Question

Find the mean of the following frequency distribution using step-deviation method.
$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 7& 10& 15& 8& 10\end{array}$

Answer 1

Let us choose a = 25, h = 10,
then di = xi - 25
and
ui = (xi−25)/10

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

Class	Frequency (fi)	Class mark (xi)	di= xi- 25	ui = (xi−25)/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				∑(fi×ui)=4

The mean of given data is given by

$\overline{x}$=a+(∑fiui/∑fi)×h

= 25 + 4/50 x 10

= 25 + 4/5

= (125+4)/5

= 129/5

= 25.8

Thus, the mean is 25.8.