My understanding is that "average" is not unambiguous. Strictly speaking, it can be:
- the (arithmetic) mean, which is how laypeople generally understand it,
- the mode, or
- the median.

In statistics classes, they tell you to make sure you know what the definition of "average" is in any given case.

Well, by giving the mean recovery rate plus/minus standard deviation in parentheses (x % +/- y), I thought it is clear that this can only be the average rate (as defined by the arithmetic mean; summing up the individual rates divided by the number of individuals), without stating that it is the mean and without giving any further explanation.

I agree with SD3: as I learnt in my schooldays, "average" can mean either the mean, the median or the mode and is therefore to be avoided unless clearly defined.

Hm, this is obviously different in German, where you are taught that the average (Durchschnitt) is the same as the arithmetic mean, but mode and median are, by definition, something different.

Anyway, if you mentioned the mean (recovery rate) in a text, and you stated the amount recovered earlier (where you presented the results) as 88 % +/- 9.5% for example, you would expect that the reader understands what is meant by 'mean' recovery rate, wouldn't you? Changing it to average recovery rate wouldn't make it clearer as I understand you.

Yes, "average" is ambiguous but "mean" is unambiguous. If the proofreader wants you to delete mean and write average instead, it might be wise to refuse.

("Ohne Gewähr": I am neither a scientist nor a mathematician.)

"Schon gut", danke :-) I think it would be wise to delete the word 'mean'. I just asked myself whether the reader would want me to use 'average' instead of 'mean' ...