Nice little paper, although maybe a little stilted. It's a good idea to think about these basic quantities a bit more deeply and why you might want to use one measure of central tendency more than another. It's good to have a solid rationale for it, and I thought this was a nice brief overview of some perspectives I wasn't aware of.

For some reason I thought the mean could be thought of as a single number that is most representative of a sample or population in an information loss (algorithmic/kolgomorov complexity, maybe relative entropy?) sense, or maximum likelihood sense (maybe under some distributional constraints?). I might be misremembering that though, and it's difficult to figure out the right search terms to track it down.