[T_D_K]

I've never heard this before, and a skim of the wiki page doesn't mention it as a prerequisite. Mind explaining? The scores are just integers, so the addition is well defined. So you're saying that the context is what's relevant?

Not that the mean is the only (or even the most useful) statistic.

[svantana]

Well, take decibels for example. They are a log scale physical intensity, so averaging them make no sense whatsoever (e.g. absolute silence is negative infinity dB). I would argue these scores are more like labels than actual numbers (i.e. a 3 plus a 5 doesn't really equal an 8 in any real sense). You can of course take the mean of any collection of numbers, but I've heard many a statistician lament such careless practices. The median is at least more easily interpreted for cases like this.

[T_D_K]

Ah, thanks. The decibels example makes sense (an alternative would be to take the log first, and then convert it back after averaging?), and I can see how the 0-10 system can also be viewed as categorical rather than discrete.

[kakkun]

It's because the NPS rating numbers are ordinal, meaning that you can put the rating numbers in order, but the likelihood gap between the numbers may not be equal.

For example, 6 on the NPS scale would be less likely to recommend compared to 7 and 7 would be less likely than 8. However, the gap between 6 and 7 and the gap between 7 and 8 may not be equal. If you were to get the mean of 6, 7, and 8, you would get a value of 6, but there is no guarantee that the average of the participants' likelihood to recommend was actually equal to a 6.

Measuring the mean would work if the interval between the numbers were equal. See here for details: https://en.wikipedia.org/wiki/Level_of_measurement