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Variance and Standard Deviation Calculator — result sheet
Calculate population and sample variance and standard deviation from a numeric list.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Population variance = Σ(x−μ)²/n; sample variance = Σ(x−x̄)²/(n−1); standard deviation is the square root.
Both denominator conventions are shown because a complete population and a sample used to estimate a population have different variance definitions.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Numbers — Enter 2–1,000 finite numbers separated by commas or spaces.
Worked example
| Input | Value |
|---|---|
| Numbers | 2, 4, 4, 4, 5, 5, 7, 9 |
Mean = 5; population variance = 4; sample variance ≈ 4.571; sample SD ≈ 2.138.
Assumptions and limits
- The list contains at least two finite real observations.
- Sample variance uses Bessel’s correction with n−1.
- The values are treated as equally weighted observations.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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