Yes, a both funny and insightful lesson on how weak basic indicators (mean, standard deviation, correlation) can be, the interest and limits of box-plot with quartiles and whiskers, the benefit of the violin-plot.
> For the median and average to be equal, the points less than the median and greater than the median must have the same distribution (i.e., there must be the same number of points that are somewhat larger and somewhat smaller and much larger and much smaller).
[0, 2, 5, 9, 9] has both median and mean = 5, but the two sides don't really have the same distribution.
Totally true...thoughts on how I could rephrase? I guess it's more the "weight" of points greater than and less than the median should be the same, so symmetric distributions definitely have it, asymmetric may or may not. Definitely open to revising...
https://www.autodesk.com/research/publications/same-stats-di...