1. **Problem:** Given the data set 2, 1, 5, 4, find the variance. 2. **Formula for variance:** $$\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n}$$ where $x_i$ are data points, $\bar{x}$ is the mean, and $n$ is the number of data points. 3. **Calculate the mean:** $$\bar{x} = \frac{2 + 1 + 5 + 4}{4} = \frac{12}{4} = 3$$ 4. **Calculate each squared deviation:** $$(2 - 3)^2 = (-1)^2 = 1$$ $$(1 - 3)^2 = (-2)^2 = 4$$ $$(5 - 3)^2 = 2^2 = 4$$ $$(4 - 3)^2 = 1^2 = 1$$ 5. **Sum of squared deviations:** $$1 + 4 + 4 + 1 = 10$$ 6. **Calculate variance:** $$\text{Variance} = \frac{10}{4} = 2.5$$ **Final answer:** The variance is 2.5, which corresponds to option A.