If the mena of few observations is 40 and standard deviation is 8, then what is the coefficient of variation?

Options

A. `1%`
B. `10%`
C. `20%`
D. `30%`

Explanation

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

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

### Step 2: Identify the Given Values
From the problem, we have:
- Mean = 40
- Standard Deviation = 8

### Step 3: Substitute the Values into the Formula
Now, we will substitute the values of the mean and standard deviation into the formula:
\[ \text{CV} = \left( \frac{8}{40} \right) \times 100 \]

### Step 4: Calculate the Fraction
Calculate the fraction:
\[ \frac{8}{40} = 0.2 \]

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

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

### Summary
The coefficient of variation for the given observations is 20%.

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