Re: power law distributions. I'm not sure what you mean about finite versus infinite variance. Are you referring to whether you are analyzing a bounded versus u

Re: power law distributions. I'm not sure what you mean about finite versus infinite variance. Are you referring to whether you are analyzing a bounded versus unbounded scale? Even if a scale is unbounded, that still wouldn't make a dataset any more likely to power law distributed. A power law distribution would be, however, somewhat more likely to be observed in cases where there is only an upper- or lower-bound (though again, not always... it really depends). Re: appropriate averages. Your case (metered billing) is an interesting one. I don't see why the mode is necessarily wrong - the next customer is most likely to spend the amount that is currently your most popular amount). However, in order to calculate a mode, you likely would want to bin your amounts into ranges so that $10.11 isn't treated as distinct from $10.12, etc. You're definitely right about one summary statistic not being sufficient. I would advocate for visualization and summary statistics, with some estimate of your confidence in the estimate displayed visually.