Author(s):

Kady Schneiter (Utah State University)

**Instructions**:

- Use the radio buttons to choose to toss a coin or roll a die.
- An experiment consists of 10000 trials (tosses or rolls).
- Press the 'Get data' button to conduct an experiment.
- By default, the applet plots the percentage of successes (a success is a 'head' for the coin or a 'three' for the die) by the number of trials.
- Up to 25 experiments can be overlayed on the same plot.
- The current or newest experiment is plotted in orange; previous experiments are shown in a default plot color.
- The radio buttons at the bottom of the applet allow you to choose to plot the percentage of successes minus the expected percentage of successes or the absolute number of successes minus the expected number of successes.
- Use the 'reset' button to clear the plot.

In illustration of the law of averages, you will observe that as the number of trials increases, the percentage of successes approaches the expected percentage of successes while the difference between the observed and expected number of successes increases.

** Scale ** - Note that the scale on the horizontal axis is not constant. The plots may appear to show sudden jumps or dramatic differences at 100 and 1000 tosses, this is a result of the change of scale at those positions.

**Display ** – The 'Display' menu in the upper left hand corner of the applet allows the user to adjust the speed of the experiments and change the appearance of the plot.

Kady Schneiter (Utah State University), "Law of Averages Applet - Instructions," *Convergence* (June 2010), DOI:10.4169/loci003491