The 95% of non-normally distributed points around a mean/median

Question

I asked users to tap a location repeatedly. To calculate the size of a target in that location, such that 95% of users will hit that target successfully, I usually measure 2 std of the tap offsets from the centroid. That works if the tap offsets are normally distributed, but my data now is not distributed normally. How can I figure out the equivalent of a 2 std around the mean/median?

Answer 1

If you're only measuring in one dimension, the region encompassed by +/-2 std in a Normal distribution corresponds fairly well to the central 95% of the distribution. Perhaps it's worth working with quantiles instead - take the interval corresponding to that within the 2.5th and 97.5th percentiles - this will be robust to skew or any other departure from normality.