Question

Find the mean of the following data, using step-deviation method:

Class	5 – 15	15 – 25	25 – 35	35 – 45	45 – 55	55 – 65	65 – 75
Frequency	6	10	16	15	24	8	7

Answer 1

Let us choose a = 40, h = 10, then `d_i = x_i – 40 and u_i =(x_i-40)/10`

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

Class	Frequency `(f_i)`	Class mark `(x_i)`	`d_i = x_i` – 40	`u_i = (x_i−40)/10`	`(f_i u _i)`
5 – 15	6	10	-30	-3	-18
15 – 25	10	20	-20	-2	-20
25 – 35	16	30	-10	-1	-16
35 – 45	15	40	0	0	0
45 – 55	24	50	10	1	24
55 – 65	8	60	20	2	16
65 – 75	7	70	30	3	21
Total	`Ʃ f_i` = 86				`Ʃ f_i u_i  `= 7

The mean of the data is given by,

x = a + `((sumf_i u_i)/(sumf_i)) xx h`

    = 40 + `7/86 xx 10`

    = `40+ 70 / 86`

    = 40 + 0.81

    = 40.81