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]