Question

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variations is

Answer 1

We know that, Deviation $=|x_i-\overline{x}|$

But given that,

${|x_1-\overline{x}|}^2+{|x_2-\overline{x}|}^2+{|x_3-\overline{x}|}^2+.............+{|x_{10}-\overline{x}|}^2=250$

$\sum _{i=1}^{10}{|x_i-\overline{x}|}^2=250$

$S.D.=\sqrt{\frac{1}{n}\sum _{i=1}^{10}{|x_i-\overline{x}|}^2}$

$=\sqrt{\frac{1}{10}\times 250}=\sqrt{25}=5$

Coefficient of variation

$=\frac{S.D.}{x}\times 100$

$=\frac{5}{50}\times 100=10$

Hence, this is the answer.