Question

If $n=10,\bar{x}=12$ and $\sum x_i^2=1530$, then the coefficient of variation is

• A. $35\%$
• B. $42\%$
• C. $30\%$
• D. $25\%$

Answer 1

Answer: (D)

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 $v$ $n=\frac{\sigma }{\overline{x}}\times 100$
$=\frac{3}{12}\times 100=25\%$