# 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 :

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:

*Co*variance (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)