Statistic

A statistic (singular) is the result of applying a statistical algorithm to a set of data. In the calculation of the arithmetic mean, for example, the algorithm directs us to sum all the data values and divide by the number of data items. In this case, we call the mean a statistic. To be complete in describing any use of a statistic, one must describe both the procedure and the data set.

The popular use of the term to mean a single measurement, or datum, differs from this meaning. A statistician would normally call an individual person's height a statistic only if that person were chosen randomly from some population of interest, but more often would use the term to refer to, for example, the median height of a group of people.

Often the concept is defined by saying that a statistic is an observable random variable. Statisticians often contemplate a parametrized family of probability distributions, any member of which could be the distribution of some measurable aspect of each member of a statistical population from which a sample is drawn randomly. The value of the parameter is not observable, since it depends on the whole population rather than on the sample. For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such men are measured; the average of those 100 numbers is a statistic; the average of the heights of all members of the population is not a statistic (unless that has somehow also been ascertained). The difference between that observable sample average and the unobservable population average is an example of a random variable that is not a statistic; the reason it is random is that the sample was chosen randomly.

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