In general what is the expectation of the sum of yi minus ybar squared

$\displaystyle E(\sum( y_i - \bar{y})^2) = E(\sum( y_i^2 - 2\bar{y}y_i + \bar{y}^2)) = $

$\displaystyle E(\sum y_i^2 -\sum \bar{y}^2)) = \sum E(y_i^2) -\sum E(\bar{y}^2)$

is this the same as the sum of of VAR(Y)?