ABSTRACT
When Graunt and Halley and Quetelet made their inferences, they made them on the basis of their examination of frequency distributions. Tables, charts, and graphs – no matter how the information is displayed – all can be used to show a listing of data, or classifications of data, and their associated frequencies. These are frequency distributions. By extension, such depictions of the frequency of occurrence of observations can be used to assess the expectation of particular values, or classes of values, occurring in the future. Real frequency distributions can then be used as probability distributions. In general, however, the probability distributions that are familiar to the users of statistical techniques are theoretical distributions, abstractions based on a mathematical rule, that match, or approximate, distributions of events in the real world. When bodies of data are described, it is the graph and the chart that are used. But the theoretical distributions of statistics and probability theory are described by the mathematical rules or functions that define the relationships between data, both real and hypothetical, and their expected frequencies or probabilities.
