Question

The coefficient of variation of $9,3,11,5,7$, is

• A. $\frac{100 \sqrt{2}}{7}$
• B. $\frac{200 \sqrt{2}}{3}$
• C. $\frac{200 \sqrt{2}}{7}$
• D. $\frac{100 \sqrt{2}}{3}$

Answer 1

Answer: (C)

Given numbers are $9,3,11,5,7$.
Now, mean$(\bar{x})=\frac{9+3+11+5+7}{5}=\frac{35}{5}=7 $
Variance $\sigma^{2}=\frac{1}{5}\left(9^{2}+3^{2}+11^{2}+5^{2}+7^{2}\right)-(7)^{2} $
$=\frac{1}{5}(81+9+121+25+49)-49 $
$=\frac{285}{5}-49=57-49=8$
$\therefore $ Coefficient of variation
$\frac{\sigma^{2}}{x} \times 100=\frac{\sqrt{8}}{7} \times 100=\frac{200 \sqrt{2}}{7}$