1. **State the problem:** Find the sample variance for the data set $\{2,4,6,8\}$. 2. **Formula for sample variance:** $$s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$$ where $n$ is the number of data points, $x_i$ are the data points, and $\bar{x}$ is the sample mean. 3. **Calculate the mean:** $$\bar{x} = \frac{2 + 4 + 6 + 8}{4} = \frac{20}{4} = 5$$ 4. **Calculate each squared deviation:** $$(2 - 5)^2 = (-3)^2 = 9$$ $$(4 - 5)^2 = (-1)^2 = 1$$ $$(6 - 5)^2 = 1^2 = 1$$ $$(8 - 5)^2 = 3^2 = 9$$ 5. **Sum of squared deviations:** $$9 + 1 + 1 + 9 = 20$$ 6. **Calculate sample variance:** $$s^2 = \frac{20}{4 - 1} = \frac{20}{3} \approx 6.67$$ **Final answer:** The sample variance of the data set $\{2,4,6,8\}$ is approximately $6.67$.