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Population Variance Calculator — result sheet
Calculate the population mean, population variance, standard deviation, and root-mean-square value for five values.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: μ = Σx/N; σ² = Σ(x-μ)²/N; σ = √σ²; RMS = √(Σx²/N).
Population variance divides the squared deviations by N because the five supplied values are treated as the complete population of interest. A sample estimate would use a different denominator.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Value 1 — minimum -1000000000; maximum 1000000000
- Value 2 — minimum -1000000000; maximum 1000000000
- Value 3 — minimum -1000000000; maximum 1000000000
- Value 4 — minimum -1000000000; maximum 1000000000
- Value 5 — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Value 1 | 2 |
| Value 2 | 4 |
| Value 3 | 6 |
| Value 4 | 8 |
| Value 5 | 10 |
Mean: 6; population variance: 8; standard deviation: 2.828.
Assumptions and limits
- The five supplied values are treated as the full finite population, not a sample drawn to estimate a larger population.
- All observations have equal weight and share one measurement unit.
- Variance uses squared units; standard deviation and RMS return to the original unit.
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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