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 = $\frac{x_i-40}{10}$}.

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

Class	Frequency (fi)	Class mark (xi)	di = xi − 40	ui = $\frac{{\mathbf{x}}_{\mathbf{i}}\mathbf{-}\mathbf{40}}{\mathbf{10}}$	fiui
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	∑ fi = 86				∑ fiui = 7

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i{f}_i{u}_i}}{{\displaystyle \sum _i{f}_i}}\right)\times h \\ =40+\frac{7}{86}\times 10 \\ =40+\frac{70}{86} \\ =40+0.81 \\ =40.81 \end{gathered}$$

​Thus, the mean is 40.81.