If the coefficient of variation of some observation is 60 and their standard deviation is 20, then their mean is

Options

A. 35
B. 34
C. 38.3
D. 33.33

Answer

To find the mean given the coefficient of variation and the standard deviation, we can use the formula for the coefficient of variation (CV):

\[ CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100 \]

Given:
- Coefficient of Variation (CV) = 60
- Standard Deviation (SD) = 20

We can rearrange the formula to solve for the Mean (M):

\[ CV = \frac{SD}{M} \times 100 \]

Substituting the known values into the equation:

\[ 60 = \frac{20}{M} \times 100 \]

Now, we can simplify this equation:

1. Divide both sides by 100:

\[ \frac{60}{100} = \frac{20}{M} \]

2. This simplifies to:

\[ 0.6 = \frac{20}{M} \]

3. Now, cross-multiply to solve for M:

\[ 0.6M = 20 \]

4. Divide both sides by 0.6:

\[ M = \frac{20}{0.6} \]

5. Calculate the value of M:

\[ M = \frac{20 \times 10}{6} = \frac{200}{6} \approx 33.33 \]

Thus, the mean is approximately \(33.33\).

### Final Answer:
The mean is \(33.33\).