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

Options

A. `(19.76)/(35.16)xx10`
B. `(35.16)/(19.76)xx100`
C. `(19.76)/(35.16)`
D. None of these

Answer

To find the coefficient of variation (CV) for the given distribution of marks, we can follow these steps:

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

### Step 2: Identify the given values
From the problem, we have:
- Mean (μ) = 35.16
- Standard Deviation (σ) = 19.76

### Step 3: Substitute the values into the formula
Now, we will substitute the given values into the CV formula:
\[ CV = \left( \frac{19.76}{35.16} \right) \times 100 \]

### Step 4: Calculate the fraction
First, calculate the fraction:
\[ \frac{19.76}{35.16} \approx 0.561 \]

### Step 5: Multiply by 100
Now, multiply the result by 100 to get the coefficient of variation:
\[ CV \approx 0.561 \times 100 \approx 56.1 \]

### Final Answer
Thus, the coefficient of variation is approximately **56.1%**.

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