But means and standard deviations are the results of modeling a gaussian distribution, and if the model fit is too bad, these metrics simply don't apply for this dataset.

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Means and standard deviations are general properties one can compute for any statistical distribution which doesn't have pathologically fat tails. (Granted, it would've been conceptually cleaner for Yvain to present the mean & SD of log donations, but there's nothing stopping us from using his mean & SD to estimate the parameters of e.g. a log-normal distribution instead of a normal distribution.)