Question

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. Then Co-efficient of variation is

• A. $10\%$
• B. $40\%$
• C. $50\%$
• D. None

Answer 1

The correct option is A $10\%$

$\sum (x-\overline{x}{)}^2=250$, $\overline{x}=50$

$\Rightarrow$ Standard deviation $\left(\sigma \right)=\sqrt{\frac{250}{10}}=\sqrt{25}=5$

$\Rightarrow$ Coefficient of variation $=\sqrt{\frac{\sum (x-\overline{x}{)}^2}{n}}$

$=\frac{\sigma }{Mean}\times 100$

$=\frac{5}{50}\times 100$

$=10\%$