4 - Examples

Summary

…lies, damn lies, and statistics.

Mark Twain

Here are a few randomly chosen and occasionally whimsical uses for your new knowledge about the workings of chance. The situations I shall describe all have to do with everyday life. In such applications, the difficulty is not only in the mathematical scheme but also in the frequently unstated assumptions that lie beneath it. It helps to be able to identify the repeatable random experiment and, when many trials are being treated as independent, to be able to argue that they are in fact unconnected.

The examples have been chosen to illustrate the role of statistical fluctuations, because this is the most interesting aspect of randomness for the physical applications to follow. A statistician or a mathematician would choose other examples, but, then, such a person would write a different book.

Polling

Opinion polls are second only to weather forecasts in bringing probability, often controversially, into our daily lives. ‘Polls Wrong,’ a headline might say after an election. Opinions change, and often suddenly. A pollster needs experience and common sense; his or her statistical knowledge need not be profound. But, there is a statistical basis to polling. Consider the question: ‘If 508 of 1000 randomly selected individuals prefer large cars to small, what information is gleaned about the car preferences of the population at large?’ If we ignore the subtleties just alluded to, the question is equivalent to the following one.