In the following summation:
${\sum_{i=1}^{N}\left(x_{i}-\bar{x}\right)^{2}}$
Do I first add all the $x_i - \bar{x}$ then I square the sum?
Or do I square each $x_i - \bar{x}$ as I add them up?
Sorry for the silly question -- but the syntax is confusing me if the square is included in every iteration of the sum or just at the end...
Square each $x_i-\bar x$ as you add them up.
The summand is $(x_i-\bar x)^2$.
For the first case, the sum would look like this:
$$\left(\sum_{i=1}^{N}(x_{i}-\bar{x})\right)^{2}$$
(and will equal to zero:)
$$\left(\sum_{i=1}^{N}(x_{i}-\bar{x})\right)^{2} = \left(\sum_{i=1}^{N}x_{i}-\sum_{i=1}^{N}\bar{x}\right)^{2} = \left(N\bar x-N\bar x\right)^{2}=0$$
