Question: Senator Foghorn described a political rival, Dewey Cheatum, this way: "Dewey Cheatum is a very polarizing person. People either love him or hate him." Suppose a large number of voting- age adults were asked to rate Dewey Cheatum on a 10-point scale. Respondents could give Cheatum a rating ranging between 1 (they strongly disapprove of him) and 10 (they strongly approve of him).

1. If Senator Foghorn’s characterization of Dewey Cheatum is correct, what would a bar chart of approval ratings look like? Sketch a bar chart that would fit Foghorn’s description.
2. Still assuming that Senator Foghorn is correct, which of the following sets of values, Set 1 or Set 2, is more plausible? Set 1: mean, 5; median, 5; mode, 5. Set 2: mean, 5; median, 5, mode, 2. Explain your choice. Why is the set of numbers you have chosen more plausible than the other set of numbers?
3. Now assume that the data show Senator Foghorn to be incorrect, and that the following characterization best describes the bar chart of approval ratings: "Dewey Cheatum is a consensus-builder, not a polarizer. He generally elicits positive ratings from most people, and there is little variation in these ratings." Sketch a bar chart that would fit this new description. Invent plausible values for the mean, median, and mode of this distribution.

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