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

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Class (Weekely wages rupees)	Class Mark xi	di = xi − A	$u_i=\frac{{{\displaystyle d}}_i}{h}$	Frequency (Number of workers) fi	Frequency × deviation fi × ui
1000 - 2000	1500	−2000	−2	25	−50
2000 - 3000	2500	−100	−1	45	−45
3000 - 4000	3500 = A	0	0	50	0
4000 - 5000	4500	1000	1	30	30
				$\underset{}{\sum f_i=150}$	$\sum _{}{f}_i{u}_i=-65$

Required Mean = $A+h\frac{\sum _{}{f}_i{u}_i}{\sum _{}{f}_i}$
$=3500-\left(\frac{65}{150}\right)1000$
= 3500 − 433.33
​= Rs 3066.67
Hence, the mean of the weekly wages is Rs 3066.67.