What does the Statistics strand in OCR Maths A cover?

It covers statistical sampling (populations, the census and the sampling methods), data presentation and interpretation (averages, spread, histograms, box plots, outliers and correlation), probability (mutually exclusive, independent and conditional events with Venn, tree and table representations), statistical distributions (the binomial and Normal models, standardising and the Normal approximation to the binomial), and hypothesis testing (for a binomial proportion, a Normal mean and a correlation coefficient). It is grounded in a pre-release large data set and assessed in Paper 2.

Which Statistics topics carry the most marks in OCR Maths A?

Distributions and hypothesis testing are the heaviest, because binomial and Normal calculations and full tests appear as long structured questions in Paper 2. Data presentation and probability are reliable mid-tariff topics, and sampling provides short, high-value marks if you know the methods and their trade-offs precisely. Confident calculator use for binomial and Normal probabilities is the single biggest time-saver.

What techniques recur across the OCR Statistics content?

Choosing and describing a sampling method, calculating the mean and standard deviation from summary statistics, reading quartiles from a cumulative frequency graph, applying the addition and multiplication laws and the conditional probability formula, using the binomial formula and cumulative tables, standardising to the standard Normal and using the inverse Normal, and carrying out a full hypothesis test with a contextual conclusion. These are automatic by exam day.

What is the most common Statistics mistake in OCR Maths A?

Reading the second Normal parameter as the standard deviation instead of the variance, and forgetting the continuity correction in the Normal approximation to the binomial. Other frequent errors are confusing mutually exclusive with independent events, using the wrong denominator for a conditional probability, putting a whole significance level in one tail of a two-tailed test, forgetting that the sample mean has variance divided by n, and omitting the contextual conclusion of a hypothesis test.

How should I revise the OCR Statistics content?

Work topic by topic against the specification, drilling each technique until it is automatic, then practise mixed problems under timed conditions. Become fluent with your calculator's binomial and Normal functions and the inverse Normal. Keep a sheet of standard results: the sampling methods, the variance formula, the binomial formula and its mean and variance, the standardising formula, and the hypothesis-testing steps. Work with the large data set so you recognise its variables and quirks, and always conclude tests in context.

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OCR A-Level Maths A Statistics: sampling, data, probability, distributions and hypothesis testing

A deep-dive OCR A-Level Mathematics A guide to the Statistics strand: statistical sampling, data presentation and interpretation, probability, the binomial and Normal distributions, and hypothesis testing, grounded in the pre-release large data set and examined in Paper 2.

Generated by Claude Opus 4.820 min readH240/2.01-2.05Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What the Statistics strand demands
Sampling and data
Probability
Distributions and hypothesis testing
How the Statistics content is examined
Check your knowledge

What the Statistics strand demands

The Statistics strand of OCR A-Level Mathematics A (H240) sits alongside Pure in Paper 2 (Pure Mathematics and Statistics). It develops the judgement to collect, summarise and model data, and to test claims with evidence. A pre-release large data set runs through the strand, so questions reward familiarity with real data, and a calculator with statistical functions is allowed and expected.

This guide walks through the five Statistics topics in specification order, then sets out the exam patterns OCR repeats. Each topic has a matching dot-point page with worked exam questions; this overview ties them together.

Sampling and data

Statistical sampling (2.01) covers populations and samples, the census, and the sampling methods (simple random, systematic, stratified, quota and opportunity) with their advantages, disadvantages and sources of bias. Data presentation and interpretation (2.02) covers the mean, median and mode, range, interquartile range, variance and standard deviation, histograms with frequency density, box plots and cumulative frequency, identifying outliers, comparing distributions, and interpreting correlation and the regression line.

Probability

Probability (2.03) covers the probability of events and complements, mutually exclusive and independent events, Venn diagrams, tree diagrams and two-way tables, the addition and multiplication laws, and conditional probability with the formula $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ . The distinction between mutually exclusive and independent events is a recurring discriminator.

