standard deviation is misleading for non-standard distributions (fat-tailed, skewed, multi-modal, ...)
replycommon mistake people make
Not really. It's still the standard deviation, and it still gives you bounds on probability, for example the Chebyshev inequality:
replyP(|X-\mu| > k \sigma) < 1/k^2.
So, while for a normal RV, 5% of observations lie outside +/- 1.96 std.devs, for arbitrary RV (with finite variance) at most 25% of observations lie outside +/- 2 std.devs.