Question

two science classes with the same number of students took a final exam. the box - and whisker plots below (sometimes called boxplots) summarize the test scores for each class. use the box and whisker plots to answer the questions. (a) which class had test scores with a larger interquartile range (iqr)? (b) which class had the highest test score? (c) which class had a smaller range of test scores? (d) which class had a higher median test score?

Explanation:

Step1: Recall box - and - whisker plot properties

The inter - quartile range (IQR) is the length of the box in the box - and - whisker plot, the range is the difference between the maximum and minimum values (distance between the end - points of the whiskers), and the median is the line inside the box.

Step2: Compare IQRs

For Class A, the box extends from approximately 70 to 85, so IQR_A=85 - 70 = 15. For Class B, the box extends from approximately 75 to 80, so IQR_B=80 - 75 = 5. So Class A has a larger IQR.

Step3: Find the highest score

The end - point of the right - hand whisker represents the highest score. Class A has a highest score around 95 and Class B has a highest score around 85. So Class A has the highest test score.

Step4: Compare ranges

For Class A, the minimum is around 65 and the maximum is around 95, so range_A=95 - 65 = 30. For Class B, the minimum is around 65 and the maximum is around 85, so range_B=85 - 65 = 20. So Class B has a smaller range of test scores.

Step5: Compare medians

The median of Class A is around 75 and the median of Class B is around 77.5. So Class B has a higher median test score.

Answer:

(a) Class A
(b) Class A
(c) Class B
(d) Class B