1. **State the problem:** We have a sample of ages: $\{17, 29, 22, 54, 31, 16, 63, 48, 29, 36\}$. We need to find the sample mean and the mean absolute deviation (MAD) to evaluate how far the sample mean is from the actual mean. 2. **Find the sample mean:** The sample mean $\bar{x}$ is calculated by summing all values and dividing by the number of values. $$\bar{x} = \frac{17 + 29 + 22 + 54 + 31 + 16 + 63 + 48 + 29 + 36}{10}$$ $$= \frac{345}{10} = 34.5$$ 3. **Calculate the absolute deviations:** Find the absolute difference between each age and the sample mean. $$|17 - 34.5| = 17.5$$ $$|29 - 34.5| = 5.5$$ $$|22 - 34.5| = 12.5$$ $$|54 - 34.5| = 19.5$$ $$|31 - 34.5| = 3.5$$ $$|16 - 34.5| = 18.5$$ $$|63 - 34.5| = 28.5$$ $$|48 - 34.5| = 13.5$$ $$|29 - 34.5| = 5.5$$ $$|36 - 34.5| = 1.5$$ 4. **Calculate the mean absolute deviation (MAD):** Sum the absolute deviations and divide by the number of values. $$\text{MAD} = \frac{17.5 + 5.5 + 12.5 + 19.5 + 3.5 + 18.5 + 28.5 + 13.5 + 5.5 + 1.5}{10}$$ $$= \frac{126}{10} = 12.6$$ 5. **Interpretation:** The MAD is 12.6, which is relatively small compared to the range of ages, so the sample mean is a pretty good estimate for the actual mean. **Final answers:** - Sample mean = $34.5$ - Mean absolute deviation (MAD) = $12.6$ - Interpretation: The MAD is 12.6. Since this number is relatively small, the sample mean is a pretty good estimate for the actual mean. This corresponds to option A in the multiple-choice.