Question

The following box plot consists of the heights of basketball players and soccer players. Are the basketball players significantly taller than the soccer players? Explain.

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

To determine if the basketball players are significantly taller than the soccer players, we will have to find the ratio
of the difference in median heights to the IQR.

First, let’s determine if the IQR is the same or not.

Basketball players
Median height $=198cm$
Lower quartile $=197cm$
Upper quartile $=207cm$
Interquartile range $=207-197=10cm$

Soccer players
Median height $=183cm$
Lower quartile $=176cm$
Upper quartile $=186cm$
Interquartile range $=186-176=10cm$

The IQR’s are the same. Now we can test if the heights of the basketball players are significantly more than that of
the soccer players.

Difference in medians $=|198-183|=15$
Ratio of the difference in the medians to the interquartile range $=\frac{15}{10}=1.5<2$

Since this ratio is less than 2, it means that the heights of the basketball players are not significantly higher than
soccer players.