# variance

## Definitions

• WordNet 3.6
• n variance an activity that varies from a norm or standard "any variation in his routine was immediately reported"
• n variance an official dispensation to act contrary to a rule or regulation (typically a building regulation) "a zoning variance"
• n variance the quality of being subject to variation
• n variance a difference between conflicting facts or claims or opinions "a growing divergence of opinion"
• n variance the second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value
• n variance discord that splits a group
• n variance an event that departs from expectations
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Webster's Revised Unabridged Dictionary
• Variance (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.
• Variance Difference that produces dispute or controversy; disagreement; dissension; discord; dispute; quarrel. "That which is the strength of their amity shall prove the immediate author of their variance ."
• Variance (Statistics) The expected value of the square of the deviation from the mean of a randomly distributed variable; the second moment about the mean. This is also the square of the standard deviation.
• Variance The quality or state of being variant; change of condition; variation.
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Century Dictionary and Cyclopedia
• n variance In physical chemistry, that property of a chemical system which is expressed by the equation V = c + 2 — φ, where V is the variance, c the number of independent components, and φ the number of phases in which the system may exist. Systems are said to be invariant, univariant, bivariant, multivariant, etc., according to the value of V.
• n variance The state of being or the act of becoming variant; alteration; variation; change; difference.
• n variance In law, a discrepancy: Between pleadings and proof, as where a complaint mentions a wrong date, or the facts prove to be different from what was alleged.
• n variance Between the form of the writ or process by which the action was commenced and the form of the declaration or complaint. Formerly, when variances were deemed more important than now, variance was often defined as a fatal discrepancy or disagreement, etc.; but in civil cases such variances between pleading and proof as do not actually mislead the adverse party are now disregarded as immaterial, and many others are amendable. Under what is known in the United States as the Code Practice, vari ance is used to designate a discrepancy in some particulars only, and is amendable if it has not misled, while a failure of proof as to the entire scope and meaning of an allegation is not regarded as a mere variance, but fatal.
• n variance Difference that produces disagreement or controversy; dispute; dissension; discord.
• n variance Variableness; inconstancy.
• n variance In a state of controversy or dissension; in a state of opposition or enmity.
• n variance Synonyms and Disagreement, etc. See difference.
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Chambers's Twentieth Century Dictionary
• n Variance vā′ri-ans state of being varied: an alteration: a change of condition:
• adj Variance diverse, variable, inconstant
• n Variance vā′ri-ans (law) a discrepancy: difference that arises from, or produces, dispute
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## Quotations

• Jonathan Swift
“Poor nations are hungry, and rich nations are proud; and pride and hunger will ever be at variance.”

## Etymology

Webster's Revised Unabridged Dictionary
L. variantia,

## Usage

### In literature:

I could not sleep or rest; my mind and brain were at variance with themselves.
"The Tragedy of the Chain Pier" by Charlotte M. Braeme
But, Sir, the office and its business are at variance.
"The Works of the Right Honourable Edmund Burke, Vol. II. (of 12)" by Edmund Burke
Drake's theology was at variance with that of the Founder of our faith.
"Drake, Nelson and Napoleon" by Walter Runciman
Their pleasures are at variance with morality.
"Renaissance in Italy, Volume 1 (of 7)" by John Addington Symonds
It is hardly necessary to observe that this grotesque theory is utterly at variance with the facts, as now known.
"Rambles and Recollections of an Indian Official" by William Sleeman
It will readily be judged that a man of this character could ill agree with Grotius: accordingly they were soon at great variance.
"The Life of the Truly Eminent and Learned Hugo Grotius" by Jean Lévesque de Burigny
I hate to think of having my husband at variance with the man who stands in place of my father.
"A Friend of Caesar" by William Stearns Davis
As long as those two princes are at variance, so long the liberties of Germany are safe.
"The Works of the Right Honourable Edmund Burke, Vol. IV. (of 12)" by Edmund Burke
His name was so at variance to his size that we called him "Hillock," for short.
"The Scientific American Boy" by A. Russell (Alexander Russell) Bond
He is at variance with Manetho on Egyptian, with Ptolemy on Babylonian, chronology.
"The Seven Great Monarchies Of The Ancient Eastern World, Vol 2. (of 7): Assyria" by George Rawlinson
She will begin to blame your least actions because they are at variance with her ideas, or her secret intentions.
"The Physiology of Marriage, Complete" by Honore de Balzac
But my doubts are not now of your love, but of your firmness in resisting a control at variance with your duty to yourself.
"Guy Rivers: A Tale of Georgia" by William Gilmore Simms
The Gods above 15 No longer dwell at variance.
"The Iliad of Homer" by Homer
Perhaps some will read this reply with impatience; being able, as they think, to cite facts totally at variance with it.
"Essays on Education and Kindred Subjects" by Herbert Spencer
The facts, however, were utterly at variance with these ingenious suppositions.
"The Major Operations of the Navies in the War of American Independence" by A. T. Mahan
Moreover, the treaty by no means covered the whole ground of variance between the English and the Welsh.
"The History of England" by T.F. Tout
Is not all this inconsistent with reason, and at variance with the cardinal truth, that there is one time only?
"International Conference Held at Washington for the Purpose of Fixing a Prime Meridian and a Universal Day. October, 1884." by Various
They felt, that, in many respects, their interests were not identical, and in some absolutely at variance.
"Salem Witchcraft, Volumes I and II" by Charles Upham
There is some variance, in different parts of the Bagobo area, in the beliefs concerning the spirits or souls of a man.
"The Wild Tribes of Davao District, Mindanao" by Fay-Cooper Cole
But the space of her variance from his ideal was between them, and the voice reached him faintly across it.
"A Pair of Patient Lovers" by William Dean Howells
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### In poetry:

