1. **Problem:** Calculate the sample variance of the math test scores: 70, 75, 80, 85, 90. 2. **Formula:** Sample variance $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$ where $n$ is the number of scores, $x_i$ each score, and $\bar{x}$ the sample mean. 3. **Step 1: Calculate the mean** $$\bar{x} = \frac{70 + 75 + 80 + 85 + 90}{5} = \frac{400}{5} = 80$$ 4. **Step 2: Calculate each deviation from the mean and square it** - $(70 - 80)^2 = (-10)^2 = 100$ - $(75 - 80)^2 = (-5)^2 = 25$ - $(80 - 80)^2 = 0^2 = 0$ - $(85 - 80)^2 = 5^2 = 25$ - $(90 - 80)^2 = 10^2 = 100$ 5. **Step 3: Sum the squared deviations** $$100 + 25 + 0 + 25 + 100 = 250$$ 6. **Step 4: Divide by $n-1 = 4$ to get sample variance** $$s^2 = \frac{250}{4} = 62.5$$ **Final answer:** The sample variance of the math test scores is $62.5$.