For a given distribution of marks, the mean is 35.16 and its standard deviation is 19.76. The coefficient of variation is

Options

A. `(35.16)/(19.76)`
B. `(19.76)/(35.16)`
C. `(35.16)/(19.76)xx100`
D. `(19.76)/(35.16)xx100`

Explanation

To find the coefficient of variation for the given distribution of marks, we will follow these steps:

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

\[ CV = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 \]

### Step 2: Identify the given values
From the question, we have:
- Mean (\( \mu \)) = 35.16
- Standard Deviation (\( \sigma \)) = 19.76

### Step 3: Substitute the values into the formula
Now, we will substitute the values of the standard deviation and mean into the formula:

\[ CV = \left( \frac{19.76}{35.16} \right) \times 100 \]

### Step 4: Calculate the fraction
First, we calculate the fraction:

\[ \frac{19.76}{35.16} \approx 0.561 \]

### Step 5: Multiply by 100
Now, we multiply the result by 100 to get the coefficient of variation:

\[ CV \approx 0.561 \times 100 \approx 56.1 \]

### Step 6: Final Result
Thus, the coefficient of variation is approximately:

\[ CV \approx 56.1\% \]

### Summary of the Solution
The coefficient of variation for the given distribution of marks is approximately **56.1%**.

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