**Link**: Mean, variance and standard deviation

## What is covariance?

**Covariance** measures **variables in pair**. It can tell us the relationship of the variable and how much it change together.

### A simple example

Instead of picking mRNAs from 5 cells in Gene X, we pick them from 5 cells in Gene X and Gene Y. The result could be, high mRNAs number in X can also have high number in Y, which is, there’s a **positive trend** where the values for X and Y increase together.

### Three types of relationships

- Positive trend
- Negative trend
- No relationship and no trend

### Covariance and correlation

Covariance is needed for Correlation. Unlike covariance, **correlation** is not sensitive to the scale of the data.

## How to calculate covariance

A positive covariance: positive trends, and vice versa.

### Understand and interpret the covariance value

We can only sure of its trend by positive/negative. It’s hard to inteprete its high/low value because it all depends. Besides, **covariance values** are sensitive to the scale of the data.

Due to this reason, **covariance** itself is not so useful, but its other results (**correlation** or PCA) would be more interesting and useful.