Sampling Distribution of the Variance

This applet allows exploration of sampling distributions of variances. This applet illustrates that the distribution of the variances of many samples from a normal distribution is proportional to a chi-squared distribution.

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 variance of the sample is added (in blue) to the distribution of variances 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 variance 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 Chi-Sq " button to turn on (or off) a display of the best-fitting curve proportional to a chi-square distribution.
  4. Clicking on a graph pops it up in a separate window.