Statistics and Probability · Limit theorems

Central limit theorem

Why the average of almost any large sample ends up looking approximately Normal, regardless of the original distribution's shape.

Also known as: CLT, why sample means look Normal.

Start a lesson on Central limit theorem

Learn first

• Law of large numbers: A sample average gets closer to the true average as you collect more data.
• Common continuous distributions: The handful of continuous shapes, Uniform, Normal, Exponential, that keep showing up in real measurements and waiting times.

Leads to

• Sampling and sampling distributions: How a statistic, like a sample mean, itself varies from sample to sample if you repeated the study.

Related topics

• Sampling and sampling distributions: How a statistic, like a sample mean, itself varies from sample to sample if you repeated the study.