If the coefficient of variation and standard deviation are 60 and 18 respectively, the arithmetic mean of distribution Is :

Options

A. 60
B. 30
C. 35
D. 21

Answer

To find the arithmetic mean of the distribution given the coefficient of variation and standard deviation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Coefficient of Variation (CV)**:
The coefficient of variation is defined as:
\[ CV = \left( \frac{\text{Standard Deviation}}{\text{Arithmetic Mean}} \right) \times 100 \]

2. **Rearrange the Formula**:
We can rearrange the formula to solve for the arithmetic mean:
\[ \text{Arithmetic Mean} = \frac{\text{Standard Deviation} \times 100}{CV} \]

3. **Substitute the Given Values**:
We are given:
- Standard Deviation (SD) = 18
- Coefficient of Variation (CV) = 60

Now substitute these values into the rearranged formula:
\[ \text{Arithmetic Mean} = \frac{18 \times 100}{60} \]

4. **Calculate the Arithmetic Mean**:
- First, multiply 18 by 100:
\[ 18 \times 100 = 1800 \]
- Next, divide 1800 by 60:
\[ \frac{1800}{60} = 30 \]

5. **Conclusion**:
The arithmetic mean of the distribution is:
\[ \text{Arithmetic Mean} = 30 \]

### Final Answer:
The arithmetic mean of the distribution is **30**.