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:
The
product is taken from
i = 1 to
n.
Note:
This quantity is often calculated directly from experimental measurements (e.g. determination
of concentrations by
electrode potential measurements, or
), although its significance may not always have been recognized. The problem is that
the average value of a
variable (such as
) 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.
Source:
PAC, 1994, 66, 595
(Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations
1994))
on page 602
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A.Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.
