Statistics and Probability
AA HL Topic 4: Statistics and Probability (4.1–4.16)
Topic 4 is the biggest single chunk of AA HL and it never disappears — it turns up on Paper 1, Paper 2, and almost always as the Paper 3 investigation. The GDC does the arithmetic; what separates a 7 from a 4 is knowing which formula to reach for ( or ? binomial or Poisson? Pearson's or Spearman's ?) and being able to justify that choice in words when a question says 'comment on' or 'determine'. HL bolts four genuinely new ideas onto the SL core: Bayes' theorem, continuous random variables defined by a pdf, the Poisson distribution, and the algebra of combining and transforming random variables. All four are guaranteed marks if the mechanics are automatic.
Overview: How This Topic Fits Together
Everything in this topic flows in one direction: raw data a summary of that data (descriptive statistics) a model of how such data behaves in general (probability distributions) a statement about the population or relationship the sample came from (inference). Every exam question sits somewhere on that chain, and the command term tells you where.
- Descriptive statistics never mentions 'the population' — it only describes the numbers you were actually given.
- Probability distributions are theoretical models (binomial, Poisson, normal) — you plug in parameters, not raw data.
- Inference is the only place the word 'estimate' is honest — it's where a sample statistic is used to say something about a wider population or a relationship between two variables.
The shape of the chapter
Command terms that decide how you're marked
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Write down | State a value read straight off the GDC or a table — no working required | AO1 | 1 mark for the correct value; a wrong value with no working scores 0 (there's nothing to award method marks for) |
| Calculate / Find | Produce a numerical answer; method can be GDC-only unless the question says 'show that' | AO2 | Method mark for the correct formula/setup, then an answer mark for the correct value |
| Show that | Derive a GIVEN result — every substitution step must be visible | AO2/AO3 | Marks sit on the intermediate lines; a GDC-only final line matching the given answer can score 0 if no working is shown |
| Determine | Find a value or reach a decision using a stated rule (e.g. the 1.5×IQR outlier test) | AO3 | State the rule, apply it with numbers, then state the conclusion — skipping the stated rule costs a mark even if the final number is right |
| Comment on / Interpret | Give a statement tied to the actual context and units, not a bare mathematical fact | AO3 | 'Positive correlation' alone scores 0 for interpretation; it must say what increases with what, in context |
Key point
Overview