science of collecting and classifying a group of facts according to their relative number and determining certain values that represent characteristics of the group. The most familiar statistical measure is the arithmetic mean, which is an average value for a group of numerical observations. A second important statistic or statistical measure is the standard deviation, which is a measure of how much the individual observations are scattered about the mean. The chi-square test is a method of determining the odds for or against a given deviation from expected statistical distribution. Other statistics indicate other characteristics of the group of observations. In addition to the problem of computing certain statistics for a particular group of observations, there is the problem of sampling. This is an attempt to determine for what larger group (called the population) of individuals or characteristics the statistics for this particular group (called the sample) would be a representative figure and how representative a figure it would be for a given larger group. This second problem of sampling can be solved only by resorting to the theory of probability and higher mathematics. In most applications of statistics to scientific and social research, insurance, and finance, the statistician is interested not only in the characteristics of the sample but also in those of some much larger population. Consequently, the theory of sampling is the most important part of statistical theory.

See J. F. Freund, Modern Elementary Statistics (1988); D. S. Moore and G. P. McCabe, Introduction to the Practice of Statistics (1989); D. H. Sanders, Statistics (1989).

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