Calculate the coefficient of variation of the following set of data 2,4,6 and 8 knowing that they form a population

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%.