Topic 4 is the largest topic in Maths AI by weighting (~35–40%). SL covers descriptive statistics, probability, binomial/normal distributions, and chi-squared tests. HL extends to t-tests, reliability of estimates, Poisson distribution, and advanced hypothesis testing.
Sampling methods: simple random, systematic, stratified, convenience, quota. Reliability vs bias. Presenting data: frequency tables, histograms, cumulative frequency, box plots. Outliers: 1.5 × IQR rule. Using technology to compute summary statistics rapidly.
Scatter diagrams and describing correlation (direction, strength, form). Pearson\'s correlation coefficient r (−1 ≤ r ≤ 1). Regression line of y on x (least squares): ŷ = a + bx. Interpolation vs extrapolation. R² as coefficient of determination. Spearman\'s rank correlation for non-linear relationships.
Combined events, conditional probability, tree diagrams. Expected value E(X) = Σxᵢpᵢ. Binomial distribution for counting successes. Normal distribution for continuous data. Using GDC for binomial/normal probabilities and inverse normal calculations.
Framework: H₀ (null hypothesis), H₁ (alternative), significance level α (usually 5%), p-value, conclusion. Chi-squared test for independence: compare observed vs expected frequencies in contingency tables. Chi-squared goodness of fit test. HL: one-sample and two-sample t-tests for means, paired t-tests, and testing correlation significance.
Topic 4 is the dominant topic in Maths AI, accounting for approximately 35–40% of the course at both SL and HL. You should expect at least two major exam questions on statistics/probability in each paper. Hypothesis testing (especially chi-squared) appears almost every exam session. Strong GDC skills for statistical calculations are essential.
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