A statistic (singular) is the result of applying a function (statistical algorithm) to 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: the term is used both for the function and for the value of the function on a given sample.

A statistic is distinct from an unknown statistical parameter, which is not computable from a sample. A key use of statistics is as estimators in statistical inference, to estimate parameters of a distribution given a sample. For instance, the sample mean is a statistic, while the population mean is a parameter.

Examples

In the calculation of the arithmetic mean, for example, the algorithm consists of summing all the data values and dividing this sum by the number of data items. Thus the arithmetic mean is a statistic, which is frequently used as an estimator for the generally unobservable population mean parameter.

Other examples of statistics include

• Sample mean and sample median
• Sample variance and sample standard deviation
• Sample quantiles besides the median, e.g., quartiles and percentiles
• t statistics, chi-square statistics, f statistics
• Order statistics, including sample maximum and minimum
• Sample moments and functions thereof, including kurtosis and skewness
• Various functionals of the empirical distribution function

Observability

A statistic is an observable random variable, which differentiates it from a parameter, a generally unobservable quantity describing a property of a statistical population.

Statisticians often contemplate a parameterized family of probability distributions, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. 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 (such as by measuring every member of the population). The average height of all (in the sense of genetically possible) 25-year-old North American men is a parameter and not a statistic.

Statistical properties

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

Footnotes