or equally, the mean is the central point which minimises the sum of squares of deviation.

Use least mean square regression?

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- Oct 25th 2007, 07:07 PMchopetHow to prove that the variance about mean is min?
or equally, the mean is the central point which minimises the sum of squares of deviation.

Use least mean square regression? - Nov 2nd 2007, 03:31 AMchopet
hello. anyone here can provide me solutions or give me guidance?

Thanks. - Nov 2nd 2007, 05:37 AMCaptainBlack
Do you mean this:

Show that the mean $\displaystyle \bar{x}$ is the value of $\displaystyle k $ which minimises the second moment of a RV $\displaystyle X$ about $\displaystyle k$?

That is $\displaystyle k=\bar{x}$ minimises:

$\displaystyle

\int (x-k)^2 p(x) ~dx

$

Differentiate wrt $\displaystyle k$ and solve:

$\displaystyle

\frac{d}{dk}f(k)=0

$

RonL