Statistical Applets Central Limit Theorem

The Central Limit Theorem says that the distribution of sample means x of n observations from any population with finite variance gets closer and closer to a Normal distribution as n increases. More specifically, for a population of individual observations with mean μ and standard deviation σ, the Central Limit Threorem says that the means x of samples of size n drawn from this population will approximate a Normal distribution whose mean is also μ and whose standard deviation is σ / √n. This applet illustrates the Central Limit Theorem by allowing you to generate thousands of samples with various sizes n from a exponential, uniform, or Normal population distribution. You can then compare the distribution of sample means against the Normal distribution with the standard deviation predicted by the Central Limit Theorem.	Choose a population distribution (Exponential, Uniform, or Normal) and a sample size, then click the button to generate 10,000 samples and plot the distribution of sample means. Click "Show Normal Curve" to compare this distribution with the Normal curve predicted by the Central Limit Theorem.

Statistical Applets

Central Limit Theorem

The Central Limit Theorem says that the distribution of sample means x of n observations from any population with finite variance gets closer and closer to a Normal distribution as n increases. More specifically, for a population of individual observations with mean μ and standard deviation σ, the Central Limit Threorem says that the means x of samples of size n drawn from this population will approximate a Normal distribution whose mean is also μ and whose standard deviation is σ / √n.

This applet illustrates the Central Limit Theorem by allowing you to generate thousands of samples with various sizes n from a exponential, uniform, or Normal population distribution. You can then compare the distribution of sample means against the Normal distribution with the standard deviation predicted by the Central Limit Theorem.

Choose a population distribution (Exponential, Uniform, or Normal) and a sample size, then click the button to generate 10,000 samples and plot the distribution of sample means. Click "Show Normal Curve" to compare this distribution with the Normal curve predicted by the Central Limit Theorem.