The heights of the starting players on each of two basketball teams are shown in the table below.Heights of Starters on Team A and Team BTeam A70 in.72 in.75 in.68 in.70 in.Team B71 in.73 in.71 in.72 in.73 in.Jacob found that the mean height of Team A is 71 and the mean height of Team B is 72. He believes that because Team B has a greater mean, it also has a greater mean absolute deviation. Which explains Jacob’s error?

Team A’s heights total 355 inches, so its mean is 355 ÷ 5 = 71 inches. Team B’s heights total 360 inches, so its mean is 360 ÷ 5 = 72 inches; both means are correct. But the mean alone does not determine the mean absolute deviation: Team A’s MAD is 2 inches, while Team B’s is 0.8 inch. So Team B has the greater mean but the smaller MAD, making choice C, “Both of the means are correct, but the reasoning is incorrect,” the right answer.

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