CLT Demo


The CLT Demo program illustrates statistics’ Central Limit Theorem. To use it, choose a probability distribution from the drop-down at the top-left of the window and set the required parameters, then click the Reset button. The software will then generate a random sample of size n from the desired probability distribution. The yellow histogram (“Individual Histogram”) and the green histogram (“Cumulative Histogram”) will reflect the observations in the sample. The blue histogram (“x-Mean Histogram”) will display a single bar indicating the mean of the random sample.

When you click the Reset button, the “Iteration #” slider will be enabled. By sliding it to the right, you can generate more random samples of size n (one per iteration). The Individual Histogram will reflect the observations in the current sample only. The Cumulative Histogram reflects the observations in all samples generated so far. The x-Mean Histogram reflects the means of the samples generated so far. As the number of iterations increases, this should begin to look like a normal distribution.

For example, if you move the “Iteration #” slider to iteration 200, the Individual Histogram will reflect the observation from the 200th sample generated, the Cumulative Histogram will reflect the distribution of all observations from samples 1 through 200, and the x-Mean Histogram contains the distribution of the means of samples 1 through 200.

You can set the number of observations per sample (n) using the “# Observations” field. You can set the number of bins in the Individual and Cumulative Histograms using the “# Bins” field, and the number of bins in the x-Mean Histogram using the “# x-Mean Bins” field.

You can also move the slider by clicking on it and using the left and right arrow keys on the keyboard. Note that the slider moves backwards, too, to remove samples from the histograms.

Important: The n from the statement of the CLT is “# Observations”, not the iteration number. As n gets large, the normal approximation for x-bar gets better. As the iteration number increases, the x-Mean Histogram looks more normal simply because you have generated more observations from a (quasi-)normal distribution.

For more information, see the Read Me file, which is distributed with the software.

Screen Shot


THE AUTHOR OF THIS SOFTWARE MAKES NO CLAIMS, EXPRESSED OR IMPLIED, ABOUT THE PERFORMANCE OF THIS SOFTWARE, INCLUDING, BUT NOT LIMITED TO, THE STABILITY OF THE SOFTWARE OR THE QUALITY OF THE SOLUTIONS IT RETURNS.  The author shall not be held liable for any damage or injury that results from the use of this software, including, but not limited to, damage to computer software or hardware.


CLT Demo is for Windows-based systems.

Current Version

Version 1.0


You may download CLT Demo free of charge and use it for educational, research, or not-for-profit purposes.  I would appreciate your filling out and submitting the following form before downloading; however, if you wish to download the software anonymously, simply skip the form and click the download link below.

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Click here to download a zip file that contains two files:

  • CLTDemo.exe: contains the application
  • ReadMe.txt: describes the software and how to use it

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