This paper presents some theoretical considerations about the variance of a fuzzy set and introduces a covering–based algorithm for computing the bounds of the variance of an interval Type–2 fuzzy set. The proposed algorithm obtains the bounds of all possible variances of an interval Type–2 fuzzy set unlike other algorithms which are based on the center of centroid of an interval Type–2 fuzzy set to obtain a relative variance which is proven to be always bigger than the absolute variance. A comparison to the relative variance of an interval Type–2 fuzzy set is given through different examples where the proposed algorithm shows better precision than the KM algorithm.