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Q.
The sum of the squares of deviations for $10$ observations taken from their mean $50$ is $250$. The coefficient of variation is
Solution:
Let, $x i, i=1,2 \ldots 10$ be 10 observations
We have $\displaystyle\sum_{i=1}^{10}(x i-50)^{2}=250$
Now $\sigma^{2}=\frac{1}{10} \displaystyle\sum_{i=1}^{10}(x i-50)^{2}$
$=\frac{250}{10}=25\,\,\,\sigma=5$
$\therefore C . V=\frac{\sigma}{x} \times 100$
$=\frac{5}{50} \times 100=10 \%$