The definition of covariance is
Cov(x, y) = E[ (X-E(X)) * (Y-E[Y]) ]
where E is abbreviation of expectation. It is same with Mean.
X = [1 2 3 4 5];
E(X) -> 3 or 3.75
3 is the result of "sum(X)/5"
3.75 is the result of "sum(X)/(5-1)"
In the statistics, mean is divided by N-1 to avoid outlier data affection.
*Example of Covariance
X = [ 2 3 4 2 1 4]
Y = [ 2 4 2 1 6 8]
meanX = sum(X) / 6 -> 2.667
(X - meanX) -> [-0.6667 0.3333 1.3333 -0.6667 -1.6667 1.3333]
(X - meanX) * (X -meanX) -> [ 0.4444 0.1111 1.7778 0.4444 2.7778 1.7778]
cov(x, x) -> sum( ( (X - meanX) * (X -meanX) ) ) / (N-1)
cov of X, Y is like that
-> cov(x,x) cov(x,y)
-> 1.4667 0.5333
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