Distributions and hypothesis testing

Statistical distributions (2.04) covers discrete random variables, the binomial distribution $B(n, p)$ and its conditions, mean and variance, the Normal distribution $N(\mu, \sigma^2)$ , standardising to the standard Normal, the inverse Normal, and the Normal approximation to the binomial with a continuity correction. Hypothesis testing (2.05) sets up null and alternative hypotheses, one- and two-tailed tests, significance levels and critical regions, and runs tests for a binomial proportion, a Normal mean (using $\bar{X} \sim N(\mu, \frac{\sigma^2}{n})$ ), and a correlation coefficient.

How the Statistics content is examined

A typical OCR profile for the Statistics strand:

Short technique questions. Describing a sampling method, finding a mean and standard deviation, or reading a cumulative frequency graph.
Probability problems. Venn, tree and table questions, the laws, and conditional probability.
Distribution calculations. Binomial and Normal probabilities, the inverse Normal, and the Normal approximation.
Full hypothesis tests. A complete test for a proportion, mean or correlation, ending with a conclusion in context.

Check your knowledge

A mix of recall and technique questions covering the Statistics content. Attempt them under timed conditions, then check against the solutions.

State the sampling interval for a systematic sample of $50$ from $2000$ . (1 mark)
Data has $\sum x = 200$ , $\sum x^2 = 4400$ , $n = 10$ . Find the standard deviation. (2 marks)
Events $A$ , $B$ are independent with $P(A) = 0.5$ , $P(B) = 0.6$ . Find $P(A \cap B)$ . (2 marks)
$X \sim B(15, 0.2)$ . State the mean and variance. (2 marks)
$X \sim N(100, 25)$ . Find $P(X > 105)$ . (2 marks)
For a two-tailed $1\%$ test, what probability is in each tail? (1 mark)

Solutions

Step 1: Calculate the sampling interval

In systematic sampling, divide the population size by the required sample size to find the interval $k$ between selected items. Every $k$ -th member of the population is then chosen.

k = \dfrac{2000}{50} = 40

Step 2: Calculate the mean and standard deviation from grouped data

The mean is estimated as $\bar{x} = \dfrac{\sum fx}{\sum f}$ and the variance uses $\mathrm{Var}(X) = \dfrac{\sum fx^2}{\sum f} - \bar{x}^2$ . Taking the square root of the variance gives the standard deviation.

Mean $= 20$ ; variance $= \dfrac{4400}{10} - 20^2 = 440 - 400 = 40$ , so $\sigma = \sqrt{40} \approx 6.32$ .

Step 3: Find the probability of the intersection of independent events

For independent events, the probability that both occur equals the product of their individual probabilities. Independence means that knowing $A$ occurred gives no information about whether $B$ occurred.

P(A \cap B) = 0.5 \times 0.6 = 0.3

Step 4: State the mean and variance of a binomial distribution

For $X \sim B(n, p)$ , the mean is $np$ and the variance is $np(1-p)$ . These results follow from summing the mean and variance over $n$ independent Bernoulli trials each with success probability $p$ .

Mean $= 15(0.2) = 3$ ; variance $= 15(0.2)(0.8) = 2.4$ .

Step 5: Standardise and look up the normal probability

To find probabilities from $X \sim N(\mu, \sigma^2)$ , convert to the standard normal $Z$ using $Z = \dfrac{X - \mu}{\sigma}$ . Note that $\sigma^2 = 25$ so $\sigma = 5$ , and then the standard normal table gives $P(Z > 1)$ .

Z = \dfrac{105 - 100}{5} = 1, \quad \text{so } P(Z > 1) \approx 0.1587

Step 6: Identify the tail probability for a two-tailed test

In a two-tailed test at significance level $\alpha$ , the critical region is split equally between both tails, placing $\alpha/2$ in each. For a $1\%$ test, each tail contains $0.5\%$ .

$0.5\%$ in each tail.

Sources & how we know this

OCR A Level Mathematics A (H240) specification — OCR (2017)