See the Central Limit Theorem in Action
Watch sample means from any skewed population pile up into a normal curve as sample size grows. Drag to change n and feel why the Central Limit Theorem is the backbone of inferential statistics.
I.01 / CENTRAL LIMIT THEOREM
Central Limit Theorem
Normal distribution basics down. Now for statistical inference. What shape does the average of many samples take? Here comes the Central Limit Theorem: whatever you start with — dice, Poisson, anything — the average is pulled toward that same normal curve.
Slightly outrageous fact — no matter how skewed the base distribution is,
if you take n samples and average, then repeat, the distribution of those averages
converges on its own to a bell (normal).
The lab below shows left = the raw skewed source side-by-side with right = the sample-mean distribution,
so you can watch the bell emerge. Crank n up and the bell tightens (SE = σ/√n).
Trials0
Mean of sample means—
SD of sample means—
Theoretical SE = σ/√n—