Question

The coefficient of variation of two distributions are $50\%$ and $60\%$, and their arithmetic means are $30$ and $25$, respectively. The difference in their standard deviation is

• A. $1$
• B. $1.5$
• C. $2.5$
• D. $0$

Answer 1

The correct option is D

$0$

Explanation for the correct option:

Finding the difference between two standard deviations.

Given:

The coefficient of variance of first distribution be $C{V}_1=50$

The coefficient of variance of second distribution be $C{V}_2=60$

The arithmetic mean of first distribution be $\overline{x_1}=30$

The arithmetic mean of Second distribution be $\overline{x_2}=25$

We know that,

$CV=\left[\frac{\sigma }{\overline{x}}\right]\times 100$ Where $\sigma$ denotes the standard deviation, $\overline{x}$ denotes mean.

$$\begin{gathered} \Rightarrow C{V}_1=\left[\frac{{\sigma }_1}{\overline{x_1}}\right]\times 100 \\ \Rightarrow 50=\left[\frac{{\sigma }_1}{30}\right]\times 100\left[\text{Given}\right] \\ \Rightarrow {\sigma }_1=\frac{30\times 50}{100} \\ =15 \end{gathered}$$

The standard deviation for the first distribution be ${\sigma }_1=15$

similarly,

$$\begin{gathered} \Rightarrow C{V}_2=\left[\frac{{\sigma }_2}{\overline{x_2}}\right]\times 100 \\ \Rightarrow 60=\left[\frac{{\sigma }_2}{25}\right]\times 100\left[\text{Given}\right] \\ \Rightarrow {\sigma }_2=\frac{60\times 25}{100} \\ =15 \end{gathered}$$

The standard deviation for the second distribution be ${\sigma }_2=15$

Calculate the difference between two standard deviation:

$$\begin{gathered} \Rightarrow {\sigma }_1-{\sigma }_2=15-15 \\ =0 \end{gathered}$$

Hence, Option(D) is the correct answer.