Question

two english 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 a higher median test score? (b) which class had a smaller range of test scores? (c) which class had test scores with a larger interquartile range (iqr)? (d) which class had the highest test score?

Explanation:

Step1: Analyze the median

The median is represented by the line inside the box. For Class A, the median is around 72. For Class B, the median is around 78. So Class B has a higher median.

Step2: Analyze the range

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). For Class A, assume minimum \( = 63 \), maximum \( = 80 \), range \( = 80 - 63=17 \). For Class B, assume minimum \( = 63 \), maximum \( = 90 \), range \( = 90 - 63 = 27 \). So Class A has a smaller range.

Step3: Analyze the IQR

The IQR is \( \text{IQR}=Q_{3}-Q_{1} \). For Class A, assume \( Q_{1}=68 \), \( Q_{3}=75 \), \( \text{IQR}=75 - 68 = 7 \). For Class B, assume \( Q_{1}=68 \), \( Q_{3}=83 \), \( \text{IQR}=83 - 68=15 \). So Class B has a larger IQR.

Step4: Analyze the highest score

Looking at the maximum value (the end of the whisker or the out - lier point). Class A's maximum is around 80, Class B's maximum is around 90. So Class B has the highest test score.

Answer:

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