The central limit theorem, one sample at a time
Starting from a skewed exponential population, the animation builds sampling distributions of the mean for sample sizes of 1, 2, 5, and 30. Single draws mirror the population's skew, but as sample size grows the distribution of averages tightens and rounds into a bell shape, overlaid against a true normal curve for comparison. Useful for statistics students and teachers introducing the Central Limit Theorem and its independence from population shape.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Start from a skewed exponential population. Averages of one draw copy that skew; averages of 2, 5 and then 30 draws pile up into a bell curve, matching the normal curve laid on top. Whatever the population looks like, sample means become normal as the sample size grows.
Make the next one in this series
- Show how sample size affects the standard error of the mean with shrinking spread visuals.
- Compare the Central Limit Theorem starting from a uniform versus a bimodal population.
- Animate how confidence intervals rely on the normal approximation from the Central Limit Theorem.
