# Mathematics | Covariance and Correlation

**Covariance** and **Correlation** are two mathematical concepts which are commonly used in the field of probability and statistics. Both concepts describe the relationship between two variables.

**Covariance –**

- It is the relationship between a pair of random variables where change in one variable causes change in another variable.
- It can take any value between -infinity to +infinity, where the negative value represents the negative relationship whereas a positive value represents the positive relationship.
- It is used for the linear relationship between variables.
- It gives the direction of relationship between variables.

**Formula –**

**For Population:**

**For Sample**

Here,

x’ and y’ = mean of given sample set

n = total no of sample

xi and yi = individual sample of set

**Example –**

**Correlation –**

- It show whether and how strongly pairs of variables are related to each other.
- Correlation takes values between -1 to +1, wherein values close to +1 represents strong positive correlation and values close to -1 represents strong negative correlation.
- In this variable are indirectly related to each other.
- It gives the direction and strength of relationship between variables.

**Formula –**

Here,

x’ and y’ = mean of given sample set

n = total no of sample

xi and yi = individual sample of set

**Example –**

**Covariance versus Correlation –**

Covariance | Correlation |
---|---|

Covariance is a measure of how much two random variables vary together | Correlation is a statistical measure that indicates how strongly two variables are related. |

involve the relationship between two variables or data sets | involve the relationship between multiple variables as well |

Lie between -infinity and +infinity | Lie between -1 and +1 |

Measure of correlation | Scaled version of covariance |

provide direction of relationship | provide direction and strength of relationship |

dependent on scale of variable | independent on scale of variable |

have dimensions | dimensionless |

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