00440 IUPAC Gold Book - arithmetic mean 10.1351/goldbook.A00440 A00440 current synonym: average 1 The sum of a series of observations divided by the number of observations. Symbol: \(\bar{x}\). It can be calculated by the formula: \[\bar{x}=\frac{\sum x_{i}}{n}\] All summations are taken from 1 to \(n\). Note that the arithmetic mean is an unbiased estimate of the population mean, i.e. \(\mu\) is the limiting value for \(\bar{x}\), as \(n\rightarrow \infty\). 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) https://goldbook.iupac.org/terms/view/A00440/html https://goldbook.iupac.org/terms/view/A00440/json https://goldbook.iupac.org/terms/view/A00440/plain Citation: 'arithmetic mean' 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.A00440 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-07-25T09:04:54+00:00