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
$\frac{{\sigma }^2}{x}\times 100=\frac{\sqrt{8}}{7}\times 100=\frac{200\sqrt{2}}{7}$