René Andrae has given the astronomy community a great paper, not to be published, but definitely to be read, about:
Error propagations, means, medians, maximum likelihood points, thresholds, marginalisations, etc. all are nuances that everyone should be clear about, but that most of us are sometimes a little confused about if we are to be honest.
This is a great concise reference paper that comes in very handy, and is highly recommended. Thank you René.
A sister paper, critical of usual practice is this paper by Hogg, Bovy & Lang.
If you want to delve further into the subject of statistical inference, this book: Information Theory, Inference, and Learning Algorithms by David McKay (available for free on the author’s website) is the next step.