Formal definition: Mean frequency in Hz is calculated with both:

as the time-derivative, and

as the frequency-derivative of frequency f.
Note that the mean is of the squared spectral derivative. A similar result could be obtained with power, but empirically, we find the derivative to be
The mean feature replaces the peak frequency.
Note that in contrast to peak-frequency, mean frequency provides a smooth estimate of the center of derivative power. In contrast to peak frequency, mean-frequency does not ‘stick’ to any frequency trace, as shown in the example above.