Question

The following box plot shows the distances basketball players and swimmers can sprint in the same amount of time. Are the swimmers significantly faster than the basketball players? Explain.

• A. Yes, because the ratio of the difference in the medians to the IQR is equal to 2.
• B. No, because the ratio of the difference in the medians to the IQR is less than 2.
• C. The data sets cannot be compared, as they have different IQR.
• D. Yes, because the ratio of the difference in the medians to the IQR is greater than 2.

Answer 1

The correct option is B No, because the ratio of the difference in the medians to the IQR is less than 2.

Basketball Players:
Median distance $=172m$
Lower quartile $=166m$
Upper quartile $=176m$
IQR $=176-166=10m$

Swimmers:
Median distance $=188m$
Lower quartile $=180m$
Upper quartile $=190m$
IQR $=190-180=10m$

Since the IQR for both is the same, we can now compare the two data sets.
Difference in the medians $=|188-172|=16$

The ratio of the difference in the medians to the IQR $=\frac{16}{10}=1.6$
Since the ratio of the difference in medians to the IQR is less than 2, we can say that swimmers are not significantly faster than basketball players.

Hence, the answer is option B.