Question

Calculate the standard deviation and coefficient of variation for the following distribution.

Marks $\left(x\right)$	$10$	$20$	$30$	$40$	$50$
Number of students $\left(f\right)$	$4$	$3$	$6$	$5$	$2$

Answer 1

Scores $x$	Frequence $f$	$fx$	Deviation from mean $d=(x-\overline{x})$	$d^2$	$f{d}^2$
$10$	$4$	$40$	$-19$	$361$	$1444$
$20$	$3$	$60$	$-9$	$81$	$243$
$30$	$6$	$180$	$+1$	$1$	$6$
$40$	$5$	$200$	$+11$	$121$	$605$
$50$	$2$	$100$	$+21$	$441$	$882$
	$n=20$	$\sum fx=580$			$\sum f{d}^2=3180$

(i) Arithmetic mean $=\overline{x}=\frac{\sum fx}{n}=\frac{580}{20}=29$
$\therefore Mean=\overline{x}=29$
(ii) $\sigma =\sqrt{\frac{\sum f{d}^2}{n}}=\sqrt{\frac{3180}{20}}=\sqrt{159}=12.61$
$\therefore \sigma =12.61$
(iii) $C.V=\frac{\sigma }{\overline{x}}\times 100=\frac{12.61}{29}\times 100=\frac{1261}{29}=43.48$
$\therefore C.V.=43.48$