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 will follow the definitions and formulas related to mean, variance, standard deviation, and coefficient of variation.

### Step 1: Understand the given data
We are given:
- Mean (μ) of 10 observations = 50
- Sum of the squares of deviations from the mean = 250

### Step 2: Calculate the Variance
The variance (σ²) can be calculated using the formula:
\[ \sigma^2 = \frac{\text{Sum of squares of deviations}}{N} \]
where \(N\) is the number of observations.

Here, \(N = 10\) and the sum of squares of deviations is 250.

So,
\[ \sigma^2 = \frac{250}{10} = 25 \]

### 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:
\[ CV = \frac{\sigma}{\mu} \times 100\% \]
Substituting the values we have:
\[ CV = \frac{5}{50} \times 100\% = 0.1 \times 100\% = 10\% \]

### Conclusion
The coefficient of variation of these observations is **10%**.

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