If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from…
If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from the mean is 250, then the coefficient of variation of those observations is
25
50
10
5
Solution
Given, number of observation, $n=10$,
Mean, $\bar{x}=50$ and $\sum|x i-\bar{x}|^2=250$
Variance, $\sigma^2=\sum_{i=1}^n \frac{\left|x_i-\bar{x}\right|^2}{n}$
$\begin{gathered}
\Rightarrow \sigma^2=\sum_{i=1}^{10} \frac{\left|x_i-\bar{x}^2\right|}{10} \\
=\frac{250}{10}=25 \Rightarrow \sigma=5
\end{gathered}$
$\therefore$ Cofficient of variation,
$\text { C.V. }=\frac{\sigma}{x} \times 100=\frac{5}{50} \times 100=10$