A box-and-whisker plot is a graph of the five-number summary: the minimum, Q1, Q2, Q3, and maximum.
Structure of a Box-and-Whisker Plot
Minimum Q1 Q2 Q3 Maximum
|─────────────[────┼────]─────────────|
(whisker) (box) (whisker)
Example ①
Draw a box-and-whisker plot for data with minimum 2, Q1=5, Q2=8, Q3=11, and maximum 14.
Solution: Mark the five values above on a number line, represent Q1〜Q3 with a box (rectangle), and represent minimum〜Q1 and Q3〜maximum with whiskers (line segments).
Draw a box-and-whisker plot for data with minimum 2, Q1=5, Q2=8, Q3=11, and maximum 14.
Solution: Mark the five values above on a number line, represent Q1〜Q3 with a box (rectangle), and represent minimum〜Q1 and Q3〜maximum with whiskers (line segments).
Key Points
- Width of the box = Q3−Q1 (interquartile range IQR)
- Line in the center of the box = Q2 (median)
- Whisker endpoints = minimum and maximum
Practice Problems
- For the data: 1, 3, 5, 6, 8, 9, 12, find the five-number summary (minimum, Q1, Q2, Q3, and maximum).
Answers and Explanations
- Answer: Minimum 1, Q1=3, Q2=6, Q3=9, maximum 12. The median is 6 (the fourth value). Lower half: 1,3,5 → Q1=3. Upper half: 8,9,12 → Q3=9.