Question

The following table given the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers.

Wages (Rs)	$125-175$	$175-225$	$225-275$	$275-325$	$325-375$	$375-425$	$425-475$	$475-525$
Number of workers	$2$	$22$	$19$	$14$	$3$	$4$	$6$	$1$

Answer 1

$Wages$	$x_i$	$f_i$	$f_i{x}_i$	$(x-\overline{x})$	$(x-\overline{x}{)}^2$
$125-175$	$150$	$2$	$300$	$-124.65$	$15537.6225$
$175-225$	$200$	$22$	$4400$	$-74.65$	$5572.6225$
$225-275$	$250$	$19$	$4750$	$-24.65$	$607.6225$
$275-325$	$300$	$14$	$4200$	$25.35$	$642.6225$
$325-375$	$350$	$3$	$1050$	$75.5$	$5677.6225$
$375-425$	$400$	$4$	$1600$	$125.35$	$15712.6225$
$425-475$	$450$	$6$	$2700$	$175.35$	$30747.6225$
$475-525$	$500$	$1$	$500$	$225.35$	$50782.6225$
		$\sum f_i=71$	$\sum f_i{x}_i=19500$		$\sum (x-\overline{x}{)}^2=125280.98$

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{19500}{71}=274.65$

$\sigma =\sqrt{\frac{\sum (x-\overline{x}{)}^2}{\sum f_i}}$

$=\sqrt{\frac{125280.98}{71}}$

$=\sqrt{1764.5208}$

$=42.0061\approx 42$

$\Rightarrow$ $CV=\frac{\sigma }{\overline{x}}\times 100$

$=\frac{42}{274.65}\times 100$

$=15.3$