Question

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

Options

• 10 %

• 40 %

•  50 %

• none of these

   

Answer 1

10 %

\[\text{ We have } : \]

\[X = 50, n = 10 \]

\[ \sum^{10}_{i = 1} \left( x_i - X \right)^2 = 250\]

\[ \therefore SD = \sqrt{\text{ Variance}  of X} \]

\[ = \sqrt{\frac{\sum^{10}_{i = 1} \left( x_i - X \right)^2}{n}} \]

\[ = \sqrt{\frac{250}{10}}\]

\[ = 5\]

Using  \[CV = \frac{\sigma}{X} \times 100\]

\[\Rightarrow CV = \frac{5}{50} \times 100 \]

\[ = 10\]  %