Question

For two distributions, the standard deviations are \(21\) and \(14\) respectively and their coefficients of variations are \(60\) and \(70\) respectively. Which of the following is correct for their arithmetic means?

• A. \(65,13\)
• B. \(18.5,65\)
• C. \(35,20\)
• D. \(22.85,35\)

Hint:

Use \(CV=\frac{\sigma}{\bar{x}}\times100\). If \(CV\) and standard deviation are given, then \(\bar{x}=\frac{\sigma\times100}{CV}\).

Answer 1

The Correct Option is C

Concept:
Coefficient of variation is given by: \[ CV=\frac{\sigma}{\bar{x}}\times 100 \] where \(\sigma\) is standard deviation and \(\bar{x}\) is arithmetic mean.

Step 1: For first distribution. \[ \sigma_1=21,\quad CV_1=60 \] Using: \[ CV=\frac{\sigma}{\bar{x}}\times 100 \] \[ 60=\frac{21}{\bar{x}_1}\times 100 \] \[ \bar{x}_1=\frac{21\times 100}{60} \] \[ \bar{x}_1=35 \]

Step 2: For second distribution. \[ \sigma_2=14,\quad CV_2=70 \] \[ 70=\frac{14}{\bar{x}_2}\times 100 \] \[ \bar{x}_2=\frac{14\times 100}{70} \] \[ \bar{x}_2=20 \] Thus, the arithmetic means are: \[ 35,\ 20 \] \[ \therefore \text{Correct Answer is (C)} \]