Grand means of time-varying signals (waveforms) across subjects in magnetoencephalography (MEG) and electroencephalography (EEG) are commonly computed as arithmetic averages and compared between conditions, for example, by subtraction. However, the prerequisite for these operations, homogeneity of the variance of the waveforms in time, and for most common parametric statistical tests also between conditions, is rarely met. We suggest that the heteroscedasticity observed instead results because waveforms may differ by factors and additive terms and follow a mixed model. We propose to apply the asinh-transformation to stabilize the variance in such cases. We demonstrate the homogeneous variance and the normal distributions of data achieved by this transformation using simulated waveforms, and we apply it to real MEG data and show its benefits. The asinh-transformation is thus an essential and useful processing step prior to computing and comparing grand mean waveforms in MEG and EEG.