Preferred Label : geometric mean;
Detailed label : geometric (logarithmic) mean, x g;
IUPAC definition : The i n /i th root of the product of the absolute values of the observations, taken
with the proper sign. It can be calculated with the formula: \[\overline{x}_{{g}}
(\Pi x_{i} ) {\frac{1}{n}}\] The Π product is taken from i i /i 1 to i n /i
.;
Scope note : 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.;
Origin ID : G02621;
Automatic exact mappings (from CISMeF team)
- See also
The i n /i th root of the product of the absolute values of the observations, taken
with the proper sign. It can be calculated with the formula: \[\overline{x}_{{g}}
(\Pi x_{i} ) {\frac{1}{n}}\] The Π product is taken from i i /i 1 to i n /i
.
