# Why is this zero?

• Feb 16th 2010, 04:11 PM
zhupolongjoe
Why is this zero?
I am reading my text, and they make a jump that I don't understand, and they don't give any explanation for it.

Sorry, I couldn't figure out how to put this stuff in latex...
mu=mean....greek letter (in particular, not m*u)

It gives the sum from i=1 to n of (xi-x bar)^2 + 2*(x bar-mu)*sum from i=1 to n of (xi-x bar)+n(x bar-mu)^2

It then says that this is equal to

sum from i=1 to n of (xi-x bar)^2 + n(x bar-mu)^2

Essentially they seem to be saying that

2*(x bar -mu)*sum from i=1 to n of (xi-x bar)
is zero

Is it because x bar- mu is 0? I didn't think this was the case......why is this middle term zero?
• Feb 16th 2010, 04:22 PM
matheagle
The sum is zero, NOT *(x bar -mu)*

$\sum_{i=1}^n(x_i-\bar x)= \sum_{i=1}^nx_i- \sum_{i=1}^n\bar x=n\bar x-n\bar x=0$

Because ${\sum_{i=1}^nx_i\over n}=\bar x$
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