Variance Calculator

The Variance Calculator helps you measure how spread out a set of numbers is. Enter your values, choose population or sample variance, and get your result instantly. It’s useful for students, teachers, researchers, and anyone working with statistics or data analysis.

Enter your data to calculate population or sample variance, standard deviation, and other useful statistics.

Enter your numbers

Separate values with commas, spaces, semicolons, or new lines. Positive numbers, negative numbers, and decimals are supported.

Variance type

Use population variance when your data includes the entire group. Use sample variance when your data represents a sample.

Decimal places

Try an example

Calculation Result

Your variance and summary statistics will appear below.

Population Variance

8.00

Number of values 5

Mean (average) 6.00

Standard deviation 2.83

Sum of values 30

Minimum value 2

Maximum value 10

Variance Formula

Population: σ² = Σ(x − μ)² / N
Sample: s² = Σ(x − x̄)² / (n − 1)

Calculation Details

Mean = 6.00. Sum of squared deviations = 40. Population variance = 40 / 5 = 8.00.

Population variance divides the sum of squared deviations by N. Sample variance divides it by n − 1. Sample variance requires at least two values.

What Is Variance?

Variance is a statistical measure that tells you how much a set of numbers differs from its mean (average). A low variance means the values are close to the average, while a high variance means they are more spread out.

Variance is commonly used in statistics, research, education, finance, and data analysis to understand the consistency and distribution of data.

Population Variance vs. Sample Variance

There are two main types of variance:

Population variance: Used when your data includes every member of the population you want to study. The sum of squared differences from the mean is divided by the total number of values, (N).
Sample variance: Used when your data represents a sample from a larger population. The sum of squared differences is divided by (n-1), helping account for the uncertainty of estimating population variance from a sample.

How to Use the Variance Calculator

Enter your numbers in the input box. Separate them with commas, spaces, or new lines.
Choose Population Variance or Sample Variance, depending on your data.
Select the number of decimal places you want to display.
Click an example button to try a sample dataset, or enter your own values.
View the calculated variance along with useful statistics such as the mean, standard deviation, sum, minimum, and maximum.

Example of Variance Calculation

Consider the numbers 2, 4, 6, 8, 10.

First, calculate the mean:

\displaystyle \text{Mean}=\frac{2+4+6+8+10}{5}=6

Next, find the squared differences from the mean:

\displaystyle (2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2=40

For population variance, divide by 5:

\displaystyle \text{Population Variance}=\frac{40}{5}=8

For sample variance, divide by \(5-1=4\):

\displaystyle \text{Sample Variance}=\frac{40}{4}=10

So, the population variance is 8, while the sample variance is 10.

Why Is Variance Important?

Variance helps you understand the spread and consistency of data. It can be used to compare datasets, study changes in performance, evaluate financial risk, and analyze experimental results.

For example, if two classes have the same average test score but different variances, the class with lower variance has scores that are more closely grouped around the average.

Variance Calculator