Question

which statement is true about the box plots?
number of incorrect questions on exams
marcs class
sues class
0 1 2 3 4 5 6 7 8 9 10 11 12 13
both the ranges and the interquartile ranges for the data sets are the same.
neither the ranges nor the interquartile ranges for the data sets are the same.
the interquartile ranges for the box plots are the same, but their ranges are different.
the ranges for the box plots are the same, but their interquartile ranges are different.

Explanation:

Step1: Calculate the range

• For Marc's Class:
• The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \).
• From the box - plot, the minimum value is \(2\) and the maximum value is \(11\). So, \( \text{Range}=11 - 2=9 \).
• For Sue's Class:
• The minimum value is \(3\) and the maximum value is \(12\). So, \( \text{Range}=12 - 3=9 \).

Step2: Calculate the inter - quartile range (IQR)

• For Marc's Class:
• The first quartile \(Q_1\) is \(3\) and the third quartile \(Q_3\) is \(9\).
• \( \text{IQR}=Q_3 - Q_1=9 - 3 = 6 \).
• For Sue's Class:
• The first quartile \(Q_1\) is \(5\) and the third quartile \(Q_3\) is \(10\).
• \( \text{IQR}=Q_3 - Q_1=10 - 5=5 \).

Answer:

The ranges for the box plots are the same, but their interquartile ranges are different.