OCR A Level Mathematics: Statistics (H240)

This guide covers Statistics, one of three subject-content strands in OCR A Level Mathematics A (H240), alongside Pure Mathematics and Mechanics. Statistics is examined together with Pure Mathematics in component 02, Pure Mathematics and Statistics, which carries 33⅓% of the full A Level (or 50% of the AS Level, where the equivalent component is worth 75 marks with roughly 50 of pure and 25 of statistics).

Syllabus coverage

OCR A LEVEL MATHEMATICS A H240 – STATISTICS

• Statistical sampling – understanding and evaluating different sampling methods (including random, systematic, stratified, opportunity, quota and cluster sampling), and assessing the suitability of a given method for a real statistical investigation.
• Data presentation and interpretation – interpreting and producing standard graphical and numerical summaries of data, understanding measures of central tendency and spread, and interpreting real, often large, data sets, including the specification’s pre-release large data set that some questions are based on directly; and bivariate data (2.02c-e) – interpreting scatter diagrams and regression lines, including recognising scatter diagrams that include distinct sections of the population, the informal interpretation of correlation, and understanding that correlation does not imply causation. You may be asked to add to a scatter diagram but not to draw a complete one, and calculating the equation of a regression line is excluded.
• Probability – calculating probabilities using the laws of probability, including conditional probability, mutual exclusivity and independence, and applying probability models to real situations.
• Statistical distributions – using the binomial distribution and the normal distribution to model real data and calculate probabilities, including recognising when each distribution is an appropriate model.
• Statistical hypothesis testing – carrying out and interpreting three types of test: a test for the proportion in a binomial distribution (2.05b-c, where use of the normal approximation is excluded), a test for the mean of a normal distribution with known, given or assumed variance (2.05d-e), and a test using Pearson’s product-moment correlation coefficient (2.05f-g); including stating hypotheses correctly, identifying critical regions, and interpreting the result of a test in the context of the original question.

Bivariate data and the correlation test

Pearson’s product-moment correlation coefficient, r, measures how close data points lie to a straight line (2.05f). You use and interpret it in a hypothesis test, comparing it with either a given critical value or, using a p-value, a table of critical values that OCR provides in the examination (2.05g). The data may be assumed to come from a bivariate normal distribution, and calculating a correlation coefficient is excluded – you will be given r.

Worked example: for a random sample of 15 pairs of values, r = 0.62. Test at the 5% level whether there is positive correlation in the population, given that the critical value is 0.4409.

H₀: ρ = 0, H₁: ρ > 0, where ρ is the population product-moment correlation coefficient (one-tailed, because the question asks about positive correlation). Since 0.62 > 0.4409, reject H₀. There is evidence at the 5% level of positive correlation in the population. Remember that correlation does not imply causation (2.02e): a significant result says the variables are linearly associated, not that one causes the other.

Why Statistics is assessed with a pre-release data set

Unlike Pure Mathematics or Mechanics, Statistics at OCR is examined partly through familiarity with a genuine, pre-released large data set, issued in advance of the exam series. Some questions in the data presentation and interpretation strand are set directly on this data, which means revision for Statistics cannot be purely abstract – a student needs to have actually explored the specific released data set, understood its variables and context, and practised summarising and interpreting it, since the exam expects familiarity with its particular structure and quirks rather than generic data-handling skill alone.

Worked example: binomial probability

A biased coin lands on heads with probability 0.6. It is tossed 5 times. Find the probability of getting exactly 3 heads.

Using the binomial distribution, X ~ B(5, 0.6):

P(X = 3) = C(5,3) × 0.6³ × 0.4² = 10 × 0.216 × 0.16 = 0.3456

Recognising that a scenario is binomial – a fixed number of independent trials, each with the same two possible outcomes and the same probability of success – is the first and most commonly mis-assessed step, before any calculation is attempted at all.

Worked example: hypothesis test set-up

A machine is supposed to produce components with a 5% defect rate. In a sample of 100 components, 9 are found to be defective. Test at the 5% significance level whether the defect rate has increased.

Null hypothesis H₀: p = 0.05 (defect rate unchanged) Alternative hypothesis H₁: p > 0.05 (defect rate has increased) – this is a one-tailed test, since the question specifically asks about an increase.

Under H₀, X ~ B(100, 0.05). The test then compares the observed value (9) against the critical region for a 5% significance level, and the conclusion must be stated in the context of the original question, never just “reject H₀” on its own. The specification also requires conclusions to be worded so that they reflect the fact that they are not certain: “There is evidence at the 5% level to reject H₀. It is likely that the defect rate has increased.” for a significant result, or “There is insufficient evidence at the 5% level to reject H₀. There is no reason to suppose that the defect rate has increased.” for a non-significant one. A flat “H₀ is rejected. The defect rate has increased.” is the form the specification lists as incorrect.

For these data, P(X ≥ 9) = 0.0631 (to 4 d.p.), which is greater than 0.05, and the critical region is X ≥ 10 (P(X ≥ 10) = 0.0282). The observed 9 is not in the critical region, so H₀ is not rejected: there is insufficient evidence at the 5% level that the defect rate has increased.

Common mistakes

• Stating hypotheses in words instead of using p (the population proportion) with a correct inequality, or getting the direction of a one-tailed test wrong relative to the question’s wording.
• Confusing the sample and the population when describing a sampling method, or failing to justify why a chosen method (for example, stratified over simple random) suits the specific investigation described in a question.
• Choosing the wrong distribution to model a scenario – using a normal approximation where a binomial model is appropriate, or vice versa, without checking the conditions each distribution requires.
• Forgetting to interpret a hypothesis test conclusion in context. A numerically correct test with no contextual conclusion, or one that inverts “reject” and “do not reject,” loses marks even when the calculation itself is right.
• Treating the large data set as optional revision rather than genuine exam content – since specific questions are set directly on it, not exploring the actual released data set in advance is a common and avoidable gap.

How to approach it

Because Statistics carries a genuine data-handling component alongside its calculation-based content, split revision time between the two: practise the standard calculations (binomial and normal probabilities, hypothesis tests) until fluent, and separately spend time actually exploring the current pre-released large data set so that questions referencing it are not encountered cold in the exam. Build a habit of writing hypotheses formally in terms of a population parameter (p or μ) before attempting any calculation, since this is where marks are most often lost even by students who calculate correctly afterwards. Since Statistics is assessed alongside Pure Mathematics in the same paper, practise questions that require using a pure-maths skill (for example, algebraic manipulation to find an unknown probability) inside a statistics context, since OCR’s papers are not written to keep the two strands in fully separate questions.

Related resources

• Statistics revision notes
• Statistics practice questions

Official syllabus

OCR, AS and A Level Mathematics A (H230, H240) Specification at a Glance, Subject content, Statistics, https://www.ocr.org.uk/qualifications/as-and-a-level/mathematics-a-h230-h240-from-2017/specification-at-a-glance/, fetched and verified in full 2026-09-02. Full specification PDF: https://www.ocr.org.uk/Images/308723-specification-accredited-a-level-gce-mathematics-a-h240.pdf.