DfE statement P5 · Probability
Empirical samples and sample size
Empirical samples and sample size is content statement P5 of the DfE GCSE mathematics subject content, in the probability area. It is on both tiers, and it appears on both the calculator and the non-calculator papers. Below is what the specification actually requires, the 3 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: "Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size." (statement P5). 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. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.
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
- Believing an outcome is 'due' because it has not happened recently. Independent trials have no memory.
- Concluding bias from a small sample, when the specification is explicit that larger samples tend towards the theoretical probability.
- Assuming that a large sample makes the empirical probability exact rather than close.
Sample questions (10 of 14)
Nearby statements
Questions people ask
Is empirical samples and sample size on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for empirical samples and sample size?
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?
Believing an outcome is 'due' because it has not happened recently. Independent trials have no memory.
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 Probability at Foundation or at Higher.