Question

the box - plot compares the number of events that mrs. cais and mr. rolands classes won over the last 10 years on the schools field day. 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? o mrs. cais class was more successful because her interquartile range was less spread out. o mrs. cais class was more successful because she had the greater total spread. o mr. rolands class was more successful because his class always won at least one event. o mr. rolands class was more successful because his classs lower quartile was the same as mrs. cais classs upper quartile.

Explanation:

Step1: Recall box - plot concepts

The inter - quartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1) ($IQR = Q3 - Q1$). A smaller IQR indicates less spread in the middle 50% of the data. A greater total spread can be seen by looking at the range (maximum - minimum). Also, higher values in general can indicate more success.

Step2: Analyze the box - plots

For Mrs. Cai's class, the box extends from approximately 2 to 4 on the number of events won axis, and for Mr. Roland's class, the box extends from approximately 4 to 7. The median of Mr. Roland's class is higher. The range of Mr. Roland's class is also larger.

Step3: Evaluate the options

• Option 1: Lower quartile being the same is not a good measure of overall success.
• Option 2: Winning at least one event is not a strong measure of overall success compared to other factors.
• Option 3: A greater total spread doesn't necessarily mean more success.
• Option 4: A smaller inter - quartile range means the middle 50% of the data is less spread out, and since Mr. Roland's class has higher values overall (higher median and larger range), it is more successful.

Answer:

Mrs. Cai's class was more successful because her interquartile range was less spread out.