# **Central Limit Theorem Applet

This applet demonstrates the central limit theorem using simulated dice-rolling experiments. This experiment is performed repeatedly and outcomes are recorded and plotted in the form of a histogram. An article describing this applet and an alternate source for the applet can be found at http://www.amstat.org/publications/jse/v6n3/applets/clt.html.
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Date Of Record Creation 2005-06-22 14:31:00 2010-04-16 20:50:00 2005-06-22 14:31:00 http://www.stat.tamu.edu/~west/javahtml/ http://www.amstat.org/publications/jse/v6n3/west.html to166@columbia.edu, west@stat.tamu.edu 1998 R. Webster West and R. Todd Ogden Columbia University, Texas A&M University The Central Limit Theorem usually talks about the sample mean, not the sample total being Normally distributed. It would be nice to have the option of looking at the sample mean instead of just the sample total. Also, in the introduction, the one-die results are "symmetric and LIGHT tailed". If would be good to plot a Normal curve over the top of the histogram with the click of a button. Also, an accompanying worksheet would be helpful. This applet does a good job of quickly simulating die rolls so that the students can quickly see trends involved in the Central Limit Theorem. The applet allows students to see for themselves how when the number of throws of dice is increased, the shape approaches the normal curve. There is no "reset" button on the browser. If the browser is not java enabled, there may be some issues downloading java on lab computers, which often have draconian security settings. Also, there is no y-axis for the histogram. I think it would be helpful to know how many rolls total we have done so that proportions could be calculated. The applet is very self-explanatory. Any java enabled browser should be able to display it easily. It's very easy to operate the simulation. This simulation would have been much better if the author didn't tell the students what the results will be in the introduction. I would have preferred to see a series of thought questions like: What does the histogram look like for just 1 die? For 2 dice? For 3 dice? Do you notice a trend as the # of dice increase? Try increasing the # of rolls for each # of dice. What do you notice? Do the trends become more or less clear and stable as the # of rolls increase? Students might not understand if sample size (n) refers to number of dice or number of rolls. It also would have been effective to have had the normal curve superimposed on the applet. With the ability to change the number of dice and the number of throws of the dice, students should deepen their understanding of the central limit theorem. Students can get a quick demonstration of large numbers of die rolls, which is beneficial because this is a concept they naturally grasp but usually don't have the class time to test out for themselves. 4 4 4 1