- Statistic
A

**statistic**(singular) is the result of applying a function (statisticalalgorithm ) 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 asestimator s instatistical 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 thedata 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 unobservablepopulation mean parameter.Other examples of statistics include

*Sample mean andsample median

*Sample variance and samplestandard deviation

* Samplequantile s besides themedian , e.g.,quartile s andpercentile s

*t statistic s,chi-square statistic s, f statistics

*Order statistic s, including sample maximum and minimum

* Sample moments and functions thereof, includingkurtosis andskewness

* Various functionals of theempirical distribution function **Properties****Observability**A

**statistic**is an "observable"random variable , which differentiates it from a "parameter", a generally unobservable quantity [*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*] describing a property of astandardized test takers.statistical population .Statisticians often contemplate a

parameterized family ofprobability 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**.**tatistical properties**Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness,

minimum mean square error , lowvariance , robustness, and computational convenience.**Footnotes****ee also***

Statistics

*Statistical theory

*Descriptive statistics

*Statistical hypothesis testing

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