yup, thanks so much! do you have any ideas for thinking about the standard error of the grand mean?

(the above only comment only holds if we are sampling x and y without replacement).

returning to this, i don't quite see how the subsequences are iid. imagine that we sample three latitudes and three longitudes, so we'll have three subsequences, the first would be: [(x_0, y_0), (x_1, y_1), (x_2, y_2)] given the first element in the sequence (x_0, y_0), we know that Pr(x = x_0) = Pr(y = y_0) = 0 for all other x and y in the sequence. how can that be iid?

wow! that's such a great approach!