A Level Maths: Averages and Spread Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Statistical Sampling — understanding of populations and samples informs which average is appropriate
- GCSE Maths Statistics — mean, median, and mode from GCSE are assumed
- Indices — needed for handling sum(x^2) and squared deviations
A Level Maths averages and spread covers measures of central tendency (mean, median, mode) and measures of variability (range, interquartile range, variance, standard deviation) for both raw and grouped data. These are fundamental statistical tools that you use throughout the Statistics strand, especially when working with The Normal Distribution and Binomial Hypothesis Testing.
You calculate the mean, median, and mode from raw data, and from frequency tables and grouped frequency tables using midpoints. You learn the variance and standard deviation as measures of spread, computing them using the formula $S_{xx} = \sum (x – \bar{x})^2 = \sum x^2 – (\sum x)^2 / n$, then dividing by $n$ (or $n-1$ for sample variance). You handle the standard deviation from summary statistics (where the question gives you $\sum x$ and $\sum x^2$). You also work with linear interpolation to estimate the median, quartiles, and percentiles from grouped data, and use coding (linear transformations of the data) to simplify calculations.
Averages and spread are part of the Statistics strand of A Level Maths and are essential revision content for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: for grouped data, you can only ESTIMATE the mean and standard deviation using midpoints — the actual values are unknown; the standard deviation formula uses $(\sum x)^2 / n$ in the second term, NOT $\sum x^2 / n$ — square the sum, not the individual values, in that term; for interpolation, identify the correct class first (the one containing the median or quartile), then interpolate within it; and the variance is the standard deviation squared, not the other way round.