Fiducia TogetherStatistics
Averages, spread and the charts. Which average to use is a question that is actually asked.
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
The mean adds and divides; the median is the middle value in order; the mode is the most common. Range is the spread from lowest to highest; interquartile range is the middle 50%.
Where it applies
Both tiers. Higher adds cumulative frequency, box plots and histograms with unequal class widths.
How it works
Each average fails differently. The mean is pulled by outliers; the median ignores them; the mode is useless when everything appears once.
For grouped data the mean is an estimate, because the original values are gone — questions say "estimate the mean" for exactly this reason.
How to use it in your work
When asked which average is most appropriate, say WHY in terms of the data. "The median, because the one very high salary distorts the mean" is the answer.
On a histogram with unequal widths the y-axis is frequency density, not frequency. Area is frequency, and forgetting that is the classic error.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
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.