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.
In the calculation of the
arithmetic mean, for example, the algorithm consists of summing all the datavalues 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 meanparameter.
Other examples of statistics include
Sample meanand sample median
Sample varianceand sample standard deviation
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
* Various functionals of the
empirical distribution function
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 standardized testtakers.] describing a property of a statistical population.
Statisticians often contemplate a
parameterized familyof 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 hypothesis testing
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