Below is a *variance calculator*, which will calculate the variance from a list of your numbers. Enter any numbers (including negative numbers or decimals) and the tool will return the variance.

The variance calculator can work either as a *sample variance calculator* or a *population variance calculator*.

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## Variance Calculator

**Table of Contents**show ▼

## What is the Variance of a Set of Numbers?

The variance of a set of numbers is a number representing the ‘spread’ of the set. Formally, it is the squared deviation of a variable in a set from the set’s mean and is the square of the standard deviation.

There are two “types” of variance:

**Sample variance**– the variance from a sample which does not cover the entire possible sample (e.g. a random sample of people).**Usually this is the one you should use!****Population variance**– the variance as measured from an entire population (e.g. all people)

## Variance Formula

As there are two variances, there are also slightly different variance formulas. For both, first compute or estimate or otherwise find the mean or average.

### Population Variance Formula

The formula for population variance is:

Where:

- δ2 = population variance
- N = number in the population
- xi = observation in the population
- μ = the mean in the population

### Sample Variance Formula

The formula for sample variance is:

Where:

- s2 = sample variance
- n = number of observations in the sample
- xi = observation in the sample
- m = the mean of the sample

### Examples of Finding a Variance

Usually time, money, and practicality limit us from looking at an entire population. In that case, we usually take a sample of a whole – let’s walk through computing sample variance for a small sample of human weights.

Let’s say you measure **5** adult men and find they weigh: **140, 170, 200, 210, and 320** pounds. The average of those numbers is **208 lbs**.

Find the difference for each one:

Now, square each number:

Now, add the numbers up and divide by 4 (because we have 5 samples, minus 1 – for a population, you don’t correct and divide by 5):

At this point, you could find the standard deviation (an easier number to reason with in your head!) by taking the square root of the variance of 4670 – 68.3 lbs.

## Using the Variance Calculator

To use the variance calculator, enter all your numbers in the box. The input is quite forgiving – separate numbers with non-numbers and it should work. (Try commas, spaces, new lines, tabs, and the like.) In the **Type** pull-down, devide if you want the variance of a Population or Sample.

When you’re done, hit the **Compute Variance** button and we’ll show you the median of the list. To check we understood, look at the list length in the **Number of Values Input** box.

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