StatLab

An interactive, visual introduction to probability and statistics. Drag, click, and sample. The mathematics responds in real time.

Each chapter pairs short explanations with a demo you can play with. The chapters follow the free OpenStax textbook, so you can read a section there and then come here to see it move. No account, no tracking, nothing to install.

Core Concepts

Thirteen chapters in the order they build on each other. Advanced Concepts branch off the chapter they depend on.

Chapter 1 · Core Sampling and Data How we get data, and why the way we sample decides what we can conclude.
Chapter 2 · Core Descriptive Statistics Pictures and numbers that summarize the shape, center, and spread of a data set.
Chapter 3 · Core Probability Topics Probability as long-run frequency, and the rules for combining events.
- Chapter 14 · Advanced Counting Multiplying choices, and telling permutations from combinations.
- Chapter 15 · Advanced Bayesian Inference Updating belief with data, through Bayes’ theorem, likelihood, and posteriors.
Chapter 4 · Core Discrete Random Variables Random variables that count things, their expected values, and the named distributions.
Chapter 5 · Core Continuous Random Variables Densities, area as probability, and the exponential model of waiting times.
Chapter 6 · Core The Normal Distribution The bell curve, z-scores, and the 68–95–99.7 rule.
Chapter 7 · Core The Central Limit Theorem Why averages of almost anything look normal, and how their spread shrinks with n.
Chapter 8 · Core Confidence Intervals What a 95% interval promises, and how to build one for a mean or a proportion.
Chapter 9 · Core Hypothesis Testing (One Sample) Null hypotheses, error types, and what a p-value really measures.
- Chapter 16 · Advanced Resampling Bootstrap and permutation methods for when formulas run out.
Chapter 10 · Core Hypothesis Testing (Two Samples) Comparing two means or two proportions, and why pairing helps.
Chapter 11 · Core The Chi-Square Distribution Testing whether counts fit a claim, and whether two variables are independent.
Chapter 12 · Core Linear Regression and Correlation Fitting a line, reading r, and knowing when prediction is safe.
- Chapter 17 · Advanced Beyond One Variable How a third variable can reverse a conclusion, and what a coefficient means with two predictors.
Chapter 13 · Core F Distribution and One-Way ANOVA Comparing several group means at once by weighing between-group against within-group variation.