Question

Find the mean of the following frequency distribution using step-deviation method:

Class	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency	25	40	42	33	10

Answer 1

Let us choose a = 45, h = 10, then `d_i = x_i - 45 and u_i =
(x_i−45)/10`

Using step-deviation method, the given data is shown as follows:

Weight	Number of packets `(f_i)`	Class mark `(x_i)`	`d_i = x_i` – 45	`u_i = (x_i−45)/ 10`	`(f_i u_i)`
20 – 30	25	35	-20	-2	-50
30 – 40	40	35	-10	-1	-40
40 – 50	42	45	0	0	0
50 – 60	33	55	10	1	33
60 – 70	10	65	20	2	20
Total	`Ʃ f_i` = 150				`Ʃ f_i u_i = ` -37

The mean of the given data is given by,

x = a + `((Ʃf_i u_i)/(Ʃf_i)) xx h`

      `= 45 - (37/150)xx10`

       = `45-37/15`

       = 45 – 2.466

       = 42.534

Hence, the mean is 42.534.