  Scatterplots can encode a third dimension by using additional channels like
size or color (e.g. bubble charts). We explore a potential misinterpretation of
trivariate scatterplots, which we call the weighted average illusion, where
locations of larger and darker points are given more weight toward x- and
y-mean estimates. This systematic bias is sensitive to a designer's choice of
size or lightness ranges mapped onto the data. In this paper, we quantify this
bias against varying size/lightness ranges and data correlations. We discuss
possible explanations for its cause by measuring attention given to individual
data points using a vision science technique called the centroid method. Our
work illustrates how ensemble processing mechanisms and mental shortcuts can
significantly distort visual summaries of data, and can lead to misconceptions
like the demonstrated weighted average illusion.
