Statistic
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/* See also */
{{Otheruses2|Statistics}}
A '''statistic''' (singular) is the result of applying a [[function (mathematics)|function]] (statistical [[algorithm]]) to a [[Data set|set of data]].
More formally, statistical theory defines a '''statistic''' as a function of a [[sample (statistics)|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 [[estimator]]s 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 [[quantile]]s besides the [[median]], e.g., [[quartile]]s and [[percentile]]s
* [[t statistic]]s, [[chi-square statistic]]s, [[f test|f statistics]]
* [[Order statistic]]s, including sample maximum and minimum
* Sample [[moment (mathematics)|moments]] and functions thereof, including [[kurtosis]] and [[skewness]]
* Various [[Functional (mathematics)|functionals]] of the [[empirical distribution function]]
==Properties==
===Observability===
A '''statistic''' is an ''observable'' [[random variable]], which differentiates it from a ''[[statistical parameter|parameter]]'', a generally unobservable quantity<ref>A parameter can only be computed if the entire population can be observed without error, for instance in a perfect census or on a population of [[standardized test]] takers.</ref> describing a property of a [[statistical population]].
Statisticians often contemplate a parameterized family of [[probability distribution]]s, 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 (statistics)|completeness]], [[consistent estimator|consistency]], [[sufficiency (statistics)|sufficiency]], [[estimator bias|unbiased]]ness, [[minimum mean square error]], low [[variance]], [[Robust statistics|robustness]], and computational convenience.
==Footnotes==
<references/>
==See also==
{{Wiktionary|statistic}}
*[[Statistics]]
*[[Statistical theory]]
*[[Descriptive statistics]]
*[[Statistical hypothesis testing]]
[[Category:Statistical theory]]
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[[es:Estadístico]]
[[fa:آماره]]
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[[nl:Steekproeffunctie]]
[[ja:統計量]]
[[fi:Tunnusluku]]
[[th:ค่าสถิติ]]
[[pt:Estatística (função)]]