If the coefficient of variation of 45% and the mean is 12 then find its s.d ?

Answer

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

### Step 1: Understand the formula for Coefficient of Variation
The coefficient of variation (CV) is defined as:

\[ CV = \frac{\text{Standard Deviation (s.d.)}}{\text{Mean}} \times 100 \]

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

Substituting these values into the formula gives:

\[ 45 = \frac{\text{s.d.}}{12} \times 100 \]

### Step 3: Rearrange the formula to solve for Standard Deviation
To isolate the standard deviation, we can rearrange the equation:

\[ \frac{\text{s.d.}}{12} = \frac{45}{100} \]

### Step 4: Multiply both sides by 12
Now, multiply both sides by 12 to solve for s.d.:

\[ \text{s.d.} = 12 \times \frac{45}{100} \]

### Step 5: Simplify the right side
Calculating the right side:

\[ \text{s.d.} = 12 \times 0.45 = 5.4 \]

### Conclusion
Thus, the standard deviation is:

\[ \text{s.d.} = 5.4 \]