Yes, unfortunately that’s exepcted, I made the example of the mean in the issue linked above. As @Sukera pointed out, tracking correlation is hard. It’s pretty easy to write a package to propagate uncertainties super quickly ignoring correlations, this is what Measurements.jl did until v0.02, but that’s also incredibly dumb and useless: almost no identies would hold, for example x + x and 2 * x would give you different results.
Regarding the mean in particular, note that most of the time users want to compute the weighted mean, for which Measurements.jl provides a specific function, which should have much more reasonable performance. Note that it ignores correlation, as warned in the docstring, because you’d usually apply to a sample of independent measurements anyways.
To be clear, Measurements.jl is slow because of an algorithmic limitation: it uses an O(n^2) algorithm to propagate uncertainties, you can understand why mean/sum are particularly bad, and get worse and worse as the size of the vector increases. There may be clever ways to reduce the complexity of the algorithm, but I never had the time to look at it. I believe the Python package uncertainties now has an algorithm which is O(n), or anyways better than O(n^2), but until a few years ago it was using basically the same algorithm as Measurements.jl (well, historically it’s the other way around). If anyone is willing to help, I’d be glad to hear from them.