Variance
Origin
Middle English: via Old French from Latin variantia ‘difference,’ from the verb variare
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 mean and from each other.
An equivalent measure is the square root of the variance, called the 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.[1]
