I see both reported in the literature. Geometric means are less sensitive to outliers (also problematic when dealing with negative values), while arithmetic means are technically closer to the average air quality people breathe but a few data points can move the mean quite a bit.
Dear Graydon,
German regulation resorts to the arithmetic averages of pollutant concentrations to assess the so-called "Maximum Immission Values".
The maximum immission concentrations as well as the maximum immission rates in average pollutant uptake are consulted.
The criteria which must be defined prior to estimating medico-scientifically substantiated maximum immission values include the objects of protection, the types of effect to be considered and the required level of protection.
In addition, the relevant exposure times have also to be taken into account when establishing maximum immission values. Exposure times have to be adjusted according to the characteristic effects of the pollutant and the response of the affected object.
Further information is given in the series of standards VDI 2310:
www.vdi.de/2310
Best,
Sascha
you may wish to try another "mean"
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
Dear Graydon
I would hate to use either metric. Distributions of such things are rarely truly normal or even lognormal. Instead they tend to be the sums of many such distributions, that with enough data often do appear normal or perhaps lognormal. The problem with any central tendency is that the laws of chemistry and physics are such that its the extremes in the distribution wherein lie all the action. If you ignore them you are in danger of throwing the baby out with the bathwater!
Dear Graydon,
I totally support John's comment. Some time ago I was working on similar problems. You may like to have a look at a paper of mine on the subject, "Calibration of lichen transplants considering faint memory effects",I am sending it attached.
Enjoy the reading!
Article Calibration of lichen transplants considering faint memory effects
A geometric mean is used when comparing different items when each item has multiple properties that have different numeric ranges. The geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting, and a given percentage change in any of the properties has the same effect on the geometric mean (see wikipedia). For air quality measurement, geometric mean is rarely used.
I would recommend first to draw an histogram to examine what kind of distribution you have. If it is non-gaussian and skewed to the left or to the right, I would use percentile
i.e the median value (percentile 50%), interquantile is the best.
The 98th percentile has been used in Canada and US for long time to characterize the air quality.
The study of the impact of fine aerosols and health impact has shown pretty well a linear relationship between percentiles (even averages) and health
see https://ehp.niehs.nih.gov/wp-content/uploads/120/3/ehp.1103671.pdf and references therein.
Hope it helps
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