The Collaborative International Dictionary of English v.0.48:

Variance \Va"ri*ance\, n. [L. variantia.]
   1. The quality or state of being variant; change of
      condition; variation.
      [1913 Webster]

   2. Difference that produces dispute or controversy;
      disagreement; dissension; discord; dispute; quarrel.
      [1913 Webster]

            That which is the strength of their amity shall
            prove the immediate author of their variance.
                                                  --Shak.
      [1913 Webster]

   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. --Bouvier.
      [1913 Webster]

   4. (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.
      [PJC]

   At variance, in disagreement; in a state of dissension or
      controversy; at enmity. "What cause brought him so soon at
      variance with himself?" --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

at variance
    adj 1: not in accord; "desires at variance with his duty";
           "widely discrepant statements" [syn: at variance(p),
           discrepant, dissonant]

Moby Thesaurus II by Grady Ward, 1.0:

116 Moby Thesaurus words for "at variance":
   against the grain, against the tide, against the wind, alienated,
   antagonistic, antiestablishment, antipathetic, assorted,
   at cross-purposes, at daggers, at daggers drawn, at enmity,
   at feud, at issue, at loggerheads, at odds, at odds with, at outs,
   at square, at strife, at variance with, at war, at war with,
   athwart, breakaway, clashing, contra, contradictory, contrariwise,
   contrary, contrasted, contrasting, counter, counter-culture,
   cranky, cross, departing, deviating, deviative, different,
   differentiated, differing, disaccordant, disagreeable, disagreeing,
   discordant, discrepant, discrete, discriminated, disharmonious,
   disjoined, disparate, disproportionate, dissentient, dissenting,
   dissident, dissimilar, dissonant, distinct, distinguished,
   divergent, diverging, divers, diverse, diversified,
   eyeball-to-eyeball, grating, heterogeneous, hostile, immiscible,
   in confrontation, in disagreement, in hostile array, in opposition,
   inaccordant, incompatible, incongruous, inconsistent, inconsonant,
   inharmonious, irreconcilable, jangling, jarring, many, motley,
   multifarious, negative, nonconforming, on the outs, opposing,
   out of accord, out of whack, poles apart, poles asunder, recusant,
   repugnant, sectarian, sectary, separate, separated, several,
   unconformable, uncongenial, underground, unequal, unharmonious,
   unlike, up in arms, variant, varied, variegated, various, varying,
   widely apart, with crossed bayonets, worlds apart