Geometric standard deviation

The geometric standard deviation (often abbreviated to GSD ) is a measure of the spread of the deviations from the geometric mean .

In general, it is calculated as follows:

${\displaystyle \sigma _{g}=\exp \left({\sqrt {{\frac {1}{n}}\cdot \sum _{i=1}^{n}\left[\ln \left({\frac {x_{i}}{{\bar {x}}_{g}}}\right)\right]^{2}}}\right)}$

with the geometric mean : ${\displaystyle {\bar {x}}_{g}}$

${\displaystyle {\bar {x}}_{g}={\sqrt[{n}]{x_{1}\cdot x_{2}\cdot \ldots \cdot x_{n}}}={\sqrt[{n}]{\prod _{i=1}^{n}{x_{i}}}}}$

In contrast to the arithmetic standard deviation , the product and not the sum is interpreted here.

This statistical figure is mainly used in the natural sciences .

Individual evidence

1. ↑ Norman Zacharias: MEG investigations on the variance stability and context dependency of the stimulus representation in the human auditory cortex , Verlag epubli GmbH (2014), ISBN 3-84428-325-0 , chapter 2, formula (2.6.6)
2. ↑ Björn Friedrich and Peter Heil: Onset-Duration Matching of Acoustic Stimuli Revisited: Conventional Arithmetic vs. Proposed Geometric Measures of Accuracy and Precision , Front. Psychol. 7: 2013 (2017), doi : 10.3389 / fpsyg.2016.02013 , Supplementary Material, Section 3, Table 1