Question

the box plot compares the number of events that mrs. cai’s and mr. roland’s classes won over the last 10 years on the school’s field day.
number of events won on field day
mrs. cai’s class \t|
mr. roland’s class \t|
0 1 2 3 4 5 6 7 8 9 10
based on the data in the box plots, what is the best evidence to show which class has had greater success on field day over the last 10 years?
○ mrs. cai’s class was more successful because her interquartile range was less spread out.
○ mrs. cai’s class was more successful because she had the greater total spread.
○ mr. roland’s class was more successful because his class always won at least one event.
○ mr. roland’s class was more successful because his class’s lower quartile was the same as mrs. cai’s class’s upper quartile.

Explanation:

1. Analyze Option 1: Interquartile range (IQR) measures spread of middle 50% of data. A less spread - out IQR doesn't indicate greater success (success is about number of events won, not spread of data). So this is incorrect.
2. Analyze Option 2: Total spread (range) is the difference between maximum and minimum values. A greater total spread also doesn't mean more success in terms of number of events won. So this is incorrect.
3. Analyze Option 3: Just because a class always won at least one event doesn't mean it won more events overall. For example, Mrs. Cai's class could have won more events in some years even if Mr. Roland's class never had 0 wins. So this is incorrect.
4. Analyze Option 4: If Mr. Roland's class's lower quartile (Q1) is the same as Mrs. Cai's class's upper quartile (Q3), it means that 25% of Mr. Roland's class's data (the lower 25%) is greater than or equal to 75% of Mrs. Cai's class's data. This implies that on average, Mr. Roland's class won more events. So this is a good indicator of greater success.

Answer:

D. Mr. Roland's class was more successful because his class's lower quartile was the same as Mrs. Cai's class's upper quartile.