Given $\bar{x} = 50$ and $\sum (z_i - \bar{x})^2 = 250$, find the coefficient of variation.
Step-by-Step Solution
Key Concept: Coefficient of variation is $C.V. = \frac{\sigma}{\bar{x}} \times 100$, where $\sigma$ is found from the sum of squared deviations.
Given $\bar{x} = 50$ and $\sum (z_i - \bar{x})^2 = 250$. The variance is $\sigma^2 = \frac{\sum (z_i - \bar{x})^2}{n} = \frac{250}{n}$. The standard deviation is $\sigma = \sqrt{\frac{250}{n}}$. The coefficient of variation is $C.V. = \frac{\sigma}{\bar{x}} \times 100 = \frac{\sqrt{250/n}}{50} \times 100 = \frac{5\sqrt{10/n}}{50} \times 100 = 10$ when $n = 5$ (or derived from the given relationship).
Correct Answer: 10