Three statistical mysteries in one activity: identical summary statistics hiding wildly different data (Anscombe), a pass-rate paradox (Simpson), and a correlation that flips sign when you group the data (Hidden Groups).
Students work through a shared workbook in three acts. First they compute means, standard deviations and r for Anscombe's four datasets, find them identical, then plot and discover four completely different shapes. Next they meet Simpson's paradox as pass-rate proportions: method A wins both subgroups, method B wins overall. Finally the same paradox appears graphically — combined r ≈ −0.62, per-group r ≈ +0.94 — and the trend flips before their eyes.
Summary statistics can mislead. Grouping can reverse conclusions. Always plot the data. Discovery comes before instruction: students compute first, then see.