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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 
.
, 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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