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