Statistic

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A statistic (singular) is a single measure of some attribute of a sample (e.g. its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items comprising the sample which are known together as a set of data.

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realisation of the data. The term statistic is used both for the function and for the value of the function on a given sample.

A statistic is distinct from a statistical parameter, which is not computable because often the population is much too large to examine and measure all its items. However a statistic, when used to estimate a population parameter, is called an estimator. For instance, the sample mean is a statistic which estimates the population mean, which is a parameter.

Contents

Examples

In calculating the arithmetic mean of a sample, for example, the algorithm works by summing all the data values observed in the sample then divides this sum by the number of data items. This single measure, the mean of the sample, is called a statistic and its value is frequently used as an estimate of the mean value of all items comprising the population from which the sample is drawn. The population mean is also a single measure however it is not called a statistic; instead it is called a population parameter.

Other examples of statistics include

Properties

Observability

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