1. **State the problem:** We need to find the variance of the yearly sales amounts (in thousands of dollars) for 5 salespeople whose sales values are 70, 70, 85, 65, and 75. 2. **Recall the formula for variance:** The variance $\sigma^2$ of a dataset is given by $$\sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2$$ where $n$ is the number of data points, $x_i$ are the data points, and $\bar{x}$ is the mean (average) of the data. 3. **Calculate the mean $\bar{x}$:** $$\bar{x} = \frac{70 + 70 + 85 + 65 + 75}{5} = \frac{365}{5} = 73$$ 4. **Calculate each squared deviation $(x_i - \bar{x})^2$:** - $(70 - 73)^2 = (-3)^2 = 9$ - $(70 - 73)^2 = 9$ - $(85 - 73)^2 = 12^2 = 144$ - $(65 - 73)^2 = (-8)^2 = 64$ - $(75 - 73)^2 = 2^2 = 4$ 5. **Sum all squared deviations:** $$9 + 9 + 144 + 64 + 4 = 230$$ 6. **Divide by the number of data points $n=5$ to find variance:** $$\sigma^2 = \frac{230}{5} = 46$$ **Final Answer:** The variance of the dataset is **46** (thousand dollars squared).