1. **Problem statement:** Find the mean absolute deviation (MAD) of the maximum speeds of the five fastest cars: {270, 265, 261, 256, 248}. 2. **Formula:** The mean absolute deviation is given by $$\text{MAD} = \frac{1}{n} \sum_{i=1}^n |x_i - \bar{x}|$$ where $\bar{x}$ is the mean of the data set. 3. **Calculate the mean:** $$\bar{x} = \frac{270 + 265 + 261 + 256 + 248}{5} = \frac{1300}{5} = 260$$ 4. **Calculate absolute deviations:** $$|270 - 260| = 10$$ $$|265 - 260| = 5$$ $$|261 - 260| = 1$$ $$|256 - 260| = 4$$ $$|248 - 260| = 12$$ 5. **Calculate MAD:** $$\text{MAD} = \frac{10 + 5 + 1 + 4 + 12}{5} = \frac{32}{5} = 6.4$$ --- 1. **Problem statement:** Find the MAD of the number of home runs in six seasons: {215, 177, 125, 130, 139, 108}. 2. **Calculate the mean:** $$\bar{x} = \frac{215 + 177 + 125 + 130 + 139 + 108}{6} = \frac{894}{6} = 149$$ 3. **Calculate absolute deviations:** $$|215 - 149| = 66$$ $$|177 - 149| = 28$$ $$|125 - 149| = 24$$ $$|130 - 149| = 19$$ $$|139 - 149| = 10$$ $$|108 - 149| = 41$$ 4. **Calculate MAD:** $$\text{MAD} = \frac{66 + 28 + 24 + 19 + 10 + 41}{6} = \frac{188}{6} \approx 31.3$$ --- 1. **Problem statement:** Find the MAD of Allyson's daily text messages last week: {18, 27, 21, 33, 37, 62, 54}. 2. **Calculate the mean:** $$\bar{x} = \frac{18 + 27 + 21 + 33 + 37 + 62 + 54}{7} = \frac{252}{7} = 36$$ 3. **Calculate absolute deviations:** $$|18 - 36| = 18$$ $$|27 - 36| = 9$$ $$|21 - 36| = 15$$ $$|33 - 36| = 3$$ $$|37 - 36| = 1$$ $$|62 - 36| = 26$$ $$|54 - 36| = 18$$ 4. **Calculate MAD:** $$\text{MAD} = \frac{18 + 9 + 15 + 3 + 1 + 26 + 18}{7} = \frac{90}{7} \approx 12.9$$ --- 1. **Problem statement:** Find the MAD of wait times of eight rides: {25, 48, 32, 64, 20, 12, 74, 5}. 2. **Calculate the mean:** $$\bar{x} = \frac{25 + 48 + 32 + 64 + 20 + 12 + 74 + 5}{8} = \frac{280}{8} = 35$$ 3. **Calculate absolute deviations:** $$|25 - 35| = 10$$ $$|48 - 35| = 13$$ $$|32 - 35| = 3$$ $$|64 - 35| = 29$$ $$|20 - 35| = 15$$ $$|12 - 35| = 23$$ $$|74 - 35| = 39$$ $$|5 - 35| = 30$$ 4. **Calculate MAD:** $$\text{MAD} = \frac{10 + 13 + 3 + 29 + 15 + 23 + 39 + 30}{8} = \frac{162}{8} = 20.3$$