Box Plots
Five-number summary visualised.
Key idea
Five-number summary visualised.
In depth
A box plot shows the five-number summary: minimum, Q1, median, Q3, maximum. The box covers the middle 50% and the whiskers show the range, making comparisons across groups easy.
Worked example
Five numbers 10, 20, 25, 35, 50 draw a box from 20 to 35 with a line at 25.
Real-world uses
- Comparing exam results from two schools side by side
- Checking clinical trial data
Common mistake
Thinking the box shows the mean, or that each section has equal numbers of values by length.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Box Plots?
Five-number summary visualised. It is a topic at the advanced level in Probability & Statistics.
Where is Box Plots used in real life?
Real-world examples: Comparing exam results from two schools side by side; Checking clinical trial data.
What should I learn before Box Plots?
Make sure you are comfortable with Quartiles and IQR, the previous topic in Probability & Statistics.
What is a common mistake with Box Plots?
Thinking the box shows the mean, or that each section has equal numbers of values by length.
How can I practise Box Plots?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Box Plots?
Move on to Outliers next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.
- Weighted Mean – Average where values have different importance.