Question

using box-and-whisker plots to compare data sets
class b
test score
55 60 65 70 75 80 85 90 95
(a) which class had the highest test score?
select
(b) which class had a higher median test score?
select
(c) a score above 70 is considered passing. which class had more passing scores?
select
(d) which class had test scores with a larger interquartile range (iqr)?

Explanation:

Step1: Analyze highest score

In a box - and - whisker plot, the end of the right - most whisker (or the outlier point if there is one) represents the maximum value. For Class A, the maximum value is around 90 (the end of the right - most whisker). For Class B, the maximum value is higher (the outlier point is further to the right on the number line).

Step2: Analyze median

The line inside the box of a box - and - whisker plot represents the median. For Class A, the median (the line inside the box) is at 75. For Class B, the median (the line inside the box) is higher (closer to 80).

Step3: Analyze passing scores (above 70)

The left - hand side of the box is the first quartile (\(Q_1\)). For Class A, \(Q_1 = 70\). So, 75% of the data (the box and the right - hand whisker) is above 70. For Class B, the left - hand side of the box ( \(Q_1\)) is less than 70 (since the box starts before 70). So, more than 75% of Class A's data is above 70, and less than 75% of Class B's data is above 70.

Step4: Analyze IQR

The inter - quartile range (IQR) is \(Q_3−Q_1\). For Class A, \(Q_3\) is 85 and \(Q_1\) is 70, so \(IQR = 85 - 70=15\). For Class B, \(Q_3\) is 80 and \(Q_1\) is 60 (approximate values from the plot), so \(IQR=80 - 60 = 20\).

Answer:

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