Question

Find the mean using the step deviation method.

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
Frequency	6	10	15	9	10

Answer 1

Let us a = 25,

h = 10,

then d_i = x_i - 25 and u_i = `(x_i − 25)/10`

Class	Frequency (fi)	Class mark (xi)	di = xi - 25	ui = `(x_i - 25)/10`	(fiui)
0 - 10	6	5	-20	-2	-12
10 - 20	10	15	-10	-1	-10
20 - 30	15	25	0	0	0
30 - 40	9	35	10	1	9
40 - 50	10	45	20	2	20
Total	`sumf_i = 50`				`sumf_iu_i = 7`

The mean of the data is given by,

`barx` = `a + ((sum f_i u_i)/(sum f_i)) xx h`

= `25 + (7/50) xx 10`

= `25 + 7/5`

= 25 + 1.4

= 26.4