To measure sound power in a reverberation room, we need to estimate the space-time average of squared sound pressure. While the time average usually presents no special problem, the space average may, particularly for acoustic signals having pure-tone or extremely narrow-band spectra. The space average is subject to a random error due to finite sample size. Tables and formulas are presented from which an experimenter may determine the confidence level of his estimate in terms of signal-bandwidth reverberation time. and number of fixed microphones or the path length for a moving microphone. The space average is also subject to a bias error if the quantity averaged is sound level or rms pressure instead of squared pressure. The bias error is also estimated. Finally, the remarkable performance of rotating diffusers is described in terms of their improvement in the statistical accuracy of the measured mean. Two ways of computing their figure of merit are described. It is shown that the rotating diffuser is effectively a parametric modulator which introduces new frequencies in the room.