I keep hearing kurtosis described graphically as the “thickness of the tails”, but I know I’m not alone in finding this unhelpful when looking at histograms and trying to determine whether something is lepto- or platykurtic - even with a Normal distribution drawn on top for comparison.

I personally prefer Wikipedia’s description which describes kurtosis as the measure of “peakedness”, rather than the “thickness” of the “tails”. When looking at a uniform or multimodal distribution, the concept of tails isn’t really useful for me. But I can see when a distribution looks more or less peaked in the middle, or wider toward the top. Try looking at the following graph with that in mind and see what I mean:

Also this:

Hope someone else finds that useful! If you have any tips of your own please share.