IBDP · Maths AI SL

Statistics and Probability

AI SL — Topic 4: Statistics and Probability

46 min readStandard≈27 teaching hours — the single largest AI SL topic. Appears in every Paper 1 and Paper 2, usually as one full 15–20 mark question plus smaller parts elsewhere.

This is the topic examiners lean on hardest, because it's the one place they can test whether you actually understand what a number means, not just whether you can press the right calculator button. A GDC will hand you $r$ , a $p$ -value, or a confidence interval in seconds — the marks live in knowing which tool to reach for, reading the question for the tail direction, and finishing with a sentence back in context. Four threads run through it: describing data you already have, inferring about a population you don't, modelling chance for single events, and modelling chance across a whole range of outcomes. They constantly borrow from each other, so treat this as one connected chapter, not four separate ones.

Overview — how the chapter fits together

One dataset, two very different jobs

Descriptive statistics summarises the sample sitting in front of you: mean, spread, a scatter diagram. Inferential statistics uses that same sample to make a claim about a population you'll never fully measure — a confidence interval, a hypothesis test, a chi-squared test. Probability and probability distributions sit underneath both: they're the machinery that tells you how much a sample result could plausibly wobble by chance alone, which is exactly what a $p$ -value is measuring.

Every stats question on AI SL is really asking: what does this number tell us about the story in the question, not just 'is the arithmetic right'.
The GDC does almost all the heavy computation — regression coefficients, $r$ , $χ^{2}$ , $p$ -values, inverse normal — so time pressure comes from setting up the right calculation, not doing it by hand.
Hypotheses, significance levels and conclusions must always reference the scenario (lifetime of bulbs, pH of lakes, rod lengths) — generic 'reject $H_{0}$ ' answers are routinely capped at partial marks.

Mind map of Statistics and Probability centred on Statistics & Probability (AI SL Topic 4).

Command terms that decide how much working you need

Command term	What it demands	AO	Mark-earning move
Write down / State	Give a fact directly from data, GDC or a formula — no derivation expected.	AO1	Full marks for the bare answer, but wrong rounding or the wrong sign still costs the mark.
Calculate	Produce a numerical answer using a defined process.	AO2	Method mark for correct setup even if arithmetic slips; final accuracy mark needs the right value to the stated sf/dp.
Show that	Justify a given answer with enough intermediate working to prove it, not just state it.	AO2/AO3	Copying the given final value without the working line in between scores zero, even if your answer 'matches'.
Determine	Multi-step process to find an unknown quantity (e.g. regression coefficients, a critical value).	AO2	Correct method with a wrong final number still earns M marks; the last A mark needs an exact match.
Interpret	Explain what a statistical value means inside the scenario, not just restate it.	AO3	' $r = 0.85$ , strong correlation' with no mention of the two variables in context loses the interpretation mark.
Comment on / Suggest	Evaluate a limitation of the model or conclusion tied to this specific data.	AO3	A generic 'the sample might not be representative' with no link to the scenario scores 0.

Key point

Every inferential answer ends with a sentence back in the scenario. 'Reject

H_{0}

' alone is not a conclusion on AI SL mark schemes — you need 'there is sufficient evidence, at the 5% level, that the mean lifetime is less than 8000 hours'.

Overview

Statistics and Probability

Overview — how the chapter fits together

One dataset, two very different jobs

The shape of the chapter

Command terms that decide how much working you need