Tutorial: Central Limit Theorem

The key concepts of the central limit theorem are described here, but sadly, browsers no longer support the Java sampling distribution applet that is featured in this tutorial.

The Central Limit Theorem (CLT) is critical to understanding inferential statistics and hypothesis testing. This tutorial uses an applet with exercises to demonstrate CLT concepts visually and interactively.

Goals of this tutorial: The goals of this exercise are (1) to illustrate interactively the basic principles of the CLT, and (2) to demonstrate when it is possible to assume that the sampling distribution of the mean is reasonably normal. The assumption of normality of the sampling distribution underlies many inferential statistical applications and tests of statistical significance.

What do I need to know? To make best use of this tutorial, you should know how z scores are related to probabilities on a normal distribution. You should have an understanding of basic descriptive statistics such as the mean and standard deviation. Familiarity with the sampling distribution of the mean will be helpful, but not required. You may want to review the WISE video on sampling distributions before this you begin tutorial.

What do I need? A piece of paper will be useful for making certain calculations, such as calculating z-scores, and recording responses to certain questions. A calculator may also be handy for making these calculations. To convert z-scores from a standardized normal distribution to probability values, you may either use a table for the standardized normal distribution (z) or the WISE pz converter.

Exercise instructions: You will be guided through a series of reviews (R), activities (A), and questions (Q). For each question, simply click on your answer choice and submit it (by either clicking the “Check answer” button or pressing “Enter” on the keyboard). Then you will be given feedback. If you get the answer wrong, read the feedback carefully to help you choose the correct response.

Begin the tutorial