Box Plots and Data Distribution
Box plots (box-and-whisker plots) display the five-number summary and allow quick visual comparison of the spread and centre of data sets.
What You Need to Know
Key Concept Diagram
Five-number summary: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum
Interquartile range IQR = Q3 - Q1, representing the middle 50% of data
Outliers are values more than 1.5 × IQR below Q1 or above Q3
Box plots from different data sets can be placed on the same scale for easy comparison
Key Vocabulary
Median
The middle value when data is arranged in order; Q2 in the five-number summary
Quartile
Values that divide ordered data into four equal parts (Q1, Q2, Q3)
Interquartile range
Q3 minus Q1; measures the spread of the middle 50% of data
Outlier
A data value that lies unusually far from the rest of the data set
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A data set has Q1 = 12 and Q3 = 20. What is the interquartile range?
Question 2
In a box plot, the box itself represents:
Question 3
IQR = 10. Which value would be flagged as an outlier above Q3 = 30?
Key Concepts Summary
- ●Five-number summary: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum
- ●Interquartile range IQR = Q3 - Q1, representing the middle 50% of data
- ●Outliers are values more than 1.5 × IQR below Q1 or above Q3
- ●Box plots from different data sets can be placed on the same scale for easy comparison