>>12291572Most times any ratio is a comparison between two quantities and therefore a comparison between the concepts behind it.
Regarding the numerator, every xi - x , yi - y is a distance to the x, y average respectively. Notice that there's no squaring for any xi - x , yi - y, then this summation is like an aiming-pointing process right into the centroid (average x, average y) of the whole data
Regarding the denominator: every xi - x , yi - y is, again, a distance to the x, y average respectively. Squaring those differences allows to quantify how dispersed are the data around their centroid (their average) Adding up those squared distances is like calculating a gross separation metric between the data and its centroid (the average)
Therefore, those two summations quantify two different concepts and the ratio is about comparing how packed AROUND THE AVERAGE are the data points (numerator) to how packed are the data points regardless its average (denominator)
