Hey ~berserk.

Hint: The variance of Var[X_bar] = Var[X]/N (N is the number of items in the sample) which implies SE(X_bar) = SE(X)/SQRT(N).

However since you are looking at the total number of institutions you are looking at Var[Sum of X's] = N*Var[X] which gives a standard deviation of SQRT(N)*SE(X).