A mathematical analysis of the variance of the average evoked-response computation as a function of the numberN of stimuli presented is made for the case when the response is disturbed by additive stationary noise. A comparison is made between the variance for purely periodic stimuli and that for stimuli of which the interstimulus durations are Gaussian distributed. In the latter situation, the interval durations may be correlated with each other, e.g. according to a Gaussian Markov process. It is deduced that, in general, the introduction of aperiodic stimulation tends to make the functional relationship between the variance andN behave as though it holds for noise with a very broad frequency spectrum; the variance is proportional to 1/N.