Question

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

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency	7	10	15	8	10

Answer 1

Let us choose a = 25, h = 10, then  `d_i = x_i – 25 and u_i = (x_i−25)/10`

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

Class	Frequency `(f_i)`	Class mark `(x_i)`	`d_i = x_i `– 25	`u_i =( x_i−25)/10`	`(f_i   u_i)`
0 –10	7	5	-20	-2	-14
10 – 20	10	15	-10	-1	-10
20 – 30	15	25	0	0	0
30 – 40	8	35	10	1	8
40 – 50	10	45	20	2	20
Total	`Ʃ f_i` = 50				`Ʃ f_i u_i = 4`

The mean of the data is given by,

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

   =`25+ 4/50 xx 10`

   =`25+ 4/5`

   =`(125+4)/5`

   = `129/5`

   = 25.8

Thus, the mean is 25.8.