Daphnis.
The sprightly Sylvia trips along the green,
She runs, but hopes she does not run unseen;
While a kind glance at her pursuer flies,
How much at variance are her feet and eyes!
"Spring - The First Pastoral ; or Damon" by Alexander Pope
What hath Love with Thought to do?
Still at variance are the two.
Love is sudden, Love is rash,
Love is like the levin flash,
Comes as swift, as swiftly goes,
And his mark as surely knows.
"Love And Thought" by James Russell Lowell
For the first time since he was born
Her son, her rose without a thorn,
They are at variance, they who were
Always such closest friends and dear.
Another face is in his dreams
Under the sunbeams and moonbeams.
"Alienation " by Katharine Tynan
Oh! who shall dare in this frail scene
On holiest happiest thoughts to lean,
On Friendship, Kindred, or on Love?
Since not Apostles' hands can clasp
Each other in so firm a grasp
But they shall change and variance prove.
"St. Mark's Day" by John Keble

### In news:

Addiction Incorporated Directed by Charles Evans Jr Variance Films December 14 through 27, Film Forum.
A Variance Films release of an Acappella Pictures presentation of a Dune Road Films production.
Credit Okazaki Hirotake / Variance Films.
Last month the Las Vegas City Council made a difficult but necessary decision to overturn a Board of Adjustments-approved variance for Ashley Salazar.
Penn Township's zoning hearing board approved a variance request by two businessmen that will allow them to park cars in the right of way along Route 72.
Immersive virtual reality enables a broad range of researchers to overcome challenges posed by space constraints, scale, or time variances.
Spoken Word Directed by Victor Nunez Variance Films Opens July 23.
The Hastings City Council spent a notable portion of its meeting debating whether or not a Hastings homeowner should be granted a variance to build a new garage.
No one specified what amount of variance between the two thermometers would be acceptable.
Borough Zoning Hearing Board meet to discuss property variances, Oct 11.
The variance granted to Andrew Lloyd of Sagewood Drive in August, allowed him to keep three pit bulls on his premises.
Country club gets variance for new chemical building.
Portland Drinking-Water Variance May Aid Bend.
The Oregon Health Authority's Public Health Division announced Tuesday its intent to grant a variance to the city of Portland from the requirement to treat the Bull Run water source for Cryptosporidium.
RAY BROOK — Harrietstown was granted a variance to build a taller retaining wall behind the Town Hall.
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### In science:

For the walk on the line with coin decoherence Brun et al. [49, 50] compute the variance as a function of the transition parameter pmeas to ﬁnd that even for very small values of pmeas (very ’close’ to quantum) the variance is already linear.
Quantum random walks - an introductory overview
In particular, if c is chosen from a distribution ν on E (supported on c for which φc is admissible), then the variance of F (c) is less than or equal to the variance of c.
Random Surfaces
One would expect that with increasing PSF width σ x the variance decreases, which would be explained by the fact that the variance is given by a weighted integration over the power spectrum P(k).
Coded mask imaging of extended sources with Gaussian random fields
For a non-clipped network with uniform resource distribution, the variance of the degree distribution maps directly onto the variance of the load balancing.
Balanced Overlay Networks (BON): Decentralized Load Balancing via Self-Organized Random Networks
This leads to the crossover from a ﬁnite variance (Gaussian) to a divergent variance (L´evy) limit.
Levy statistical fluctuations from a Random Amplifying Medium
Thus the variance, hdg2 i, of the conductance is linked to the number variance, S2 , of the energy levels.
Random Matrices
The following theorem shows how the distance between an arbitrary mean zero, ﬁnite variance random variable W and a mean zero normal with the same variance can be bounded by the distance between W and a variate W ∗ with the W -zero biased distribution deﬁned on a joint space.
Stein's method and the zero bias transformation with application to simple random sampling
It is immediate from this inequality that X is symmetry resistant and the minimum variance symmetrizer has the same variance as −X .
Symmetrization of Bernoulli
The sensitivity with respect to q is limited by the variance of the number of nodes with initial state 0*, because this variance can be seen as a rescaling of q .
Exhaustive percolation on random networks
The idea of the proof is the following: if 0 ∈ P , then we bound the variance in terms of the variance of the cone induced by each facet.
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
N , and to deﬁne the product (cid:2)KN 21 (cid:3)∧k . • Application of the rapid (in fact, exponentially fast) off-diagonal asymptotics of the Szeg˝o kernel of [SZ2] as the degree N → ∞ to obtain asymptotics of the variance current and number variance.
Number variance of random zeros on complex manifolds
From the bipotential formulas, and the analysis of the singularities of the variance current, the asymptotics of the variance are reduced to the off-diagonal asymptotics for the Szeg˝o kernel ΠN (z , w) (two point function).
Number variance of random zeros on complex manifolds
Our computation of the variance current asymptotics also gives this growth rate for the variance current (Lemma 3.7) as well as for its scaling limit (Lemma 3.9).
Number variance of random zeros on complex manifolds
The case when λN is centered Gaussian with variance 1 N translates to HN being of variance N .
Large Deviations and Random Energy Models
The singularity of this mode can also be traced back to Eq. (21), in that the mean height performs a simple random walk and has a diverging variance in the limit of t → ∞ (for any system size), i.e., its steady-state variance does not exist.
Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links
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