Sampling Distributions and the Central Limit Theorem

This applet allows exploration of sampling distributions of means. This applet introduces the basic concepts and subsequent applets focus on the effects of population distribution, sample size, and statistic. This applet illustrates that the distribution of the means of many samples from a normal distribution also has a normal distribution, but with a smaller spread or variance.

Instructions

  1. Use the button to the left of the middle graph to generate a sample from the population distribution one by one. The most recent observation appears in blue in the sample graph. When the maximum sample size of 5 is reached, the mean of the sample is added (in blue) to the distribution of means in the bottom graph. Then click the Reset button to be able to generate a new sample one by one.
  2. After you understand the process, use the buttons to the left of the bottom graph to speed up the process. First click on the "1 Sample" button. It produces a complete sample of the maximum size of five, displays it in the middle graph and its mean in the bottom graph. After doing this a few times, then use the "1000 Samples" to build quickly the sampling distribution in the bottom graph. The last of the 1000 samples is displayed in the middle graph.
  3. Click on the "Toggle Normal" button to turn a display of the best-fitting normal distribution on or off.
  4. Clicking on a graph pops it up in a separate window. This faciliates comparisons among the graphs. For exampe, after you have many samples, click on both the population (top) graph and the sampling distribution (bottom) graph to popup these graphs in separate windows and move them one above the other to compare their spreads.