Question

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

Explanation:

(a) Median

• Step1: Recall median in box - plot

The line inside the box represents the median.

• Step2: Compare medians

For Class A, the median is at a higher value on the number line (closer to 80) than Class B (closer to 70).

(b) Inter - quartile range (IQR)

• Step1: Recall IQR formula

\(IQR = Q_{3}-Q_{1}\) (where \(Q_{3}\) is the upper quartile and \(Q_{1}\) is the lower quartile).

• Step2: Compare box lengths

The length of the box in a box - plot represents the IQR. Class B's box is longer.

(c) Range

• Step1: Recall range formula

\(Range=Max - Min\)

• Step2: Compare whisker lengths

The distance from the minimum to the maximum (whiskers) is shorter for Class A.

(d) Highest score

• Step1: Identify maximum

The end of the right - most whisker (or outlier point) represents the maximum. Class B has a higher maximum.

Answer:

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