The heights of the starting players on each of two basketball teams are shown in the table. Heights of Starters on Team A and Team B Team A 70 in. 72 in. 75 in. 68 in. 70 in. Team B 71 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?
Answer
A
Both of the means are correct, but the reasoning is incorrect.
B
One of the means is incorrect, and the reasoning is also incorrect.
C
Both of the means are incorrect, and the reasoning is also incorrect.
D
One of the means is incorrect, but the reasoning is correct.
Explanation
Team A’s heights sum to 355 inches, so its mean is 355 ÷ 5 = 71 inches. Team B’s heights sum to 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. Therefore, Jacob’s reasoning is incorrect.
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