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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 thoseobservations is
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observations from the mean is 250, then the coefficient of variation of thoseobservations is
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Verified Answer
The correct answer is:
10
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,
$\text { C.V. }=\frac{\sigma}{x} \times 100=\frac{5}{50} \times 100=10$
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,
$\text { C.V. }=\frac{\sigma}{x} \times 100=\frac{5}{50} \times 100=10$
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