Choose Population or Sample

Population

Enter a list of numbers separated by commas, spaces, and/or line breaks to find the variance. The calculator will automatically remove invalid values (such as letters, words, and symbols).

Variance

Standard Deviation

Mean

Sum of Squares

Count

Sum

## How to Use This Calculator

To use this calculator, first, choose whether your data set represents a population or sample.

Next, delete the example set of numbers and enter your data set.

Your data set should be separated by commas:

`1,5.8,-50.98,18926,7509.6506832`

or spaces:

`1 5.8 -50.98 18926 7509.6506832`

or line breaks:

`15.8-50.98189267509.6506832`

or a combination of commas, spaces, and line breaks:

`1,5.8 -50.9818926 20.27509.6506832`

As you enter your data, the calculator will automatically compute the variance, standard deviation, sum of squares, mean, count, and sum of your data.

## What is Variance?

Variance is one way to measure the dispersion of values in a data set from the mean.

More specifically, variance is the average squared difference from the mean.

Low variance means the values in a data set tend to be close to the mean, while a high variance indicates that the values are more widely spread out.

## Population vs Sample

The goal of calculating variance is to measure the dispersion of data points in a population. However, we often only have access to a sample set of data.

When we only have a sample, we must use Bessel's correction to correct for bias in the estimation of population variance.

## How to Calculate Variance

Population variance is calculated by finding the sum of the squared differences between each data point and the mean (sum of squares), divided by the count of the data set (n).

Sample variance is calculated by finding the sum of the squared differences between each data point and the mean, divided by the count of the data set minus 1 (n - 1).

## Variance and Standard Deviation

Calculating variance is crucial for finding the standard deviation of a data set.

Standard deviation is the square root of the variance.