Central Limit Theorem Simulator

Build a population, take repeated random samples, and watch the sampling distribution of different sample statistics take shape.

AP Stats Tool

Population Distribution

Drag the bars up or down. Taller bars make that value more likely to be selected.

Editable
Population Mean, μ
Population SD, σ

Sampling Distribution of the Sample Mean

Each bar represents sample means from repeated random samples. This graph uses the same x-axis scale as the population distribution.

Mean of Sample Means
SD of Sample Means
Population Mean
Number of Samples
0
Big idea: a sampling distribution can be created from any sample statistic. Some statistics are centered near the corresponding population value, while others may tend to overestimate or underestimate it.