Statistics and Probability
AI HL Topic 4 — Statistics and Probability
This topic is really four toolkits stacked on top of each other: you describe data, you model randomness with probability rules, you formalise that modelling into distributions, and then you use sample data plus those distributions to make justified claims about a whole population — that's inference. Every mark in this topic comes from picking the right tool for the scenario in front of you and then showing the working that got you there, not just quoting a GDC output.
Overview
The four pillars, and how they connect
Descriptive statistics organises and summarises raw data you already have. Probability builds the rules for how random outcomes behave. Probability distributions are the formal mathematical models (binomial, Poisson, normal) that probability theory produces. Inferential statistics is where it all cashes out: you take a sample, assume a distribution, and use probability to decide what you can (and can't) claim about the wider population.
- At SL, most of this topic is computational — mean, SD, r, binomial/normal probabilities on a GDC.
- At HL, the syllabus adds the inferential layer: unbiased estimators, confidence intervals, hypothesis tests (z, t, paired-t, χ²), and the Poisson distribution.
- The GDC does almost all the arithmetic for you at HL — the marks are for setting up the right model, stating conditions, and writing the conclusion in context.
The shape of the chapter
Command terms that decide how you answer
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Derive the given (already-known) result, with every substitution step visible — not a bare GDC read-out. | AO2 | Method marks for the formula and substitution; quoting only the final number that happens to match scores 0/2. |
| State | Give a fact or result with no derivation — e.g. state H0 and H1, state the distribution and its parameters. | AO1 | 1 mark per correct, correctly-notated statement (μ not x̄ for a population parameter). |
| Determine / Calculate | Find a numerical value, GDC use is expected. | AO2 | Follow-through applies if an earlier value was wrong but the method is consistent. |
| Comment on / Interpret | Link the statistical result back to the real-world context in a full sentence. | AO3 | A generic 'there is a relationship' with no reference to the named variables scores 0 for this mark. |
| Test whether... at the ...% level | Full four-step hypothesis test: hypotheses → test statistic/p-value → decision rule → conclusion in context. | AO2/AO3 | Marks are split across all four steps — a perfect p-value with no final contextual sentence still drops the last mark. |
Key point
Overview