Question

Jamal found the median and interquartile range for the heights of players on the basketball team and the baseball team. The results are as follows.

Basketball:
median = 73
interquartile range = 5

Baseball:
interquartile range = 6
median = 72

Which of the following best describes how the data compared?

A Players on the basketball team are generally taller than players on the baseball team.

B Players on the baseball team are generally taller than players on the basketball team.

D There is less variation in heights on the baseball team than on the basketball team.

C Players on the baseball team are generally the same height as players on the basketball team.

Answer 1

Answer: The answer is A) Players on the basketball team are generally taller than players on the baseball team. This is the most likely conclusion we can draw based on the information given.

Explanation:

We know that the interquartile range (IQR) is the range of the middle 50% of the data. So for the basketball team, the heights of 50% of the players lie within the range of 73 ± 2.5 (since the IQR is 5). Similarly, for the baseball team, the heights of 50% of the players lie within the range of 72 ± 3 (since the IQR is 6).

Comparing the medians, we see that the basketball team has a median height of 73, while the baseball team has a median height of 72.

Based on this information, we can conclude that:

A) Players on the basketball team are generally taller than players on the baseball team - this is the most likely answer, as the median height of the basketball team is higher.

B) Players on the baseball team are generally taller than players on the basketball team - this is not supported by the given information.

D) There is less variation in heights on the baseball team than on the basketball team - we cannot determine this based on the given information.

C) Players on the baseball team are generally the same height as players on the basketball team - this is not supported by the given information.