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 = $\frac{x_i-25}{10}$}.

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

Class	Frequency (fi)	Class mark (xi)	di = xi − 25	ui = $\frac{{\mathbf{x}}_{\mathbf{i}}\mathbf{-}\mathbf{25}}{\mathbf{10}}$	fiui
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	∑ fi = 50				∑ fiui = 4

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i{f}_i{u}_i}}{{\displaystyle \sum _i{f}_i}}\right)\times h \\ =25+\frac{4}{50}\times 10 \\ =25+\frac{4}{5} \\ =\frac{125+4}{5} \\ =\frac{129}{5} \\ =25.8 \end{gathered}$$

​Thus, the mean is 25.8.