If the mean of 10 observation is 50 and the sum of the square of the deviations of observation from the mean is 250, then the coefficient of variation of these observation is

Options

A. 25
B. 50
C. 10
D. 5

Answer

To solve the problem step by step, we need to find the coefficient of variation (CV) given the mean and the sum of the square of the deviations from the mean.

### Step 1: Understand the given information
We have:
- Mean (μ) = 50
- Number of observations (n) = 10
- Sum of the square of deviations from the mean (Σ(xi - μ)²) = 250

### Step 2: Calculate the variance
The variance (σ²) can be calculated using the formula:
\[ \sigma^2 = \frac{\Sigma (x_i - \mu)^2}{n} \]
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 coefficient of variation (CV) is given by the formula:
\[ CV = \left( \frac{\sigma}{\mu} \right) \times 100 \]
Substituting the values we have:
\[ CV = \left( \frac{5}{50} \right) \times 100 = 10 \]

### Final Answer
The coefficient of variation of these observations is **10**.

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