You probably want a more expert answer, but just from my experience working with similar data -

In general I don't think it's necessary to "prove" that the mean signal is representative, and I don't know how this would be done. A couple of ways you could argue it, are:

1. Show the mean and median are similar. This shows the mean isn't being biased by some crazy outliers.

2. Do some kind of analysis to find how many samples are outliers.

Since these are time-series I'm not sure how you'd approach it (e.g. calculate at every time point, a representative time point etc.). Also this doesn't "test" for representativeness in terms of giving you a p-value. But I would guess it's enough to show the data, plot the mean overtop, (or otherwise present the distributions), and demonstrate it that way.

My two cents.