Question

score by two clubs
club 2
club 1
which of the following three statements are best supported by the clubs boxplots?
a the average game score of club 1 is exactly equal to the average game score of club 2
b the third quartile game score of club 1 is worse than the third quartile game score of club 2
c the worst game played by both club 1 and club 2 during the tennis season had the same score
d the median game score of club 1 is exactly equal to the median game score of club 2
e the first quartile game score of club 1 is better than the first quartile game score of club 2

Explanation:

Step1: Analyze Option A

Box - plots do not provide information about the average (mean). We cannot conclude that the average game score of Club 1 is exactly equal to the average game score of Club 2 from the box - plots.

Step2: Analyze Option B

The third quartile (Q3) of Club 1 is greater than the third quartile of Club 2. So, the statement "The third quartile game score of Club 1 is worse than the third quartile game score of Club 2" is incorrect.

Step3: Analyze Option C

The minimum value (worst game score) of Club 1 is different from the minimum value of Club 2. So, this statement is incorrect.

Step4: Analyze Option D

The line inside the box (median) of Club 1 and Club 2 is at the same position on the score axis. So, the median game score of Club 1 is exactly equal to the median game score of Club 2.

Step5: Analyze Option E

The first quartile (Q1) of Club 1 is greater than the first quartile of Club 2. A higher first - quartile score is not “better” in the sense of a lower value (if we assume lower scores are worse). If we consider the score as a performance metric (higher is better), then the first quartile of Club 1 is higher (better) than that of Club 2. But the problem does not specify whether a higher or lower score is better. However, in a general data - analysis context (without a specified direction of “better”), we focus on the numerical value. The first quartile of Club 1 is greater than that of Club 2.

Answer:

D. The median game score of Club 1 is exactly equal to the median game score of Club 2