Question

Find the arithmetic mean of the following frequency distribution using step-deviation method:
$\begin{array}{ccccccc}\text{Age(in years)}& 18-24& 24-30& 30-36& 36-42& 42-48& 48-54\\ \text{Number of workers}& 6& 8& 12& 8& 4& 2\end{array}$

Answer 1

Solution:

Class	Frequency (fi)	Mid values (xi)	ui = (xi−A)/h=(xi−33)/6	fiui
18 - 24	6	21	-2	-12
24 - 30	8	27	-1	-8
30 - 36	12	33 = A	0	0
36 - 42	8	39	1	8
42 - 48	4	45	2	8
48 - 54	2	51	3	6
Total	∑fi=40			∑(fi×ui)=2

Now, A = 33,
​​​h=6,
∑fi=40
and ∑(fi×ui)=2

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

= 33 + {6×(2/40)}

= 33 + 0.3

= 33.3

Therefore, $\overline{x}$ = 33.3 years.