Question

Find the mean of the following frequency distribution using a suitable 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 = $\frac{x_i-45}{10}$}.

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

Class	Frequency (fi)	Class mark (xi)	di = xi − 45	ui = $\frac{{\mathbf{x}}_{\mathbf{i}}\mathbf{-}\mathbf{45}}{\mathbf{10}}$	fiui
20−30	25	25	−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	∑ fi = 150				∑ fiui = −37

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i{f}_i{u}_i}}{{\displaystyle \sum _i{f}_i}}\right)\times h \\ =45-\frac{37}{150}\times 10 \\ =45-\frac{37}{15} \\ =45-2.466 \\ =42.534 \end{gathered}$$

​Thus, the mean is 42.534.