Central Limit Theorem

Central Limit Theorem makes one of the most important ideas in statistics finally click — through plain-English explanations, live simulations, and hands-on tools. No dense textbook required.
The Central Limit Theorem (CLT) explains why the average of many samples forms a bell curve, no matter what the original data looks like. This app lets you see it happen, play with it, and compute with it.
WHAT YOU CAN DO
• Concept — Start from zero. A friendly "jar of dice" story builds real intuition for why flat, skewed, or lumpy data still produces a smooth bell curve of averages.
• Simulate — Pick a population (dice, uniform, exponential, coin, or a two-spike distribution), choose a sample size n, and run up to 3000 experiments. Watch the sample means fill in a normal curve in real time.
• Chart — Explore the sampling distribution of the mean. Switch between the PDF (density) and CDF views, adjust sample size and population standard deviation, and see how the standard error σ/√n shrinks as n grows.
• Calculator — Enter the population mean, standard deviation, sample size, and a target value to get P(X̄ ≤ x), P(X̄ > x), the standard error, and the z-score instantly.
• Examples — Real-world applications worked end to end, including average dice rolls and opinion-poll margins of error.
WHY YOU'LL LIKE IT
• Built for understanding, not memorizing — every screen connects the formula to a picture.
• Interactive: change the inputs and the math updates live.
• Clean, fast, and lightweight.
• Great for students, teachers, data analysts, and anyone brushing up on statistics.
PERFECT FOR
• AP Statistics, college intro stats, and exam revision
• Data science and machine learning foundations
• Teachers looking for a clear classroom demo of the CLT
Key concepts covered: sampling distribution, sample mean, standard error, normal distribution, z-score, law of large numbers, probability, and statistical inference.
Stop guessing why the bell curve shows up everywhere — see it for yourself.