# Variance Calculator Online (Sample and Population)

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.

## 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:

• σ2: Population Variance.
• s2: Sampling Variance.
• : Mean.
• N: Number of evaluated values.
• xi: Each one of the values.

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:

• Σxᵢ = 110
• N = 10
•  = 110/10 = 11 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:

## 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. 