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In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean. The variance has a central role in statistics. It is used in descriptive statistics, statistical inference, hypothesis testing, goodness of fit, Monte Carlo sampling, amongst many others. This makes it a central quantity in numerous fields such as physics, biology, chemistry, economics, and finance. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ or Var(X).

Variance (land use)

A variance is a deviation from the set of rules a municipality applies to land use and land development, typically a zoning ordinance, building code or municipal code. The manner in which variances are employed can differ greatly depending on the municipality. A variance may also be known as a standards variance, referring to the development standards contained in code.

Variance (accounting)

In budgeting (or management accounting in general), a variance is the difference between a budgeted, planned or standard cost and the actual amount incurred/sold. Variances can be computed for both costs and revenues.

The concept of variance is intrinsically connected with planned and actual results and effects of the difference between those two on the performance of the entity or company.

Variance (album)

Variance is the third album by electronic musician Jega, released on 20 July 2009 by Planet Mu.

Variance (disambiguation)

In probability theory and statistics, variance measures how far a set of numbers are spread out.

Variance may also refer to:

  • Variance (accounting), the difference between a budgeted, planned or standard cost and the actual amount incurred/sold
  • Variance Films, a film distribution company founded in 2008
  • Variance (land use), a deviation from the set of rules a municipality applies to land use and land development
  • Variance (album) (2009), third album by electronic musician Jega
Longman Dictionary of Contemporary English


▪ Roll argued that the true market portfolio is a mean variance efficient portfolio and can not be observed.
▪ To obtain quantitative information from the mean and variance data requires the assumption of a more constrained model of the release process.
▪ The proportion of the total variance such correlations account for is of course small and their importance should be judged accordingly.
▪ On average he found that the model explained 27 percent of the total variance of returns.
▪ The best results were for the Ford Motor and the Dana corporations which predicted 45 percent of the total variance of returns.
▪ In other words just over 12 percent of the total variance is still accounted for by non-market factors.
▪ The church requested a variance to expand its parking lot.
▪ A little variance in forecast numbers may be anticipated as a consequence.
▪ Survey data indicate no variance in church attendance between blue- and white-collar workers.
▪ The variance explained by these two simulations is 60.8% and 60.6%, respectively.
▪ There was, moreover, a vehemence of utterance and gesture curiously at variance with the reticence of our Virginians.
▪ This was at variance with the Eurocheque system as exempted by the Commission in 1984.
▪ Tobacco consumption was the most important factor to explain the variance.
The Collaborative International Dictionary


Variance \Va"ri*ance\, n. [L. variantia.]

  1. The quality or state of being variant; change of condition; variation.

  2. Difference that produce dispute or controversy; disagreement; dissension; discord; dispute; quarrel.

    That which is the strength of their amity shall prove the immediate author of their variance.

  3. (Law) A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration, or between the allegation and the proof.

    A variance, in disagreement; in a state of dissension or controversy; at enmity. ``What cause brought him so soon at variance with himself?''



  1. n. an event that departs from expectations [syn: discrepancy, variant]

  2. discord that splits a group [syn: division]

  3. the second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value

  4. a difference between conflicting facts or claims or opinions; "a growing divergence of opinion" [syn: discrepancy, disagreement, divergence]

  5. the quality of being subject to variation [syn: variability, variableness] [ant: invariability, invariability]

  6. an activity that varies from a norm or standard; "any variation in his routine was immediately reported" [syn: variation]



n. 1 The act of varying or the state of being variable 2 A difference between what is expected and what happens 3 The state of differing or being in conflict 4 A discrepancy, especially between two legal documents 5 (senseid en second central moment in probability)(context statistics English) The second central moment in probability 6 (context computing programming English) covariance and contravariance generally

Douglas Harper's Etymology Dictionary


late 14c., "fact of undergoing change," from Old French variance "change, alteration; doubt, hesitation" and directly from Latin variantia, from stem of variare "to change" (see vary). Meaning "state of disagreement" is recorded from early 15c. The U.S. zoning sense of "official dispensation from a building regulation" is recorded from 1925.

Usage examples of "variance".

The dauphin and dauphiness were deeply shocked by a disaster so painfully at variance with their own happiness, which, in one sense, had caused it.

After a variety of conjectures and vague reports, each at variance with the other, and evidently deficient in the most remote connexion with the true cause of the strife, it was agreed to submit the question to the waiter, as a neutral observer, who assured us that the whole affair arose out of a trifling circumstance, originating with some mischievous boys, who, having watched two gownsmen into a cyprian temple in the neighbourhood of Saint Thomas, circulated a false report that they had carried thither the wives of two respectable mechanics.

Whatever those heterodox inclusions may mean, they were, it cannot be stressed too much, totally at variance with orthodox Christianity.

He found himself thinking that the whole arty get-up seemed oddly at variance with the way she was acting.

Indeed, it would have been at variance with his nature to take her in any other way, for though his vocation was that of an artist, and although he loved his vocation, his actual bias was towards the austerity and self--renunciation of a therapeutist, in the religious application of the term.

Nor must it be forgotten that sermons, like plays, are addressed to a mixed audience of families, and that the spiritual teachings of a lifetime may be destroyed by ten minutes of uncensored pronouncement from a pulpit, the while parents are sitting, not, as in a theatre vested with the right of protest, but dumb and excoriated to the soul, watching their children, perhaps of tender age, eagerly drinking in words at variance with that which they themselves have been at such pains to instil.

It seems our demon has acquired a variance from Ananke herself, giving him express permission to perform miracles in the furtherance of his plan.

Only his Roman nose was at variance with his other features, a lasting reminder of his years as a bareknuckle boxer.

Variances in absorption rate, bioavailability, protein binding, receptor-subtype mechanisms, efferent nerve equations, Meldrum models, gangloid ionization, ribosome protein synthesis, Cell Cleaner interaction rates-no one person could possibly have processed it all.

She was altogether at variance with Mrs Proudie on this matter, and gave Miss Dunstable great credit for her innovation.

Apart from the question of the legitimacy of the Greek dating of the sack, which seems to be at variance with the Roman data itself, the Varronian dates were thrown off by four years through the inclusion both of these desperate attempts to bring the list into conformity with the Greek dating of the sack.

We see from the table that the ratio of body to brain weight is, within the variance of measurement, roughly the same for the gracile Australopithecines, Homo habilis, Homo erectus and modern humans.

The difficulty was the greater as the customary laws of different tribes and confederations were at variance as to the compensation due in different cases.

They prized originality and spontaneity, but during his entire tour on Kaden, Hazzard had seen little variance among the natives, save in their dress, which ranged from none at all to costumes of indescribably complex and bizarre design.

I conceive it to be true that the railways are afraid to put themselves at variance with the general feeling of the people.