If the coefficient of variation of a distribution is 45% and the mean is 12, then its standard deviation is

Options

A. 5.2
B. 5.3
C. 5.4
D. none of these

Answer

To solve the problem, we need to find the standard deviation given the coefficient of variation and the mean. Here’s the step-by-step solution:

### Step 1: Understand the formula for Coefficient of Variation (CV)
The Coefficient of Variation (CV) is defined as:
\[ CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100 \]

### Step 2: Substitute the known values into the formula
We know that:
- Coefficient of Variation (CV) = 45%
- Mean = 12

Substituting these values into the formula:
\[ 45 = \frac{\text{Standard Deviation}}{12} \times 100 \]

### Step 3: Rearrange the equation to solve for Standard Deviation
To isolate the Standard Deviation, we can rearrange the equation:
\[ \frac{\text{Standard Deviation}}{12} = \frac{45}{100} \]
\[ \text{Standard Deviation} = 12 \times \frac{45}{100} \]

### Step 4: Calculate the Standard Deviation
Now, we perform the multiplication:
\[ \text{Standard Deviation} = 12 \times 0.45 = 5.4 \]

### Final Answer
Thus, the standard deviation is:
\[ \text{Standard Deviation} = 5.4 \]

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