Please wait until a button appears below. Click the button to begin the simulation. There will be a slight delay and then the Java applet will open in a new window.

This Java applet lets you explore various aspects of sampling distributions. When the applet begins, a histogram of a normal distribution is displayed at the topic of the screen.

The distribution portrayed at the top of the screen is the population from which samples are taken. The mean of the distribution is indicated by a small blue line and the median is indicated by a small purple line. Since the mean and median are the same, the two lines overlap. The red line extends from the mean one standard deviation in each direction. Note the correspondence between the colors used on the histogram and the statistics displayed to the left of the histogram.

The second histogram displays the sample data. This histogram is initially blank. The third and fourth histograms show the distribution of statistics computed from the sample data. The number of samples (replications) that the third and fourth histograms are based on is indicated by the label "Reps=."

The simulation is set to initially sample five numbers from the population, compute the mean of the five numbers, and plot the mean. Click the "Animated sample" button and you will see the five numbers appear in the histogram. The mean of the five numbers will be computed and the mean will be plotted in the third histogram. Do this several times to see the distribution of means begin to be formed. Once you see how this works, you can speed things up by taking 5, 1,000, or 10,000 samples at a time.

The following statistics can be computed from the samples by choosing from the pop-up menu:

**Mean**Standard deviation of the sample (N is used in the denominator)

Variance of the sample (N is used in the denominator)

Unbiased estimate of variance (N-1 is used in denominator)

Mean absolute value of the deviation from the mean

Range**Selecting a sample size**The size of each sample can be set to 2, 5, 10, 16, 20 or 25 from the pop-up menu. Be sure not to confuse sample size with number of samples.

**Comparison to a normal distribution**By clicking the "Fit normal" button you can see a normal distribution superimposed over the simulated sampling distribution.

**Changing the population distribution**You can change the population by clicking on the top histogram with the mouse and dragging.

The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.