The mean of a distribution is 20 and the standard deviation is 4. What is the value of the coefficient variation?
A. 10 %
B. 20%
C. 40%
D. 60%

Options

A. B
B. A
C. D
D. C

Answer

To find the coefficient of variation (CV) of the given distribution, we can follow these steps:

### Step 1: Understand the formula for Coefficient of Variation
The formula for the coefficient of variation (CV) is given by:
\[ CV = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 \]

### Step 2: Identify the values provided
From the question, we have:
- Mean (μ) = 20
- Standard Deviation (σ) = 4

### Step 3: Substitute the values into the formula
Now, we substitute the given values into the formula:
\[ CV = \left( \frac{4}{20} \right) \times 100 \]

### Step 4: Simplify the fraction
Next, we simplify the fraction:
\[ \frac{4}{20} = 0.2 \]

### Step 5: Multiply by 100
Now, we multiply by 100 to find the coefficient of variation:
\[ CV = 0.2 \times 100 = 20 \]

### Step 6: State the final answer
Thus, the value of the coefficient of variation is:
\[ \text{CV} = 20\% \]

### Conclusion
The correct answer is **B. 20%**.

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