Why is sum(sum(xy)/sum(x))/n approximately equal to sum(sum(xy))/sum(sum(x))?

Question

Mathematics

Why is sum(sum(xy)/sum(x))/n approximately equal to sum(sum(xy))/sum(sum(x))? X and Y are two-dimensional matrices of size [nxm]

Answer 1

There must be some specific properties of the matrix given. Otherwise, it is nifiga approximately equal. For example,
X= {{1, 5}, { 1, 5}}, Y={{5, 1/5}, {5, 1/5}}
on the left it will give: 1/2 (10/2 + 2/10) = 1/2 (5 + 0.2) = 2.7
and on the right: (5+5+1+1)/(1+5+1+5) = 1
In general, it is not even close. By changing the 5 in the matrix above to an arbitrarily large number, you get an arbitrarily large difference.

Answer 2

Why didn't the teacher explain? expand both into expressions with brackets and bring back