Labs / Mathematics
Central Limit Theorem
Pick a parent distribution — even a lumpy or lopsided one — then set how many values go into each average. Every sample mean drops into the lower histogram, and as it fills in you'll see those averages pile up into a bell shape centered on the true mean, no matter how strange the parent looked.
samples 0x̄ —SE —shape —
What to try
- Start on the Right-skew parent with n = 1. The averages look just as skewed — so where does the bell shape actually come from?
- Slide n up to 30. Why does the sampling distribution get narrower and more symmetric at the same time?
- The standard error readout drops as n grows. Does it halve when you double n, or does it take four times as many samples to halve it?
- Switch to the Bimodal parent — two separate humps. How can the average of two humps end up as a single bell centered between them?
- Turn on the Normal curve overlay. For which parent and which n does the real histogram hug the predicted bell almost perfectly?