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INTRODUCTION
If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, μ , of the population. This remarkable fact, known as the law of large numbers, holds true if we draw samples from a population of discrete or continuous values, or draw them from a population with a skewed distribution.
The purpose of this article is to present an Excel workbook to use in an undergraduate introductory statistics class to simulate an application of the law of large numbers. The constructed workbook spreadsheets use standard Excel functions and do not require any higher level programming. Once built, the workbook can be reused for another application of the law of large numbers.
To use the spreadsheet simulation, a user enters a discrete probability distribution that simulates the possible outcomes of any random process. The spreadsheet calculates and displays the population mean, μ , that is considered to be an average number from two perspectives. First it is an expected value - the average of the possible values that can occur weighted by their probability of occurring. It may also be viewed as the long run average of many independent observations. The simulation demonstrates this second view of the mean by drawing many random samples from the discrete probability distribution and tracking a running average. The law of large numbers guarantees that the running average will converge to μ , as the number of samples drawn increases.
A simulation of the random process begins by using the mouse to move a scroll bar on the chart sheet. Each time the scroll bar is moved to the right, a sample item is drawn from the discrete distribution. The value of the sample item, a running average of all sample items, and the population expected value μ are graphically displayed on a chart. New simulation runs are made by sliding the scroll bar left to clear the last run and then moving it to the right again. Students see that different simulation runs create different paths from left to right in the graph, but the law of large numbers says that whatever path we get, the long run...