Question

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 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?
One of the means is incorrect, but the reasoning is correct.
Both of the means are incorrect, and the reasoning is also incorrect.
Both of the means are correct, but the reasoning is incorrect.
One of the means is incorrect, and the reasoning is also incorrect.

Answer 1

Jacob's error is due to incorrect reasoning, not incorrect means. Therefore, the correct option is c) Both of the means are correct, but the reasoning is incorrect

Explanation:

The mean height of Team A is 71 inches and that of Team B is 72 inches, but the mean absolute deviation cannot be determined by simply comparing means. MAD is calculated by finding the average of the absolute differences between each data point and the mean. It is a measure of variability, not the central tendency. Therefore, having a higher mean does not necessarily mean a greater MAD, and vice versa.

MAD = Mean Absolute Deviation