Central Limit Theorem
DESCRIPTION
Watch the Central Limit Theorem emerge in real time. Choose uniform, right-skewed, bimodal, or normal populations, set sample size n, and take samples one-by-one or in bulk. The sampling distribution of x̄ converges to a bell curve regardless of population shape — see it happen live.
- central limit theorem
- sampling distribution
- standard error
- normal distribution
- sample mean
- AP Statistics
RELATED VISUALIZATIONS
Normal Distribution Explorer
Adjust mean and standard deviation to see how the normal distribution bell curve shifts and stretches. Shade probability regions to compute areas under the curve and connect z-scores to percentiles.
Confidence Interval Simulator
Simulate hundreds of confidence intervals and watch the coverage rate converge to the chosen confidence level. Adjust μ, σ, n, and confidence level (90/95/99%). Green bars capture the true mean; red bars miss it. Builds intuition for the correct long-run interpretation of CIs.
Scatter Plot & Correlation
Build scatter plots by clicking the canvas or loading preset datasets (strong positive, strong negative, moderate, none, outlier). Pearson r and r² update live. Toggle regression line, residuals, and 95% ellipse. A color-coded gauge maps r from −1 to +1. Observe how outliers distort r.
Binomial Distribution
Explore B(n, p) via PMF bars, CDF, or live simulation. Adjust n (1–60), p (0.01–0.99), and highlight any k to see P(X = k), P(X ≤ k), and other tail probabilities. Normal approximation curve overlaid for large n. Simulation mode runs up to 2000 trials and compares empirical vs theoretical.