Sometimes that's better. I think the more important point is that knowledge of the underlying distribution -- normal (Gaussian), log-normal, exponential, power

Sometimes that's better. I think the more important point is that knowledge of the underlying distribution -- normal (Gaussian), log-normal, exponential, power law, Weibull, etc -- is very important. The more skewed the underlying distribution, the less relevant the mean becomes -- and it can cause you to make some very bad inferences.