Title: standard deviation
Long Title: IUPAC Gold Book - standard deviation
DOI: 10.1351/goldbook.S05911
Status: current

Definition
The positive square root of the sum of the squares of the deviations between the observations and the mean of the series, divided by one less than the total number in the series. The standard deviation is the positive square root of the variance, a more fundamental statistical quantity.

Related Term
- deviation: https://goldbook.iupac.org//terms/view/D01650

Source
- Orange Book, 2nd ed., p. 5 (https://media.iupac.org/publications/analytical_compendium/)

Related References
- PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2216 (https://doi.org/10.1351/pac199062112167)
- PAC, 1994, 66, 595. 'Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)' on page 599 (https://doi.org/10.1351/pac199466030595)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/S05911/html
- json: https://goldbook.iupac.org/terms/view/S05911/json
- xml: https://goldbook.iupac.org/terms/view/S05911/xml

Citation: Citation: 'standard deviation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.S05911
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Accessed: 2026-07-25T07:14:36+00:00