In the paper a regulator, called the mean regulator, is presented for stochastic discrete systems. The mean regulator minimises the supremum of the mean of the absolute value of the system outputs for all disturbances in a space RD and all time. A performance index and a random disturbance space are proposed. The analysis, which is restricted to discrete-time single-input single-output stochastic systems, yields the mean regulator and considers its stability. The simulations illustrate the operation of the mean regulator.