One can obviously map a set of real numbers $x_1, x_2, \ldots x_N$ to a curve in 2-D via $y=(x-x_1)(x-x_2)\ldots(x-x_N)$.
Thinking about data visualisation, one can portray a set of $N$ observations as a curve in 2-D. Imagine you have several sets of observations and want to eyeball the difference between them, other than with a histogram.
Since data often comes as sets of real numbers (or "factors", or "levels"), rather than as complex numbers, polynomial projection via real roots seems to be a less-than-ideal solution. Worse, important statistical differences (mean, modes, moments) don't jump out much more than unimportant differences.
Is there a better way to project these sets onto curves?
