Question about COEFFICIENT OF CORRELATION

I've attached an image of a formula for sample correlation. Let's start by focusing on the numerator:

$$n*\sum{xy}-\sum{x}*\sum{y}$$ 

We know that n is 90. Let's calculate the sum of x*y, the sum of x, and the sum of y seperately.

$$\sum{xy} = 1*1*5 + 1*3*20 + 1*5*5 + 9*1*10 + 9*3*10 + 9*5*10 + 25*1*15 + 25*3*0 + 25*5*15  = 3150$$

$$\sum{x} = 1*30 + 3*30 + 5*30 = 270$$

$$\sum{y} = 1*30 + 9*30 + 25*30 = 1050$$

Plugging everything in we get:

$$n*\sum{xy}-\sum{x}*\sum{y} = 90*3150 - 270*1050 = 0$$

Since the numerator is equal to 0, it doesn't matter what the denominator is*, the whole fraction is equal to 0. The correlation is 0.


* unless all of the x's are the same number or all of the y's are the same number, in which case the denomiator would be 0 and the correlation would be undefined.