Question

The following table gives the weekly wages of workers in a factory.

Weekly wages (Rs)	No. of workers
50 – 55	5
55 – 60	20
60 – 65	10
65 – 70	10
70 – 75	9
75 – 80	6
80 – 85	12
85 – 90	8

Calculate the mean by using: 

Short-cut method

Answer 1

Short-cut method 

Weekly wages (Rs)	No. of workers (fi)	Mid-value xi	A = 72.5  di = x – A	fidi
50 – 55	5	52.5	–20	–100
55 – 60	20	57.5	–15	–300
60 – 65	10	62.5	–10	–100
65 – 70	10	67.5	–5	–50
70 – 75	9	A = 72.5	0	0
75 – 80	6	77.5	5	30
80 – 85	12	82.5	10	120
85 – 90	8	87.5	15	120
Total	80			–280

${\displaystyle \overline{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}}$

= ${\displaystyle 72.5+\left(\frac{-280}{80}\right)}$

= 72.5 – 3.5

= 69