One of the common types of averaging facilities is the averaging stack. The qualitative composition of the ore stream arriving for processing varies randomly in time. Therefore, for the study of averaging processes, in particular in averaging stacks, the most promising is the apparatus of the theory of random functions, which allows us to directly take into account the internal relations of the processes of changing the qualitative composition of the averaged mineral raw material flows. However, there are no methods in the specialized literature that allow to calculate averaging processes in stacks with the help of the theory of random functions. Usually, the efficiency of averaging stacks is usually estimated by the ratio of dispersions (or mean square deviations) of the controlled components of the qualitative composition at the input and output of the stack. In the present work, similar estimations are adopted. Without violation of generality, we consider random fluctuations X(t)of some component X of the qualitative composition.