Variance is an essential component of statistics and represents the variability of a data series about its mean. In this article, you will have an online calculator to obtain the variance and its calculation procedure at your disposal.

## Variance Calculator

## What is variance?

Variance is a measure of dispersion that evaluates how far each number in a data set is from its average. The variance is equal to the square of the standard deviation.

The formulas for calculating population and sample variance are given below:

#### (a) Population Variance:

#### (b) Sampling Variance:

Where:

: Population Variance.**Ïƒ**^{2}: Sampling Variance.**s**^{2}: Mean.**xÌ„**: Number of evaluated values.**N**: Each one of the values.**x**_{i}

Variance plays a central role in statistics, in topics such as descriptive statistics, hypothesis testing, statistical inference, Monte Carlo sampling, etc.

## How to use the online variance calculator?

To use the online variance application, you should follow the steps below:

- Select the decimal separator and the data separator.
- Enter the values of the data set.
- Click on Solve.
- At the bottom of the form, you will be able to visualize the variance calculation procedure.

An example is shown below:

### Example of variance calculation

Calculate the sample and population variance of the following data: 10, 12, 13, 16, 16, 9, 8, 8, 12, 8, 6, 16.

#### Solution

We record the data set:

Pressing the Solve button will show the procedure:

**Population Variance:** 11.4722

**Sample Variance:** 12.5152

**Population Standard Deviation:** 3.3871

**Sample Standard Deviation:** 3.5377

**Mean:** 11.1667

**Count of Data:** 12

According to the data of the problem we have:

110*Î£xáµ¢*Â =Â10*N*Â =Â110/10 = 11*xÌ„*Â =Â

x_{i} |
x_{i} – xÌ„ |
(x_{i} – xÌ„)^{2} |
---|---|---|

10 | -1.1667 | 1.3612 |

12 | 0.8333 | 0.6944 |

13 | 1.8333 | 3.361 |

16 | 4.8333 | 23.3608 |

16 | 4.8333 | 23.3608 |

9 | -2.1667 | 4.6946 |

8 | -3.1667 | 10.028 |

8 | -3.1667 | 10.028 |

12 | 0.8333 | 0.6944 |

8 | -3.1667 | 10.028 |

6 | -5.1667 | 26.6948 |

16 | 4.8333 | 23.3608 |

Î£xáµ¢ = 134 | xÌ„ = 134/12 = 11.1667 | Î£(xáµ¢ – xÌ„)Â² = 137.6668 |

At the bottom of the solution, you will find the option to copy the link to the problem to see the calculated results without re-entering the data. You can share this link with a colleague.

Finally, you can calculate other measures of dispersion and central tendency using the following options:

- Online application of the average deviation.
- Online calculator for standard deviation.
- Online calculator for mean, median, mode, and range.

## Final Reflection

Our variance calculator is an effective tool for students learning statistics and looking for a way to measure variance. This tool will help you better understand the concept of this metric.