If you need **calculate the variance of a data set**our online calculator allows you to obtain the result immediately.

All you have to do is **write each number separated by spaces or by a comma**. If you are going to enter a decimal number, you will have to use the point as decimal separator (example: 3.14).

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## What is variance

The **variance (σ ^{2}) of a random variable** is a measure of dispersion used in probability theory and is defined as the expectation of the square of the deviation of that variable from its mean.

Variance can also be defined as the **arithmetic mean of the square of the deviations from the mean** of a statistical distribution.

Finally, we can look at the variance as the square of the standard deviation.

## Variance formula

For **to calculate the variance, the following formula must be applied** mathematics:

## How to calculate the variance

To calculate the variance in a simple way, the following steps can be followed:

- Calculate the average or the average of the numbers involved.
- Subtract the average obtained from each number and square the result.
- Calculate the average of the previous results.

That way you can calculate the variance in a simple and fast way.

## Solved exercise to calculate variance

Imagine that we have the following set of numbers and we want to **to obtain the value of the variance**:

2, 4, 6, 8, 10

We will follow the steps seen in the previous step one by one, therefore, **the first thing we must do is to obtain the arithmetic mean** of the set of values:

x̄ = (2 + 4 + 6 + 8 + 10) / 5 = 6

The next step consists of **subtract the value of the average from each number** we have obtained and square it:

(2 – 6)

^{2}= 16(4 – 6)

^{2}= 4(6 – 6)

^{2}= 0(8 – 6)

^{2}= 4(10 – 6)

^{2}= 16

The following **we calculate the average of the previous results**which will give us the variance:

σ

^{2}= (16 + 4 + 0 + 4 + 16 ) / 5 = 8

Easy, isn't it?

## Calculate variance in Excel

As it could not be otherwise, we can also calculate the variance in Excel. To do so, we can make use of several functions depending on what we want to calculate.

If what we want is to calculate the variance as a function of the entire population, ie, **all arguments represent the total population**then we have to use the following function:

=VAR.P()

If, on the other hand, we find that** data represent a sample of the population**then we will have to use the following formula in excel that will give us as a result the **sample variance**:

=VAR.S()

## Sample variance

When we talk about **sample variance** we are taking into account the calculation of the variance from a sample and not from the entire total population.

In this case, we have to **apply the following mathematical formula**: