The sum of squares of deviations of 10 items about mean 50 is 250. The coefficient of variation is

Options

A. `10%`
B. `50%`
C. `30%`
D. none of these

Answer

To solve the problem step by step, we will find the coefficient of variation using the given data.

### Step 1: Identify the given data
- Number of items (n) = 10
- Mean (X̄) = 50
- Sum of squares of deviations (Σ(Xi - X̄)²) = 250

### Step 2: Calculate the variance
The formula for variance (σ²) is given by:
\[ \sigma^2 = \frac{\Sigma (X_i - X̄)^2}{n} \]
Substituting the values we have:
\[ \sigma^2 = \frac{250}{10} = 25 \]

### Step 3: Calculate the standard deviation
The standard deviation (σ) is the square root of the variance:
\[ \sigma = \sqrt{\sigma^2} = \sqrt{25} = 5 \]

### Step 4: Calculate the coefficient of variation
The formula for the coefficient of variation (CV) is:
\[ CV = \frac{\sigma}{X̄} \times 100 \]
Substituting the values we have:
\[ CV = \frac{5}{50} \times 100 = 10\% \]

### Final Answer
The coefficient of variation is **10%**.

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