If I'm understanding your question correctly, you want to quantify how well your data fits a model distribution (in this case, a normal distribution). In the data you show, the OK data is highly leptokurtic but symmetrical whereas the bad data would be poorly described by any measure of central tendency. See (Spiegelhalter, D.J., 1980, An omnibus test for normality for small samples. Biometrika, 67, p493–496. ) for an approach that quantifies how well your data fits the normal distribution versus how well it fits other candidate distributions in terms of Bayes Factor.

Brandon S Perelman Thanks for your suggestion. Let me find this paper and check more details.