By placing box-and-whisker plots for two or more data sets side by side, we can visually compare differences in their distributions.
Example ①
Suppose Class A has a box-and-whisker plot with Q1=55, Q2=70, and Q3=80, while Class B has one with Q1=60, Q2=68, and Q3=75.
(1) Which class has the higher median?
(2) Which class has the greater spread?
Solution: (1) A (Q2=70 > 68). (2) A (IQR=25 > 15).
Suppose Class A has a box-and-whisker plot with Q1=55, Q2=70, and Q3=80, while Class B has one with Q1=60, Q2=68, and Q3=75.
(1) Which class has the higher median?
(2) Which class has the greater spread?
Solution: (1) A (Q2=70 > 68). (2) A (IQR=25 > 15).
Key Points
- Compare medians: compare the sizes of Q2
- Compare spread: compare the sizes of the IQRs (box widths)
- “More stable” means the one with the smaller IQR
Practice Problems
- When Team A has Q1=40,Q2=55,Q3=65 and Team B has Q1=50,Q2=60,Q3=70, compare their medians and IQRs.
Answers and Explanations
- Answer: The median of B (60) is greater than that of A (55). The IQRs are A=65−40=25 and B=70−50=20, so A (25)>B (20). Team B has less variation in its data than Team A.