The arithmetic means of two distributions are 20 and 35 and their S.D. are 5 and 7 respectively. Find their coefficient of variation.

Explanation

To find the coefficient of variation for the two distributions, we will follow these steps:

### Step 1: Understand the formula for Coefficient of Variation (CV)
The Coefficient of Variation (CV) is calculated using the formula:
\[ CV = \left( \frac{\sigma}{\bar{x}} \right) \times 100 \]
where:
- \(\sigma\) is the standard deviation,
- \(\bar{x}\) is the mean.

### Step 2: Calculate CV for the first distribution
Given:
- Mean (\(\bar{x}_1\)) = 20
- Standard Deviation (\(\sigma_1\)) = 5

Using the formula:
\[ CV_1 = \left( \frac{\sigma_1}{\bar{x}_1} \right) \times 100 = \left( \frac{5}{20} \right) \times 100 \]
Calculating:
\[ CV_1 = \left( 0.25 \right) \times 100 = 25 \]

### Step 3: Calculate CV for the second distribution
Given:
- Mean (\(\bar{x}_2\)) = 35
- Standard Deviation (\(\sigma_2\)) = 7

Using the formula:
\[ CV_2 = \left( \frac{\sigma_2}{\bar{x}_2} \right) \times 100 = \left( \frac{7}{35} \right) \times 100 \]
Calculating:
\[ CV_2 = \left( 0.2 \right) \times 100 = 20 \]

### Final Results
- Coefficient of Variation for the first distribution, \(CV_1 = 25\)
- Coefficient of Variation for the second distribution, \(CV_2 = 20\)