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

$Class$	$Class-mark$ $x_i$	$d_i=x_i-A$	$u_i=\frac{d_i}{h}$	$f_i$	$f_i\times u_i$
$1000-2000$	$1500$	$-2000$	$-2$	$25$	$-50$
$2000-3000$	$2500$	$-1000$	$-1$	$45$	$-45$
$3000-4000$	$3500=A$	$0$	$0$	$50$	$0$
$4000-5000$	$4500$	$1000$	$1$	$30$	$30$
				$\sum f_i=150$	$\sum f_i{u}_i=-65$

$\Rightarrow$ Required mean $=A+h\frac{\sum f_i{u}_i}{\sum f_i}$

$=3500-\frac{65}{150}\times 1000$

$=3500-433.33$

$=Rs.3066.67$

Hence, the mean of the weekly wages is $Rs.3066.67$.