Variance Calculator
Verified Calculation Engine
The online Variance Calculator helps you calculate instantly and solve problems related to Statistics. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Calculates the variance (average of squared differences from mean) of a set of numbers.
Variance = Σ(x - μ)² / n
Variance equals average of squared differences from mean
Inputs
Results
Worked Examples
Example 1: Simple Data
Calculate variance: 10, 20, 30, 40, 50
- numbers: [ 10, 20, 30, 40, 50 ]
- variance: 200
Example 2: Different Values
Calculate variance: 2, 4, 6, 8, 10
- numbers: [ 2, 4, 6, 8, 10 ]
- variance: 8
About this calculator
Overview
This variance calculator measures how spread out numeric data are around their mean.
When to use
Use it in statistics coursework or data summaries where variance or related spread metrics are required.
Formula / method
Population variance uses ÷ N; sample variance uses ÷ (N − 1) when the calculator is configured for a sample estimator. Each term is (xᵢ − mean)².
Worked example
For values near a mean of 5, larger squared deviations increase variance; identical values produce variance 0.
Interpreting results
Higher variance means greater dispersion. Standard deviation is the square root of variance.
Assumptions
- Uses the population or sample convention implemented by this calculator.
- Inputs are numeric.
Limitations
- With very few points, sample variance is unstable.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Population variance uses ÷ N; sample variance uses ÷ (N − 1) when the calculator is configured for a sample estimator. Each term is (xᵢ − mean)².
Example Calculation
For values near a mean of 5, larger squared deviations increase variance; identical values produce variance 0.
Frequently Asked Questions
What is Variance Calculator?
- This variance calculator measures how spread out numeric data are around their mean.
How does Variance Calculator work?
- Population variance uses ÷ N; sample variance uses ÷ (N − 1) when the calculator is configured for a sample estimator. Each term is (xᵢ − mean)².
Why use this Math Numbers calculator?
- Use it in statistics coursework or data summaries where variance or related spread metrics are required.