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A '''statistic''' is a function of a distributed variable.  Notionally, it is a calculation made on the basis of a set numbers typically derived as a sample from some presumed underlying [[probability distribution]], and usually used in order to estimate something about the distribution from which the sample is taken. The use of a '''statistic''' to characterize a set of observations is generally justified on the basis of its [[asymptote|asymptotic]] behavior, that is, a given '''statistic''' accurately characterizes the underlying phenomena only probabilistically (this consideration is the genesis of [[confidence interval]]s in [[classical statistics]]) and is considered to be accurate only in the limit as the number of observations increases without bounds.  It should be noted however that the use of [[confidence interval]]s is somewhat problematic since their calculations are based on certain presumptions about the nature of the underlying true distribution, which may or may not prove to be good.  

A '''statistic''' is a function of a distributed variable.  Notionally, it is a calculation made on the basis of a set numbers typically derived as a sample from some presumed underlying [[probability distribution]], and usually used in order to estimate something about the distribution from which the sample is taken. The use of a '''statistic''' to characterize a set of observations is generally justified on the basis of its [[asymptote|asymptotic]] behavior, that is, a given '''statistic''' accurately characterizes the underlying phenomena only probabilistically (this consideration is the genesis of [[confidence interval]]s in [[classical statistics]]) and is considered to be accurate only in the limit as the number of observations increases without bounds.  It should be noted however that the use of [[confidence interval]]s is somewhat problematic since their calculations are based on certain presumptions about the nature of the underlying true distribution, which may or may not prove to be good.  

For example, suppose a [[random sample]] of three children is chosen from a particular class, and their heights measured as 1.42cm., 1.54cm., and 1.48cm; then the [[arithmetic mean]] of these heights is 1.48cm. We might then go on to use  this value of 1.48cm to represent the [[average]] height of a child in that class.

For example, suppose a [[random sample]] of three children is chosen from a particular class, and their heights measured as 1.42 cm., 1.54 cm., and 1.48 cm; then the [[arithmetic mean]] of these heights is 1.48 cm. We might then go on to use  this value of 1.48 cm to represent the [[average]] height of a child in that class.

Clearly the [[validity]] and [[reliability]] of such [[estimation]]s will depend enormously on a range of factors such as the type of distributions, the number in the sample, and on sampling methods used.

Clearly the [[validity]] and [[reliability]] of such [[estimation]]s will depend enormously on a range of factors such as the type of distributions, the number in the sample, and on sampling methods used.

===Formal Definition:===

==Formal Definition==

Let X₁, X₂, X₃, ...., X_n be a random sample of size n from some distribution. A statistic calculated on the sample is defined to be any [[function]] of the set of values X₁, X₂, X₃, ...., X_n, involving no unknown quantities <ref> Francis, A. (2005) Advanced Level Statistics, Stanley Thornes </ref>

Let X₁, X₂, X₃, ...., X_n be a random sample of size n from some distribution. A statistic calculated on the sample is defined to be any [[function]] of the set of values X₁, X₂, X₃, ...., X_n, involving no unknown quantities <ref>Francis, A. (2005) Advanced Level Statistics, Stanley Thornes</ref>

The point of this definition is to ensure that the process results in an actual numerical value, rather than a formula involving variables.

The point of this definition is to ensure that the process results in an actual numerical value, rather than a formula involving variables.

===Examples of Statistics:===

==Examples of Statistics==

* [[Arithmetic mean]]

* [[Arithmetic mean]]

* [[Pearson's measure of skewness]]  '' = 3*(mean - median)/standard  deviation

* [[Pearson's measure of skewness]]  '' = 3*(mean - median)/standard  deviation

===References===

==References==

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