DfE statement S4 · Statistics
Averages, spread and comparing distributions
Averages, spread and comparing distributions is content statement S4 of the DfE GCSE mathematics subject content, in the statistics area. It is on both tiers, with a Higher-only part, and it appears on both the calculator and the non-calculator papers. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)." (statement S4). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "including box plots", "quartiles and inter-quartile range". Everything else in the statement is Foundation content.
Calculator
This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.
Common mistakes
- Finding the median without putting the data in order first.
- Finding the mean from a frequency table by adding the frequency column and dividing by the number of rows, instead of totalling frequency × value.
- Giving the range as '3 to 9' rather than as the single number 6.
- Comparing two distributions with two averages and no measure of spread, which loses the comparison marks.
Sample questions (10 of 35)
Nearby statements
Questions people ask
Is averages, spread and comparing distributions on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "including box plots", "quartiles and inter-quartile range" — are Higher only; the rest is Foundation content.
Can I use a calculator for averages, spread and comparing distributions?
It depends on the paper. Paper 1 is non-calculator; Papers 2 and 3 allow one, and this topic is asked on both kinds.
What is the single most common mistake here?
Finding the median without putting the data in order first.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Statistics at Foundation or at Higher.