Central Limit Theorem Simulator

The Central Limit Theorem (CLT) is one of the most powerful and useful ideas in statistics. It states that, no matter the shape of the original distribution, the distribution of sample means taken from that population will approximate a normal distribution (a bell curve) as the sample size increases.

Below, you can see this in action. The top chart displays the distribution of the population you select. The bottom chart displays the distribution of the means of samples drawn from that population. As you increase the sample size and regenerate the samples, observe how the distribution of the sample means becomes more and more like a bell curve.

Population Distribution

Distribution of Sample Means