From a box-and-whisker plot, we can determine the median, the spread, and whether outliers are present.
Example ①
Suppose a box-and-whisker plot has Q1=10, Q2=15, Q3=22, minimum=5, and maximum=35.
(1) Find the interquartile range.
(2) State the range between what values contains 50% of the data.
Solution: (1) IQR = 22−10 = 12. (2) The range from Q1〜Q3: 10 or more and 22 or less.
Suppose a box-and-whisker plot has Q1=10, Q2=15, Q3=22, minimum=5, and maximum=35.
(1) Find the interquartile range.
(2) State the range between what values contains 50% of the data.
Solution: (1) IQR = 22−10 = 12. (2) The range from Q1〜Q3: 10 or more and 22 or less.
Key Points
- IQR (interquartile range) = Q3−Q1: the width of the middle 50% of the data
- A longer box → the data are more spread out
- The closer Q2 is to the center of the box, the more symmetrical the data are
Practice Problems
- For a box-and-whisker plot with minimum=3, Q1=7, Q2=12, Q3=18, and maximum=25, find the interquartile range and the range (maximum−minimum).
Answers and Explanations
- Answer: Interquartile range=11, range=22. IQR=18−7=11. Range=25−3=22.