Range, Quartiles and Box Plots
Spread describes how far data stretches.
About this topic
Range is maximum minus minimum, a quick measure of spread. Quartiles split sorted data into four parts: Q1 is the median of the lower half, Q2 the median, and Q3 the median of the upper half. The interquartile range IQR = Q3 − Q1 covers the middle 50%.
A box plot draws a box from Q1 to Q3 with a line at the median and whiskers extending to the smallest and largest non-outlier values. A common rule flags outliers as values more than 1.5 × IQR below Q1 or above Q3. The lengths of the box and whiskers show the spread and the skew at a glance, and they make it easy to compare several groups side by side.
Example: for the sorted data 2, 4, 5, 7, 8, 10, 14, the median is 7, Q1 is 4, Q3 is 10, so the IQR is 6 and the range is 12. Outlier fences are at 4 − 9 = −5 and 10 + 9 = 19, so none are flagged.
Box plots compare test scores, wages and weather. Remember that the range is sensitive to outliers whereas the IQR is not, and that each quarter of the data holds equal numbers of values even if the box sections differ in length.
Key ideas
- Range = max − min
- Quartiles split data into four parts
- IQR = Q3 − Q1
Quick check
Use cases: where Range, Quartiles and Box Plots helps
- Homework: review the key idea behind Range, Quartiles and Box Plots before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Range, Quartiles and Box Plots without notes.
- Visual learning: play with the interactive lab to see how Range, Quartiles and Box Plots changes when you adjust its inputs.
- Teaching a friend: explain Range, Quartiles and Box Plots in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Range, Quartiles and Box Plots?
Spread describes how far data stretches.
What will I learn in Range, Quartiles and Box Plots?
Range = max − min. Quartiles split data into four parts. IQR = Q3 − Q1.
Is Range, Quartiles and Box Plots part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Range, Quartiles and Box Plots lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Range, Quartiles and Box Plots?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.