**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 |

## Recommended Posts:

- Construct Pushdown automata for L = {0
^{n}1^{m}2^{(n+m)}| m,n ≥ 0} - Univariate, Bivariate and Multivariate data and its analysis
- Mathematics | Law of total probability
- Mathematics | Probability
- Scales of Measurement
- Cauchy's Mean Value Theorem
- Mathematics | Probability Distributions Set 4 (Binomial Distribution)
- Mathematics | Probability Distributions Set 3 (Normal Distribution)
- Mathematics | Probability Distributions Set 2 (Exponential Distribution)
- Finding nth term of any Polynomial Sequence
- Mathematics | Probability Distributions Set 1 (Uniform Distribution)
- Mathematics | Limits, Continuity and Differentiability
- Mathematics | Matrix Introduction
- Mathematics | Conditional Probability
- Mathematics | Mean, Variance and Standard Deviation

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.