Quartiles and Box Plots
Quartiles split ordered data into four equal parts, and a box plot displays them with the median and extremes.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Quartiles split ordered data into four equal parts, and a box plot displays them with the median and extremes.
- The interquartile range is Q3 minus Q1
- The box covers the middle 50 percent
- Whiskers show the minimum and maximum
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Quartiles and Box Plots?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Quartiles and Box Plots. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Quartiles and Box Plots in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Quartiles and Box Plots gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Quartiles and Box Plots in detail
Quartiles divide ordered data into four equal parts. The lower quartile (Q1) has a quarter of the data below it, the median (Q2) has half and the upper quartile (Q3) has three-quarters. The interquartile range is Q3 − Q1 and describes the spread of the middle 50%.
A box plot draws a box from Q1 to Q3 with a line at the median and whiskers to the minimum and maximum. It lets you compare distributions side by side, showing differences in centre, spread and skew. Outliers can be identified and the interquartile range is not affected by them.
How the interactive helps you understand Quartiles and Box Plots
Watch the bar chart in the interactive. Use any sliders or buttons it offers to change the values and see how the bar chart responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Quartiles and Box Plots.
Real-life uses and examples
- Use Quartiles and Box Plots when comparing prices, discounts or recipe quantities in everyday life.
- Explain Quartiles and Box Plots to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Quartiles and Box Plots in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Quartiles and Box Plots.
- Memorising the steps for Quartiles and Box Plots without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Quartiles and Box Plots
What is Quartiles and Box Plots?
Quartiles split ordered data into four equal parts, and a box plot displays them with the median and extremes.
What are the most important points about Quartiles and Box Plots?
The main points are: The interquartile range is Q3 minus Q1; The box covers the middle 50 percent; Whiskers show the minimum and maximum.
Why is Quartiles and Box Plots useful?
Understanding Quartiles and Box Plots gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Quartiles and Box Plots?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Quartiles and Box Plots?
Related topics in Mathematics include Histograms, Normal Distribution, Iteration and Number Methods.