The coefficient of variation (CV) is calculated using the formula:
CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\%
1. Calculate the mean \mu of the data set:
\mu = \frac{2 + 4 + 6 + 8}{4} = \frac{20}{4} = 5
2. Calculate the variance \sigma^2 of the population:
First, calculate the squared deviations from the mean:
For 2: (2 - 5)^2 = 9
For 4: (4 - 5)^2 = 1
For 6: (6 - 5)^2 = 1
For 8: (8 - 5)^2 = 9
Variance:
\sigma^2 = \frac{9 + 1 + 1 + 9}{4} = \frac{20}{4} = 5
3. Calculate the standard deviation \sigma:
\sigma = \sqrt{\sigma^2} = \sqrt{5}
4. Calculate the coefficient of variation (CV):
CV=\frac{\sqrt{5}}{5}\times100\%\approx44.72\%
The coefficient of variation is approximately 44.72%.