Question

The series with a greater coefficient of variation will show greater dispersion compared to the one with less coefficient of variation.

• A. True
• B. False

Answer 1

The correct option is A

True

Let us see the definition of coefficient of variation.
$C.V=\frac{\sigma }{\overline{x}}$
Lets take 2 series with same mean.

${CV}_1$ = $\frac{{\sigma }_1}{\overline{x_1}}$,
${CV}_2$ = $\frac{{\sigma }_2}{\overline{x_2}}$,
$\overline{x_1}$=$\overline{x_2}$=$\overline{x}$
Given, ${CV}_1$ = $\frac{{\sigma }_1}{\overline{x}}$, ~${CV}_2$ = $\frac{{\sigma }_2}{\overline{x}}$

${CV}_1$>${CV}_2$ $\Rightarrow$ ${\sigma }_1$ > ${\sigma }_2$

i.e., variance in case one is greater than that in case 2.

Similarly, for other cases too, we can observe that coefficient of variation can give a feeling of greater variance if it is larger.