Question

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
(a) 0
(b) 1
(c) 1.5
(d) 2.5

Answer 1

Let coefficient of variation of first distribution be CV₁ and coefficient of variation of second distribution be CV₂
Let mean be given by ${\overline{x}}_1\mathrm{and}{\overline{x}}_2$ respectively.

$$\begin{gathered} \therefore C{V}_1=\frac{{\sigma }_1}{x_1}\times 100 \\ \mathrm{i}.\mathrm{e}50=\frac{{\sigma }_1}{30}\times 100 \\ \mathrm{i}.\mathrm{e}{\sigma }_1=15 \\ \mathrm{and}C{V}_2=\frac{{\sigma }_2}{x_{{}^2}}\times 100 \\ \mathrm{i}.\mathrm{e}60=\frac{{\sigma }_2}{25}\times 100 \\ \mathrm{i}.\mathrm{e}{\sigma }_2=15 \\ \therefore {\sigma }_1-{\sigma }_2=15-15=0 \end{gathered}$$

Hence, the correct answer is option A.