Why is variance expressed in squared units?

Because we square the difference of each number from the mean to prevent positive and negative differences from canceling each other out. This causes variance to have squared units (e.g., square dollars), which is why standard deviation (the square root of variance) is often preferred for interpretation.

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance, and variance is the square of standard deviation.

Statistics Tool

Variance Calculator

Calculate sample and population variance online. See the step-by-step squared deviations, mean, and standard deviation outputs.

Interactive Variance Calculator Workspace

Live Solver

Dataset Values (separated by commas or spaces)

Calculated Variance (sample)62.5

Step-by-Step Variance Solution

Dataset Mean (Average) = 15.0000

Step 1: Calculate distance from mean for each number, and square it:
(5 - 15.00)² = (-10.00)² = 100.0000(10 - 15.00)² = (-5.00)² = 25.0000(15 - 15.00)² = (0.00)² = 0.0000(20 - 15.00)² = (5.00)² = 25.0000(25 - 15.00)² = (10.00)² = 100.0000

Step 2: Sum all squared values:
100.00 + 25.00 + 0.00 + 25.00 + 100.00 = 250

Step 3: Divide by the appropriate degrees of freedom (N - 1 = 4):
250.0000 / 4 = 62.500000

Mathematical Formula & Variables

Equation Models² = Σ(x_i - x̄)² / (n - 1) (Sample) or σ² = Σ(x_i - μ)² / N (Population)

Variance measures the average of the squared differences from the mean. It quantifies the degree of spread in a dataset.

Variable Definitions

Symbol	Description
s²	Sample variance
σ²	Population variance
x_i	Each individual value in the dataset
x̄ / μ	Dataset average/mean
n / N	Total count of numbers

How to Use the Variance Calculator

Type or paste your numbers separated by commas or whitespace.
Select Sample or Population calculation mode.
Look at the sum of squared differences, dividing steps, and the final squared variance unit.