Question

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

• A. $10\%$
• B. $40\%$
• C. $50\%$
• D. none of these

Answer 1

The correct option is A

$10\%$

We have :

$\overline{X}=50,n=10$

${\sum }_{i=1}^{10}(x_i-\overline{X}{)}^2=250$

$\therefore SD=\sqrt{\text{Variance of X}}=\sqrt{\frac{{\sum }_{i=1}^{10}(x_i-\overline{X}{)}^2}{n}}=\sqrt{\frac{250}{10}}=5$

Using CV $=\frac{\sigma }{\overline{X}}\times 100\Rightarrow CV=\frac{5}{50}\times 100=10\%$