Question

Find the mean of the following data using step-deviation method:
$\begin{array}{ccccccc}\text{Class}& 500-520& 520-540& 540-560& 560-580& 580-600& 600-620\\ \text{Frequency}& 14& 9& 5& 4& 3& 5\end{array}$

Answer 1

Solution:

Class	Frequency (fi)	Mid values (xi)	ui = (xi−A)/h=(xi−550)/20	fiui
500 - 520	14	510	-2	-28
520 - 540	9	530	-1	-9
540 - 560	5	550 = A	0	0
560 - 580	4	570	1	4
580 - 600	3	590	2	6
600 - 620	5	610	3	15
Total	∑fi=40			∑(fi×ui)=−12

Now,
A = 550, h = 20,
∑fi=40 and ∑(fi×ui)=−12

Therefore,
Mean,
$\overline{x}$ = A+{h×∑(fiui)/∑fi}

= 550 + {20×(−12)/40}

= 550 - 6

= 544

Therefore, $\overline{x}$ = 544.