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==Origin==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English]: via Old French from Latin ''variantia'' ‘[[difference]],’ from the verb ''variare''
*[http://en.wikipedia.org/wiki/14th_century 14th Century]
==Definitions==
*1: the [[fact]] or [[quality]] of being [[different]], divergent, or inconsistent: ''her light tone was at variance with her sudden trembling.''
*2: the state or fact of disagreeing or quarreling: ''they were at variance with all their previous allies.''
*3: chiefly Law a discrepancy between two [[statements]] or [[documents]].
*4: Law an official dispensation from a rule or [[regulation]], typically a building regulation.
*5: [[Statistics]] a [[quantity]] equal to the square of the standard deviation.
==Description==
In [[probability]] theory and [[statistics]], '''variance''' measures how far a set of [[numbers]] is spread out. A variance of zero indicates that all the values are [[identical]]. Variance is always non-negative: a small variance indicates that the [[data]] points tend to be very close to the mean (expected [[value]]) and hence to each other, while a high variance indicates that the data points are very spread out around the [http://en.wikipedia.org/wiki/Mean mean] and from each other.
An equivalent [[measure]] is the square root of the variance, called the [http://en.wikipedia.org/wiki/Standard_deviation standard deviation]. The standard deviation has the same [[dimension]] as the data, and hence is comparable to deviations from the mean.
The variance is one of several descriptors of a [[probability]] [[distribution]]. In particular, the variance is one of the [[moments]] of a distribution. In that [[context]], it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are [[advantageous]] in terms of [[mathematical]] and computational [[simplicity]].
The variance is a [[parameter]] that describes, in part, either the [[actual]] probability distribution of an observed [[population]] of numbers, or the theoretical probability distribution of a not-fully-observed population from which a sample of numbers has been drawn. In the latter case, a sample of data from such a distribution can be used to construct an estimate of the variance of the underlying distribution; in the simplest cases this estimate can be the sample variance.[http://en.wikipedia.org/wiki/Variance]
[[Category: Statistics]]
==Origin==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English]: via Old French from Latin ''variantia'' ‘[[difference]],’ from the verb ''variare''
*[http://en.wikipedia.org/wiki/14th_century 14th Century]
==Definitions==
*1: the [[fact]] or [[quality]] of being [[different]], divergent, or inconsistent: ''her light tone was at variance with her sudden trembling.''
*2: the state or fact of disagreeing or quarreling: ''they were at variance with all their previous allies.''
*3: chiefly Law a discrepancy between two [[statements]] or [[documents]].
*4: Law an official dispensation from a rule or [[regulation]], typically a building regulation.
*5: [[Statistics]] a [[quantity]] equal to the square of the standard deviation.
==Description==
In [[probability]] theory and [[statistics]], '''variance''' measures how far a set of [[numbers]] is spread out. A variance of zero indicates that all the values are [[identical]]. Variance is always non-negative: a small variance indicates that the [[data]] points tend to be very close to the mean (expected [[value]]) and hence to each other, while a high variance indicates that the data points are very spread out around the [http://en.wikipedia.org/wiki/Mean mean] and from each other.
An equivalent [[measure]] is the square root of the variance, called the [http://en.wikipedia.org/wiki/Standard_deviation standard deviation]. The standard deviation has the same [[dimension]] as the data, and hence is comparable to deviations from the mean.
The variance is one of several descriptors of a [[probability]] [[distribution]]. In particular, the variance is one of the [[moments]] of a distribution. In that [[context]], it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are [[advantageous]] in terms of [[mathematical]] and computational [[simplicity]].
The variance is a [[parameter]] that describes, in part, either the [[actual]] probability distribution of an observed [[population]] of numbers, or the theoretical probability distribution of a not-fully-observed population from which a sample of numbers has been drawn. In the latter case, a sample of data from such a distribution can be used to construct an estimate of the variance of the underlying distribution; in the simplest cases this estimate can be the sample variance.[http://en.wikipedia.org/wiki/Variance]
[[Category: Statistics]]
