Fiducia TogetherCumulative frequency and box plots
Graphs showing how data accumulates, and the five-figure summary.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A cumulative frequency graph plots running totals against the upper bound of each class, producing an S-shaped curve. A box plot shows the minimum, lower quartile, median, upper quartile and maximum.
Where it applies
Higher tier maths.
How it works
From a cumulative frequency curve you read off the median at half the total, the lower quartile at a quarter and the upper at three quarters. The interquartile range is the difference between the quartiles and measures the spread of the middle half.
Box plots make two distributions easy to compare.
How to use it in your work
Plot at the UPPER bound of each class, not the midpoint. That is the standard error.
When comparing box plots, compare an average AND a measure of spread, and say what it means in context.
Read the axis carefully — cumulative frequency questions often ask 'how many scored more than', which is the total minus the reading.
Where to get help
Your teacher and your board's specification. Bitesize for worked examples, and the subject song for the topic list.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.