IB Math AI HL Unit 4: Statistics & Probability

IB Maths AI HL Unit 4: Statistics and Probability, topic by topic

Each topic in this unit has a free page with step-by-step worked examples and the key formulas, then exam-style questions with mark schemes.

• Chi-Square Goodness of Fit, Independence and Error Types questions20 questions · 3 worked examples
• Confidence Intervals and Hypothesis Testing for Means questions25 questions · 3 worked examples
• Data Collection and Non-Linear Regression questions23 questions · 3 worked examples
• Linear Combinations of Random Variables & the Central Limit Theorem questions22 questions · 3 worked examples
• Markov Chains and Transition Matrices questions13 questions · 3 worked examples
• Random Variables and Poisson questions47 questions · 3 worked examples

Learn it first: AI HL Unit 4 notes

• Chi-squared test and confidence intervals
• Linear regression and residual analysis
• Normal and Poisson distributions
• Hypothesis testing
• Markov chains and transition matrices

Where marks go in AI HL Unit 4

From the IB subject reports we summarise on AI HL Examiner Insights, in our own words:

• Hypothesis tests: hypotheses in words, the wrong test, and conclusions that don't follow. Write H₀ and H₁ with symbols for population parameters (μ, ρ, p). Choose the test from the design (paired data → paired t; σ unknown → t). State the p-value, compare it with the stated significance level, then conclude in context. For goodness of fit: df = cells − 1 − parameters estimated.
• Distributions: variances add, the normal is continuous, the binomial coefficient. For independent X and Y: Var(X ± Y) = Var(X) + Var(Y); Var(aX) = a²Var(X). State the final distribution, e.g. X − Y ~ N(20, 25), before finding probabilities.

The questions here are original, written in the style of IB papers with IB-style mark schemes; for real papers see the IB Maths AI HL past papers page.

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