AQA A-Level Mathematics Statistics: a complete overview of sampling, data, probability, distributions and hypothesis testing

What the Statistics content demands

Statistics is one of the two applied strands of AQA A-Level Mathematics. It teaches you to collect, summarise and interpret data, to reason about chance, to model variation with standard distributions, and to test claims with formal hypothesis tests. The examiners test calculation, the correct choice of model and method, and clear interpretation in context.

This guide walks through all seven statistics topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Sampling and data

The content opens with statistical sampling: populations and samples, the trade-offs of sampling versus a census, and the methods of simple random, systematic, stratified, quota and opportunity sampling. Data presentation and interpretation covers measures of location and spread, histograms, box plots and cumulative frequency, identifying outliers, and describing correlation with scatter diagrams and regression lines. Both topics lean on AQA's large data set.

Probability and distributions

Probability develops the addition and multiplication rules, mutually exclusive and independent events, Venn and tree diagrams, and conditional probability. Statistical distributions introduces discrete random variables, probability distributions and the requirement that probabilities sum to one, and the idea of choosing a model to fit a situation.

The binomial and normal distributions

The binomial distribution models the number of successes in a fixed number of independent trials, using $P(X = r) = \binom{n}{r}p^r(1-p)^{n-r}$ and the mean $np$, with cumulative probabilities from a calculator. The normal distribution models continuous data, using standardising with $z = \frac{x - \mu}{\sigma}$, inverse problems, and the normal approximation to the binomial.

Hypothesis testing

Hypothesis testing brings the strand together: null and alternative hypotheses, significance levels, one-tailed and two-tailed tests for a binomial proportion and for a normal mean, critical regions, and conclusions stated in context.

How the Statistics content is examined

A typical AQA profile for Statistics:

• Sampling and data questions. Choosing and justifying a sampling method, calculating averages and spread, drawing or reading graphs, and identifying outliers.
• Probability calculations. Using the addition and multiplication rules, tree and Venn diagrams, and conditional probability.
• Distribution calculations. Binomial and normal probabilities from a calculator, the mean of a binomial, and standardising for the normal distribution.
• Hypothesis tests. Full tests with hypotheses, a significance comparison or critical region, and a conclusion in context.

Check your knowledge

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

1. A school of $600$ students has $360$ boys. A stratified sample of $50$ is taken. How many boys should it contain? (2 marks)
2. $P(A) = 0.6$, $P(B) = 0.3$, $P(A \cap B) = 0.1$. Find $P(A \cup B)$. (2 marks)
3. $X$ follows a binomial distribution with $n = 12$ and $p = 0.25$. Find the mean. (1 mark)
4. A normal distribution has mean $100$ and standard deviation $15$. Standardise the value $130$. (2 marks)
5. Write suitable hypotheses to test whether a proportion of $0.5$ has decreased. (2 marks)
6. State one condition needed for a binomial model to apply. (1 mark)