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  4. The sum of square of deviations for 10 observations taken from mean 50 is 250. The coefficient of variation is

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Q. The sum of square of deviations for $10$ observations taken from mean $50$ is $250$. The coefficient of variation is

Bihar CECEBihar CECE 2010

Solution:

We know the formula
$ {{\sigma }^{2}}=\frac{\sum {{(x-x)}^{2}}}{n} $
$ \Rightarrow $ $ {{\sigma }^{2}}=\frac{250}{10} $
$ \Rightarrow $ $ \sigma =5 $
$ \therefore $ Coefficient of variation
$ CV=\frac{\sigma }{x}\times 100 $
$ \Rightarrow $ $ CV=\frac{5}{50}\times 100 $
$ \Rightarrow $ $ CV=10 $