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Q.
If $n=10, \bar{x}=12$ and $\sum x_{i}^{2}=1530$, then the coefficient of variation is
Statistics
Solution:
We have, $n =10, \overline{ x }=12$ and $\sum x _{ i }^{2}=1530$
$\therefore \sigma^{2}=\frac{1}{10}\left(\sum_{i=1}^{10} x _{ i }^{2}\right)-\left(\frac{1}{10} \sum_{ i =1}^{10} x _{ i }\right)^{2}$
$\Rightarrow \sigma^{2}=\frac{1530}{10}-(12)^{2} $
$\Rightarrow \sigma^{2}=153-144$
$\Rightarrow \sigma^{2}=9$
$ \Rightarrow \sigma=3$
Coefficient of $v$ $n =\frac{\sigma}{\overline{ x }} \times 100$
$=\frac{3}{12} \times 100=25 \%$