If the coefficients of variations for two distributions are 40 and 50 and their S.D. are 16 and 25 respectively. Find their means.

Explanation

To find the means of two distributions given their coefficients of variation and standard deviations, we can use the formula for the coefficient of variation (CV):

\[ \text{CV} = \frac{\sigma}{\bar{x}} \times 100 \]

Where:
- \( \sigma \) = standard deviation
- \( \bar{x} \) = mean

### Step-by-Step Solution:

1. **Identify the given values for the first distribution:**
- Coefficient of Variation (CV1) = 40
- Standard Deviation (σ1) = 16

2. **Use the formula to find the mean for the first distribution:**
\[ \text{CV1} = \frac{\sigma_1}{\bar{x}_1} \times 100 \]
Rearranging the formula to solve for the mean (\(\bar{x}_1\)):
\[ \bar{x}_1 = \frac{\sigma_1 \times 100}{\text{CV1}} \]
Substituting the values:
\[ \bar{x}_1 = \frac{16 \times 100}{40} \]
\[ \bar{x}_1 = \frac{1600}{40} = 40 \]

3. **Identify the given values for the second distribution:**
- Coefficient of Variation (CV2) = 50
- Standard Deviation (σ2) = 25

4. **Use the formula to find the mean for the second distribution:**
\[ \text{CV2} = \frac{\sigma_2}{\bar{x}_2} \times 100 \]
Rearranging the formula to solve for the mean (\(\bar{x}_2\)):
\[ \bar{x}_2 = \frac{\sigma_2 \times 100}{\text{CV2}} \]
Substituting the values:
\[ \bar{x}_2 = \frac{25 \times 100}{50} \]
\[ \bar{x}_2 = \frac{2500}{50} = 50 \]

### Final Results:
- Mean of the first distribution (\(\bar{x}_1\)) = 40
- Mean of the second distribution (\(\bar{x}_2\)) = 50