Question

The following box plot shows the number of donut stalls at two carnivals over a week. Does Carnival B have significantly more donut stalls than Carnival A? Explain.

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

Answer 1

The correct option is A The data sets cannot be compared, as they have different IQR.

Carnival A
Median: $56$
Lower quartile: $46$
Upper quartile: $72$
Interquartile range: $72-46=26$

Carnival B
Median: $94$
Lower quartile: $80$
Upper quartile: $100$
Interquartile range: $100-80=20$

Since the IQR of both the data sets are different, we cannot compare them.

Therefore, the correct answer is option D.