Question

The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method.

Weekly wages (Rupees)	1000 - 2000	2000 - 3000	3000 - 4000	4000 - 5000
No. of workers	25	45	50	30

Answer 1

Class (Weekly wages rupees)	Class Mark (xi)	di = xi − A = xi − 2500	ui = `"d"_"i"/"g"` = `"d"_"i"/1000`	Frequency (Number of workers) (fi)	Frequency × deviation (fi × ui)
1000 - 2000	1500	−1000	−1	25	−25
2000 - 3000	2500 →A	0	0	45	0
3000 - 4000	3500	1000	1	50	50
4000 - 5000	4500	2000	2	30	60
				∑fi = 150	∑fiui = 85

Required Mean = `(∑"f"_"i""u"_"i")/(∑"f"_"i")`

= `85/150`

= 0.57
Mean = `(barX) = "A" + bar("u")"g"`
= 2500 + 0.57 (1000)
= 2500 + 570 
​= Rs 3070
Hence, the mean of the weekly wages is Rs 3070.