The author wrote the requirements for the selection of the averaging time for the interrupted noise method of measuring reverberation time in the international standard ISO 354:1985 "Acoustics-Measurement of sound absorption in a reverberation room". When this standard was revised to become ISO 354:2003, the evaluation range used to measure the reverberation time was changed from 30 dB to 20 dB. Because the working group which revised the standard did not know the reasons for the averaging time requirements, they incorrectly changed them to supposedly take account of the change to the evaluation range. The purpose of this paper is to give the reasons for the averaging time requirements so that they are corrected and not incorrectly changed again. It is necessary that the averaging time is not so large that information is discarded and so that, in the case of exponential averaging devices, the measured decay rate is not biased by the decay rate of the exponential averaging device. On the other hand, it is desirable that the averaging time be as large as possible so that the ensemble standard deviation of the measured reverberation times is as small as possible.