# Thread: Why is this zero?

1. ## 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?

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