Question

The series with 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 = $\frac{\sigma }{x}$
Lets take 2 series with same mean,

.${CV}_1$ = $\frac{{\sigma }_1}{x_1}$,
(${CV}_2$ = $\frac{{\sigma }_2}{x_2}$),
$\overline{x_1}$=$\overline{x_2}$=$\overline{x}$.
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 to we can observe that Coefficient of variation can give a feeling of greater variance if it is larger.