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Suppose we have a list of numbers
, and we wish to find
some number
that is as close as possible to as many of
the
as possible. To make this a mathematically precise
goal, we need to define some numerical measure of this closeness. Suppose we let
, which can also be notated using
, uppercase Greek sigma, as
. Then minimizing
can be used as a definition of optimal closeness. (Why would we not want to use
?) Prove that the value of
that
minimizes
is the average of the
.











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