Recent studies of the mathematical relationship between time and forgetting suggest that it is a power function rather than an exponential function, a finding that has important theoretical consequences. Through computational analysis and reanalyses of published data, we demonstrate that arithmetic averaging of exponential curves can produce an artifactual power curve, particularly when there are large and systematic differences among the slopes of the component curves. A series of simulations showed that the amount of power artifact is small when the slopes of the component curves are normally or rectangularly distributed and when the performance measure is noise free. However, the simulations also showed that the artifact can be quite large, depending on the shape of the noise distribution and restrictions in the performance range. We conclude that claims concerning the form of memory functions should consider whether the data are likely to contain artifact caused by averaging or by the presence of range-restricted noise.