If coefficient of variation is 60 and standard deviation is 24, then arithmetic mean is :

Options

A. `20/7`
B. `7/20`
C. `1/40`
D. `40`

Answer

To find the arithmetic mean when the coefficient of variation (CV) and standard deviation (SD) are given, we can use the formula for the coefficient of variation:

\[ CV = \left( \frac{SD}{\text{Mean}} \right) \times 100 \]

Given:
- Coefficient of Variation (CV) = 60
- Standard Deviation (SD) = 24

We need to find the arithmetic mean (Mean).

### Step-by-Step Solution:

1. **Set up the equation using the CV formula:**
\[ 60 = \left( \frac{24}{\text{Mean}} \right) \times 100 \]

2. **Rearrange the equation to isolate the Mean:**
\[ \frac{24}{\text{Mean}} = \frac{60}{100} \]

3. **Simplify the right side:**
\[ \frac{60}{100} = 0.6 \]
So we have:
\[ \frac{24}{\text{Mean}} = 0.6 \]

4. **Cross-multiply to solve for Mean:**
\[ 24 = 0.6 \times \text{Mean} \]

5. **Divide both sides by 0.6 to find the Mean:**
\[ \text{Mean} = \frac{24}{0.6} \]

6. **Calculate the Mean:**
\[ \text{Mean} = 40 \]

Thus, the arithmetic mean is **40**.