  Idealized probability distributions, such as normal or other curves, lie at
the root of confirmatory statistical tests. But how well do people understand
these idealized curves? In practical terms, does the human visual system allow
us to match sample data distributions with hypothesized population
distributions from which those samples might have been drawn? And how do
different visualization techniques impact this capability? This paper shares
the results of a crowdsourced experiment that tested the ability of respondents
to fit normal curves to four different data distribution visualizations: bar
histograms, dotplot histograms, strip plots, and boxplots. We find that the
crowd can estimate the center (mean) of a distribution with some success and
little bias. We also find that people generally overestimate the standard
deviation, which we dub the "umbrella effect" because people tend to want to
cover the whole distribution using the curve, as if sheltering it from the
heavens above, and that strip plots yield the best accuracy.
