1. **Stating the problem:** We are given the data set: 7, 3, 1, 5, 13, 7, 19, 16. We need to find: - a) The mean ($\bar{X}$) - b) The mode (Mo) - c) The median (Me) 2. **Formula and explanation:** - Mean ($\bar{X}$) is the sum of all data points divided by the number of data points: $$\bar{X} = \frac{\sum x_i}{n}$$ - Mode (Mo) is the value that appears most frequently in the data. - Median (Me) is the middle value when data is ordered. If $n$ is even, median is the average of the two middle values. 3. **Calculating the mean:** Sum of data: $7 + 3 + 1 + 5 + 13 + 7 + 19 + 16 = 71$ Number of data points: $n = 8$ $$\bar{X} = \frac{71}{8}$$ Show canceling for division: $$\bar{X} = \frac{\cancel{71}}{\cancel{8}}$$ (no common factors to cancel) Calculate: $$\bar{X} = 8.875$$ 4. **Finding the mode:** Data sorted: 1, 3, 5, 7, 7, 13, 16, 19 The number 7 appears twice, more than any other number. So, $$Mo = 7$$ 5. **Finding the median:** Data sorted: 1, 3, 5, 7, 7, 13, 16, 19 Since $n=8$ (even), median is average of 4th and 5th values: $$Me = \frac{7 + 7}{2} = \frac{14}{2} = 7$$ **Final answers:** - Mean ($\bar{X}$) = 8.875 - Mode (Mo) = 7 - Median (Me) = 7