Re: collection of mathematically elegant tricks

One of the neat tricks is used in showing that the sum of squares about a constant is minimized when that constant is the average. It can be demonstrated by calculus, but I find the algebraic proof to be more elegant.

Sum(xi-c)^2 = Sum(xi-xbar)^2 + N*(c-xbar)^2.

Since N*(c-xbar)^2 >/= 0, it follows that Sum(xi-c)^2 is minimzed for c = xbar.

Jack
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