Matematika

Kalkulačka rozptylu

Variance & Standard Deviation

Dataset

What is Variance Calculator?

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Rozptyl měří, jak rozložené hodnoty dat jsou od jejich průměru. Směrodatná odchylka je druhá odmocnina rozptylu a je ve stejných jednotkách jako původní data.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

Vzorec

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f(x)Rozptyl populace: σ² = Σ(xᵢ − μ)² / N

Variable Legend

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Symbol	Jméno	Jednotka	Popis
N	N value	—	Variable used in the calculation

How to Variance Calculator

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1Population variance: σ² = Σ(xᵢ − μ)² / N
2Sample variance: s² = Σ(xᵢ − x̄)² / (n−1)
3Use n−1 (Bessel's correction) for sample data
4Standard deviation σ = √variance

Worked Examples

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Example 1

Given:Dataset: 2, 4, 4, 4, 5, 5, 7, 9 (n=8)

Výsledek:Mean = 5; Variance = 4; SD = 2

Real-World Applications

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Academic homework and exam preparation

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Engineering and architecture calculations

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Everyday measurement tasks around the home

Interpreting Standard Deviation

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Data range	Contains approx...	Empirical rule
Mean ± 1σ	68% of data	Normal distribution
Mean ± 2σ	95% of data	Normal distribution
Mean ± 3σ	99.7% of data	Normal distribution
Beyond ±3σ	0.3% of data	Potential outliers

Frequently Asked Questions

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What is Variance?

Variance measures how spread out data values are from their mean. Standard deviation is the square root of variance and is in the same units as the original data

How accurate is the Variance calculator?

The calculator uses the standard published formula for variance. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Variance calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Variance calculator use?

The core formula is: Population variance: σ² = Σ(xᵢ − μ)² / N. Each step in the calculation is shown so you can verify the result manually.

References

›Variance — Khan Academy

Deep Dive

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Standard Deviation vs Variance

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Reviewed October 2026

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