A box-and-whisker plot visualizes the distribution of data using the five-number summary (minimum, Q1, Q2, Q3, and maximum).
Criteria for Outliers
Let the interquartile range be IQR = Q3 - Q1:
A value smaller than Q1 - 1.5×IQR or larger than Q3 + 1.5×IQR may be regarded as an outlier.
Example ①
When Q1 = 10 and Q3 = 20, find the IQR and the criteria for outliers.
Answer: IQR = 10. Criteria: below 10 - 15 = -5 or above 20 + 15 = 35.
When Q1 = 10 and Q3 = 20, find the IQR and the criteria for outliers.
Answer: IQR = 10. Criteria: below 10 - 15 = -5 or above 20 + 15 = 35.
Key Point
- IQR = Q3 - Q1 (interquartile range)
- Guideline for outliers: outside the range from Q1 - 1.5IQR to Q3 + 1.5IQR
Practice Problems
- Find Q1, Q3, and IQR for the data: 2, 4, 5, 7, 9, 12, 15, 20.
Answers and Explanations
- Answer: Q1 = (4+5)/2 = 4.5, Q3 = (12+15)/2 = 13.5, IQR = 9.