Question

Find the coefficient of variation of the following data. $18,20,15,12,25$.

Answer 1

Let us calculate the A.M of the given data.
A. M $\overline{x}=\frac{12+15+18+20+25}{5}$
$=\frac{90}{5}=18$.

x	$d=x-18$	$d^2$
$12$	$-6$	$36$
$15$	$-3$	$9$
$18$	$0$	$0$
$20$	$2$	$4$
$25$	$7$	$49$
	$\sum d=0$	$\sum d^2=98$

$\sigma =\sqrt{\frac{\sum d^2}{n}}=\sqrt{\frac{98}{5}}$
$=\sqrt{19.6}\simeq 4.428$
$\therefore$ The coefficient of variation $=\frac{\sigma }{\overline{x}}\times 100$
$=\frac{4.428}{18}\times 100=\frac{442.8}{18}$
$\therefore$ The coefficient of variation is $24.6$.