Co-Variance in Statistics easily explained with Toy example

Co-Variance:

Lest take a random Variables [Heights , Weights]

height   weight
120cm    50
130cm    60
150cm    80
.
.
.
140cm    75
130cm    65

Co-variance Quantify relationship between 2 Parameters i.e.

If Height Increase and Weight also Increase

If Height Decrease and Weight also Decrease

[Positive Co-Variance]

If Height Increase and Weight Decrease

If Height Decrease and Weight Increase

[Negative Co-Variance]

Mathematical Formula is represented as :

Note : Cov(X,Y) = Var(X)

Co-Variance [2 variable] & Variance [1 variable]

So now lets focus on our height and weight example:

height   weight
120cm    50
130cm    60
150cm    80
.
.
.
140cm    75
130cm    65

So first calculate mean of both features (height and weight): So ,mean of height = 135 , mean of weight = 66.25.

And mathematical formula of Co-Variance is:

Covariance (height, weight) = (xi-mean)*(yi -mean)

Covariance (height, weight) = (120–135)*(50–66.25) = (-15) * (-16.25)

i.e. Xi and Yi both are negative that means positive Co-Variance.

Drawback of Co-Variance:

X (increase) and Y (increase) = positive Co-Variance (But it do not says how much positive)
X (Increase) and Y (Dec) = Negative Co-Variance (But it do not says how much Negative)