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 a higher median test score?
select
(b) a score above 70 is considered passing. which class had more passing scores?
select
(c) which class had test scores with a larger interquartile range (iqr)?
select
(d) which class had the highest test score?
select

Explanation:

Step1: Analyze Median (Part a)

In a box - and - whisker plot, the median is represented by the line inside the box. For Class A, the median line is at 75 (from the plot, the middle line of the box for Class A is at 75). For Class B, the median line is at 72 (approximate, as the middle line of the box for Class B is between 70 and 75, closer to 72). So Class A has a higher median.

Step2: Analyze Passing Scores (Part b)

A passing score is above 70. For Class A, the lower whisker starts at a value above 70 (the left end of the box for Class A is at 70, and the whisker starts a bit after, but more importantly, the number of students: since the two classes have the same number of students, we look at the proportion of data above 70. For Class B, the lower whisker starts at 55, and a large part of the data (the left part of the box) is at 70 or below. For Class A, almost all the data (except the leftmost dot which is at 68 maybe, but the box starts at 70) is above 70. Wait, actually, in box - plots, the box represents the interquartile range (IQR), and the whiskers represent the minimum and maximum (excluding outliers). For Class A: the minimum is around 68, Q1 (first quartile) is 70, median 75, Q3 (third quartile) 80, maximum 95. For Class B: minimum 55, Q1 70, median 72, Q3 88, maximum 92. The number of students above 70: in Class A, the data from Q1 (70) to maximum (95) is 75% of the data (since IQR is 25th to 75th percentile, and above Q1 is 75%? Wait, no. The total number of students is the same. For Class A, the minimum is just below 70, so the number of students with score ≤70 is very small (maybe 1 or 2). For Class B, the Q1 is 70, so 25% of the students are at or below 70 (since Q1 is the 25th percentile). So Class A has more students with score above 70.

Step3: Analyze IQR (Part c)

IQR is Q3 - Q1. For Class A: Q3 is 80, Q1 is 70, so IQR = 80 - 70 = 10. For Class B: Q3 is 88, Q1 is 70, so IQR = 88 - 70 = 18. So Class B has a larger IQR.

Step4: Analyze Highest Test Score (Part d)

The highest test score is the rightmost dot (maximum) of each box - plot. For Class A, the maximum is at 95. For Class B, the maximum is at 92. So Class A has the highest test score.

Answer:

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