Question

Find the mean of the following frequency distribution using a suitable method:
$\begin{array}{cccccc}\text{Class}& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Frequency}& 25& 40& 42& 33& 10\end{array}$

Answer 1

Let us choose a = 45, h = 10,
then di = xi - 45
and ui = (xi−45)/10

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

Class	Frequency (fi)	Class mark (xi)	di= xi- 45	ui = (xi−45)/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				∑(fi×ui)=−37

The mean of given data is given by

$\overline{x}$=a+(∑fiui/∑fi)×h

= 45 + (-37/150) x 10

= 45 - 37/15

= 45 - 2.466

= 42.534

Thus, the mean is 42.534.