The mean of a distribution is 15 and the standard deviation is 5 . What is the value of coefficient variation ?

Options

A. 0.1666
B. 0.6666
C. 0.3333
D. 1

Answer

To find the coefficient of variation (CV) given the mean and standard deviation, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Given Values**:
- Mean (μ) = 15
- Standard Deviation (σ) = 5

2. **Formula for Coefficient of Variation**:
The formula for the coefficient of variation (CV) is:
\[ CV = \left( \frac{\sigma}{\mu} \right) \times 100 \]
where:
- \( \sigma \) is the standard deviation
- \( \mu \) is the mean

3. **Substitute the Values into the Formula**:
Substitute the values of standard deviation and mean into the formula:
\[ CV = \left( \frac{5}{15} \right) \times 100 \]

4. **Simplify the Fraction**:
Simplify \( \frac{5}{15} \):
\[ \frac{5}{15} = \frac{1}{3} \]

5. **Calculate the Coefficient of Variation**:
Now, substitute back into the equation:
\[ CV = \left( \frac{1}{3} \right) \times 100 \]

6. **Final Calculation**:
\[ CV = \frac{100}{3} \approx 33.33 \]

7. **Express in Percentage**:
The coefficient of variation is approximately 33.33%.

### Final Answer:
The coefficient of variation is **33.33%**.

---