Question

Following are the runs scored by two batsmen in $5$ cricket matches. Who is more consistent in scoring runs.

Batsman A	$38$	$47$	$34$	$18$	$33$
Batsman B	$37$	$35$	$41$	$27$	$35$

Answer 1

Batsman A

x	$d=x-\overline{x}$	$d^2$
$18$	$-16$	$256$
$33$	$-1$	$1$
$34$	$0$	$0$
$38$	$4$	$16$
$47$	$13$	$169$
$170$	$0$	$442$

Now $\overline{x}=\frac{170}{5}=34$
$\sigma =\sqrt{\frac{\sum d^2}{n}}$
$=\sqrt{\frac{442}{5}}=\sqrt{88.4}$
$\simeq 9.4$
Coefficient of variation, C.V$=\frac{\sigma }{\overline{x}}\times 100$
$=\frac{9.4}{34}\times 100$
$=\frac{940}{34}$
$=27.65$
$\therefore$ The coefficient of variation for the runs scored by batsman A is $27.65$ ............$\left(1\right)$
Batsman B

x	$d=x-\overline{x}$	$d^2$
$27$	$-8$	$64$
$35$	$0$	$0$
$35$	$0$4	$0$
$37$	$2$	$4$
$41$	$6$	$36$
$175$	$0$	$104$

$\overline{x}=\frac{175}{5}=35$
$\sigma =\sqrt{\frac{\sum d^2}{n}}$
$=\sqrt{\frac{104}{5}}=\sqrt{20.8}$
$\simeq 4.6$
Coefficient of variation
$=\frac{\sigma }{\overline{x}}\times 100$
$=\frac{4.6}{35}\times 100$
$=\frac{460}{35}=\frac{92}{7}=13.14$
$\therefore$ The coefficient of varaition for the runs scored by batsman B is $=13.14$ ...........$\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, the coefficient of variation for B is less than the coefficient of variation for A.
$\therefore$ Batsman B is more consistent than the batsman A in scoring the runs.