> In this particular application, the shapes are the areas between the
> lines created when graphing several time series on a chart (e.g., the
> price of several stocks, graphed over time)

It sounds to me like what you need is actually some kind of line of best fit
rather than a centre. The usual idea is to find a line (if you do want a
point, then this works for a point too) such that the squared distance of
all the points in your region from the line (or point) is minimised. You can
find this by using a correlation coefficient (a quick Google turned up this
page which sums up the process pretty well:
http://helios.bto.ed.ac.uk/bto/statistics/tress11.html). For data in more
than two dimensions you'll need to use a more complicated process called
principal components analysis.

Best
Danny

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