Syllabus breakdown

AI SL Statistics and Probability syllabus points

The official syllabus elements assessed across Paper 1 and Paper 2 in Topic 4.

  1. 4.1Sampling techniques: random, stratified, systematic, quota, convenience, and sampling bias
  2. 4.4Linear correlation: scatter plots, Pearson's product-moment correlation coefficient $r$, line of best fit $y$ on $x$
  3. 4.5Spearman's rank correlation coefficient $r_s$: monotonic trends, ranking data with ties
  4. 4.8$\chi^2$ test for independence: contingency tables, expected frequencies $f_e = \frac{\text{row total} \times \text{column total}}{\text{grand total}}$, degrees of freedom $(r-1)(c-1)$, $p$-values
  5. 4.9$\chi^2$ goodness of fit test: testing uniform, binomial, and normal expected frequencies
  6. 4.10Normal distribution: standard normal curve, $z$-scores $z = \frac{x - \mu}{\sigma}$, GDC normCDF and invNorm commands

Interactive guides

Topic 4 Interactive Study Guides

Each guide features full notes, 10 progressive practice exercises with complete markschemes, formula sheets with common pitfalls, and an exam mini test.

Lesson 4.8 (Core AI Exam Focus)

χ² Test for Independence

Two-way contingency tables, calculating expected frequencies, degrees of freedom, and drawing conclusions using critical values and $p$-values.

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Lesson 4.4 & 4.5

Spearman's Rank & Linear Regression

Evaluating linear vs non-linear monotonic trends, ranking data, Pearson's $r$ vs Spearman's $r_s$, and the regression line $y$ on $x$.

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Lesson 4.10

Normal Distribution & z-Scores

Bell curve symmetry, standardized $z$-values, finding probabilities between limits, and inverse normal percentile problems on GDC.

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Exam insights

Key ideas & Hypothesis Testing Decision Rules

  • The $p$-value Decision Rule:
    • If $p < \alpha$ (significance level, usually $0.05$), reject $H_0$. There is significant evidence of an association.
    • If $p \ge \alpha$, do not reject $H_0$. There is insufficient evidence of an association.
  • Test Statistic Rule: If $\chi^2_{\text{calc}} > \chi^2_{\text{crit}}$, reject $H_0$.
  • Expected Frequencies Condition: The $\chi^2$ test is only valid if all expected frequencies $f_e \ge 5$.

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