IB Math AI SL · Topic 4
Statistics and probability
The largest topic in the course — eleven sections — and the one where the exam rewards language as much as calculation. Computing a p-value is routine; concluding from it in context is where grades separate.
What the syllabus covers
Eleven assessed sections, SL 4.1 to 4.11 — from sampling bias through to formal hypothesis tests.
How it is examined
Hypothesis testing appears in SL Paper 2 exactly as it does beyond school statistics — as a procedure whose steps must all be visible.
Recent SL papers embed χ² tests and t-tests inside real scenarios — spending by weekend customers, crop yields — and award separate marks for hypotheses, p-value, and conclusion.
Conclusions must compare the p-value to the significance level and interpret the decision back into the scenario's language; 'reject H₀' alone is incomplete.
Regression questions check direction: predicting y requires the y-on-x line, a distinction examiners regularly penalise.
Distribution work (binomial, normal, inverse normal) is GDC-based but expects the setup — distribution chosen and parameters stated — before the output.
The booklet devotes five pages here — probability rules, expected value, binomial mean and variance — but no procedures at all: there is no normal formula and no χ² recipe to copy. The tests live in the GDC's statistics menu, so choosing which test to open is itself the examined skill.
Real papers also test sampling judgement in words — naming whether a plan was convenience, systematic or stratified sampling, then stating one disadvantage of it.
A marked question, mark by mark
A normal-distribution exercise with the contextual sentence that decides the final mark.
Rehearse the whole testing procedure, marked step by step
From SL 4.1 sampling to SL 4.11 t-tests, every generated exercise comes back with each mark awarded or withheld and a reason — including the contextual sentences students habitually omit.
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Normal distribution · SL 4.9
Seed 2E87
Battery lifetimes are modelled by a normal distribution with mean 120 hours and standard deviation 8 hours.
- (a)Find the probability that a battery lasts fewer than 110 hours.
- (b)Interpret this probability in context.
Your work
z = (110 − 120)/8 = −1.25
P(Z < −1.25) ≈ 0.106
Marks awarded
- M1Mark awarded. Standardised correctly with μ = 120 and σ = 8 before applying technology.
- A1Mark awarded. 0.106, correct to three significant figures.
- R1Mark not awarded. No interpretation: the 0.106 was never linked to the proportion of batteries failing before 110 hours.
Where marks are actually lost
In this topic the calculator is rarely the problem — the surrounding language is.
Skipping the formal statement of H₀ and H₁ at the start of a test.
CostThe first marks of every hypothesis question are given away before any calculation happens.
Ending with 'reject H₀' instead of comparing the p-value to the significance level in a sentence about the scenario.
CostThe conclusion mark is explicitly reserved for the comparison and its meaning.
Predicting with the x-on-x line, or reading r ≈ ±1 as causation.
CostDirection of prediction and correlation-versus-causation are standing examiner penalties.
Trusting Pearson's r on clearly monotonic-but-nonlinear data where Spearman's rank is appropriate.
CostAppropriateness-of-measure judgements are marked, especially in the presence of outliers.
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