The covariance cov(x;y) well describes the degree of variation of two variables X and Y, but it has a serious drawback:
it is dependent on the scale of the variables and their variance.
Especially in the social studies compareable measurement scales cannot always be found. As an example the values for the variables intelligence (0-35 points) and school performance (0-9 points) obviously differ much. We already know one measure to make the two compareable: the transformation to standard-z-values.
If we relate the covariance cov(x;y) to the product of the standard deviation of X and Y, the differences in scale and spread are compensated for. |

This formula is equal to:

Both variables X and Y are being z-transformed here.
bzw. 
The covariance of the z-transformed values of the variables X and Y
look like this:
  
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