Question

Find the mean of the following data, using step-deviation method:
$\begin{array}{cccccccc}\text{Class}& 5-15& 15-25& 25-35& 35-45& 45-55& 55-65& 65-75\\ \text{Frequency}& 6& 10& 16& 15& 24& 8& 7\end{array}$

Answer 1

Let us choose
a = 40, h = 10,
then di = xi - 40 and ui = (xi−40)/10

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

Class	Frequency (fi)	Class mark (xi)	di= xi- 40	ui = xi−40/10	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				∑(fi×ui)=7

The mean of given data is given by

$\overline{x}$=a+(∑fiui/∑fi)×h

= 40 + (7/86) $\times$ 10

= 40 + 70/86

= 40 + 0.81

= 40.81

Thus, the mean is 40.81.