i - 37.5}{5})`	`(f_i u_i)`
25-30	27.5	14	-2	-28
30-35	32.5	22	-1	-22
35-40	37.5	16	0	0
40-45	42.5	6	1	6
45-50	47.5	5	2	10
50-55	52.5	3	3	9
55-60	57.5	4	4	16
		`N = 70`		`\sum f_i u_i = -9`

Formula

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

Substitution

\[ \overline{X} = 37.5 + 5 \times \frac{-9}{70} \]

\[ \overline{X} = 37.5 - 0.642857\ldots \]

Final answer

\[ \overline{X} = 36.86 \]