In this contribution we will deal with the problem of variability of interval data. The issue is to find lower and upper bounds for the interval of possible values for the variance of given interval data. This leads to the problem of minimizing/maximizing the sum of squares of the distance between the components of the n-dimensional vector and their average value. As the maximization is more difficult than the minimization, we present here some theoretical results concerning the solution. Furthermore, we introduce preliminary algorithms for solving both problems which take into consideration their special structure.