{"term":{"id":"02621","doi":"10.1351\/goldbook.G02621","code":"G02621","status":"current","longtitle":"IUPAC Gold Book - geometric (logarithmic) mean, x_̄g","title":"geometric mean","version":"2.0.2","lastupdated":"2008-10-07","definitions":[{"id":"1","text":"The nth root of the product of the absolute values of the observations, taken with the proper sign. It can be calculated with the formula: x(bar)g =(Π.|xi|)(1\/n) product is taken from i = 1 to n.","notes":{"1":"This quantity is often calculated directly from experimental measurements (e.g. determination of concentrations by electrode potential measurements, or pH), although its significance may not always have been recognized. The problem is that the average value of a variable (such as pH) that is a function of concentration is not the same as the value of the function at the average concentration. In the case of electrode potentials, the average potential is equivalent to the geometric mean concentration. The correct procedure is to transform to units of concentration before averaging. There is one notable case where the geometric mean is appropriate, namely, when the analyte itself is distributed in a log-normal fashion, as in certain environmental and geological samples."},"links":[{"title":"electrode potential","type":"internal","url":"https:\/\/goldbook.iupac.org\/terms\/view\/E01956"},{"title":"variable","type":"internal","url":"https:\/\/goldbook.iupac.org\/terms\/view\/V06600"}],"math":[{"alttext":"x(bar)g =(Π.|xi|)(1\/n)","latex":"\\overline{x}_{\\text{g}}=(\\Pi |x_{i}|)^{\\frac{1}{n}}"},{"alttext":"Π","latex":"\\mathit{\\Pi}"},{"alttext":"pH","latex":"\\text{pH}"},{"alttext":"pH","latex":"\\text{pH}"}],"sources":["PAC, 1994, 66, 595. 'Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)' on page 602 (https:\/\/doi.org\/10.1351\/pac199466030595)"]}],"referencedin":[{"title":"Wikipedia - متوسط هندسي (ar)","url":"https:\/\/ar.wikipedia.org\/wiki\/متوسط_هندسي"}],"links":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/G02621\/html","json":"https:\/\/goldbook.iupac.org\/terms\/view\/G02621\/json","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/G02621\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/G02621\/plain","pdf":"https:\/\/goldbook.iupac.org\/terms\/view\/G02621\/pdf"},"citeas":"IUPAC. Compendium of Chemical Terminology, 2nd ed. (the \"Gold Book\"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https:\/\/doi.org\/10.1351\/goldbook.","license":"Licensed under Creative Commons Attribution-NoDerivatives (CC BY-NC-ND) 4.0 International (https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/)","collection_reuse":"For parties interested in reusing the entire IUPAC Gold Book please contact IUPAC here https:\/\/www.cognitoforms.com\/IUPAC1\/ContactInformationForm","disclaimer":"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.","accessed":"2023-05-31T10:37:08+00:00"}}