Question

The coefficient of variation for the given distribution is

• A. $28.6$
• B. $0.306$
• C. $30.6$
• D. $306$

Answer 1

The correct option is A $28.6$

Lett $A=10$

$Size$ $x_i$	$Frequency$ $f_i$	$f_i{x}_i$	$(x_i-A{)}^2$	$f_i(x_i-A{)}^2$
$4$	$1$	$4$	$36$	$36$
$6$	$2$	$12$	$16$	$32$
$8$	$3$	$24$	$4$	$12$
$10$	$5$	$50$	$0$	$0$
$12$	$3$	$36$	$4$	$12$
$14$	$2$	$28$	$16$	$32$
$16$	$1$	$16$	$36$	$16$
	$\sum f_i=17$	$\sum f_i{x}_i=170$		$\sum f_i(x_i-A{)}^2=140$

$\Rightarrow$ $\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{170}{17}=10$

Now, $S.D\left(\sigma \right)=\sqrt{\frac{\sum f_i(x_i-A{)}^2}{\sum f_i}}$

$=\sqrt{\frac{140}{17}}$

$=2.86$

$\Rightarrow$ Coefficient of variation $=\frac{\sigma }{\overline{x}}\times 100$

$=\frac{2.86}{10}\times 100$

$=28.6$