If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

Options

A. 2025
B. 450
C. 45
D. 4.5

Answer

To find the variance given the mean and the coefficient of variation, we can follow these steps:

### Step 1: Understand the given information
- Mean (μ) = 100
- Coefficient of Variation (CV) = 45%

### Step 2: Use the formula for Coefficient of Variation
The Coefficient of Variation is defined as:
\[ CV = \frac{\sigma}{\mu} \times 100 \]
where:
- \( \sigma \) is the standard deviation
- \( \mu \) is the mean

### Step 3: Substitute the known values into the CV formula
Substituting the values we have:
\[ 45 = \frac{\sigma}{100} \times 100 \]

### Step 4: Simplify the equation
This simplifies to:
\[ 45 = \sigma \]
So, the standard deviation \( \sigma \) is 45.

### Step 5: Calculate the variance
The variance (V) is given by the square of the standard deviation:
\[ V = \sigma^2 \]
Substituting the value of \( \sigma \):
\[ V = 45^2 = 2025 \]

### Final Answer
The value of the variance is **2025**.

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