Problem 5. Happy Family In class, we defined the mean absolute deviation from the median as a measure of the spread of a dataset. This measure takes the absolute deviations, or distances, of each value in the dataset from the median, and computes the mean of these absolute deviations. We can think of this one measure of spread as a member of a family of analogously defined measures of spread: mean absolute deviation from the median median absolute deviation from the median mean absolute deviation from the mean median absolute deviation from the mean While all four of these measures capture the notion of spread, they do so in different ways, and so they may have different values for the same dataset. a) Consider the histogram shown below. 1. Draw a histogram showing the rough shape of the distribution of the absolute deviations from the mean in the histogram above. 3 b) 2. In the above histogram, which of these two measures is greater, or are they about the same? Justify your answer, identifying a feature in the graph that helped you get there. mean absolute deviation from the mean median absolute deviation from the mean Solution: Write your solution here. Consider the histogram shown below. 1. Draw a histogram showing the rough shape of the distribution of the absolute deviations from the median in the histogram above. 2. In the above histogram, which of these two measures is greater, or are they about the same? Justify your answer, identifying a feature in the graph that helped you get there. mean absolute deviation from the median median absolute deviation from the median Solution: Write your solution here.