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Variance Calculator

Calculate population or sample variance instantly. Enter your data set to measure how widely your values are spread around their mean.

Calculate Variance

Enter your numerical data and choose the appropriate variance type.

Separate numbers using commas, spaces, or line breaks. Decimal and negative values are supported.
Select Variance Type
Variance Result
0
Mean 0
Data Values 0
Sum of Squared Deviations 0
Variance Type Population

What Is Variance?

Variance is a statistical measurement that shows how far the values in a data set are spread out from their average or mean. A smaller variance indicates that the values are generally close to the mean, while a larger variance indicates greater variation.

Variance is widely used in statistics, mathematics, finance, science, research, business analysis, and data analytics. It helps measure the amount of variability within a group of numerical values.

Variance measures the average squared distance of each value from the mean.

How Does the Variance Calculator Work?

The calculator follows the standard statistical process for finding variance. It first calculates the mean of all values and then measures how far each number differs from that mean.

  1. Enter all numerical values in your data set.
  2. Calculate the mean by adding all values and dividing by the total number of values.
  3. Find the difference between each value and the mean.
  4. Square each difference so negative and positive deviations are treated equally.
  5. Add all squared deviations and divide by the correct denominator.

Variance Formula

Population Variance

σ² = Σ(x − μ)² ÷ N

Population variance is used when your data includes every member of the population being studied.

Sample Variance

s² = Σ(x − x̄)² ÷ (n − 1)

Sample variance is used when your data represents only a sample taken from a larger population. It uses n − 1 as the denominator.

Variance Calculation Example

Consider the following numbers:

2, 4, 6, 8, 10

First, calculate the mean:

Mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 6

Next, calculate the difference between each value and the mean, then square each result:

(2−6)² + (4−6)² + (6−6)² + (8−6)² + (10−6)²

The sum of squared deviations is 40.

Population Variance = 40 ÷ 5 = 8

Population Variance vs Sample Variance

Population variance should be used when you have data for every member of the group you want to study. The calculation divides the sum of squared deviations by the total number of values.

Sample variance is used when you only have a smaller sample taken from a larger population. It divides by one less than the total number of values, which helps provide a better estimate of the population variance.

Frequently Asked Questions

Variance measures how widely the values in a data set are spread around their mean or average.
Population variance divides by the total number of values, while sample variance divides by one less than the total number of values.
No. Variance cannot be negative because the differences from the mean are squared before they are added together.
A variance of zero means that every value in the data set is exactly the same.
No. Standard deviation is the square root of variance. Both measure data spread, but they are expressed differently.
Yes. The calculator supports whole numbers, decimals, positive values, and negative values.