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Balance Scale Simulation

Module by: David Lane

Begin by answering the questions, even if you have to guess. The first time you answer the questions you will not be told whether you are correct or not.

Once you have answered all the questions, answer them again using the simulation to help you. This time you will get feedback about each individual answer.

Show Simulation

General Instructions

This demonstration allows you to change the shape of a distribution and see the point at which the distribution would balance. The graph is a histogram of 600 scores. The mean, median, and mode are all equal to 8. You can see that the histogram is balanced on the tip of the triangle.

You can change the shape of the histogram by painting with the mouse. Notice that the triangle beneath the X-axis automatically moves to the point where the histogram is balanced. Experiment with different shapes and see if you can determine whether there is a relationship between the mean, median, and/or the mode and the location of the balance point.

Step by Step Instructions

First, draw a distributon with a positive skew such as the distribution shown below. The mean, median, and mode will not be equal for a skewed distribution. Note which statistic is highest and which is lowest. Which one is the point where the distribution is balanced?

balance_demo.png

Now draw a distributon with a negative skew.

balance_demo2.png

Compare the statistics for this distributon, and see which one corresponds to the balance point.

Experiment with different distributions and see if you have discovered a rule for the balance point that holds for all distributions you try.

Summary

For every distribution, the balance point is the mean.

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