This applet demonstrates the central limit theorem using simulated dice-rolling experiments. An "experiment" consists of rolling a certain number of dice (1-5 dice are available in this applet) and adding the number of spots showing. This experiment is "performed" repeatedly, keeping track of the number of times each outcome is observed. These outcomes are plotted in the form of a histogram.

Type of Material:

Java applet, simulation

Recommended Uses:

In-class lecture demo or could be used as part of a lab or homework assignment if the instructor writes questions to accompany the simulation.

Technical Requirements:

Java-enabled web browser

Identify Major Learning Goals:

To understand the concept of the central limit theorem. The student will see the Central Limit Theorem in action using a simple die-rolling simulation.

Target Student Population:

Any introductory statistics class that covers the central limit theorem.

Prerequisite Knowledge or Skills:

Have some knowledge of histograms, means, standard deviation, basic probability, random variables and the normal distribution. Students should understand basic sampling distributions and at least be introduced to the Central Limit Theorem before using the applet.

Content Quality

Rating:

Strengths:

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.

Concerns:

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.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

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.

Concerns:

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.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

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.

Concerns:

There is no reset button if you want to clear the distribution. One has to press the refresh 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.

Creative Commons:

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