Introduction to Research Design and Statistics
Proving that the sum of squared deviations about the sample mean is a minimum
Show that Σ(X - c)2 is a minimuum when c = 
.
Differentiate with respect to c.
Set derivative to zero and solve for c.
Let's try a different tack, suppose there is some value other than the sample mean,
say (+c), for which the sum of squared deviation is a minimum. We will crank on the formula
algebraically and see what happens.
For any value of c different from zero the sum of squared deviation about this point,
(+c), will be greater than
the sum of squared deviations about .
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Phil Ender, 14sep0498
