variance has 8 distinct synonyms spread across 5 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value
a difference between conflicting facts or claims or opinions
“a growing divergence of opinion”
the quality of being subject to variation
an official dispensation to act contrary to a rule or regulation (typically a building regulation)
“a zoning variance”
Synonyms, antonyms and the broader and narrower relations for variance come from Princeton University’s WordNet. Full sources and licences.