Coefficent of variation of two distributions are 60% and 75%, and their standard deviations are 18 and 15 respectively. Find their arithmetic means.

Options

A. 30, 30
B. 30, 20
C. 20, 30
D. 20, 20

Answer

To find the arithmetic means of the two distributions given their coefficients of variation and standard deviations, we can use the relationship between the coefficient of variation (CV), standard deviation (σ), and mean (μ).

### Step-by-Step Solution:

1. **Understand the Formula**: The coefficient of variation (CV) is defined as:
\[ CV = \frac{\sigma}{\mu} \times 100 \]
From this, we can rearrange the formula to find the mean:
\[ \mu = \frac{\sigma}{CV} \times 100 \]

2. **Calculate the Mean for the First Distribution**:
- Given:
- Coefficient of Variation (CV) = 60%
- Standard Deviation (σ) = 18
- Substitute the values into the formula:
\[ \mu_1 = \frac{18}{60} \times 100 \]
- Simplify the calculation:
\[ \mu_1 = \frac{18 \times 100}{60} = \frac{1800}{60} = 30 \]

3. **Calculate the Mean for the Second Distribution**:
- Given:
- Coefficient of Variation (CV) = 75%
- Standard Deviation (σ) = 15
- Substitute the values into the formula:
\[ \mu_2 = \frac{15}{75} \times 100 \]
- Simplify the calculation:
\[ \mu_2 = \frac{15 \times 100}{75} = \frac{1500}{75} = 20 \]

4. **Final Result**: The arithmetic means for the two distributions are:
\[ \mu_1 = 30 \quad \text{and} \quad \mu_2 = 20 \]

### Answer:
The arithmetic means are 30 and 20.