Particle size, statistics geometric mean

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

Particle size averages This. section describes how to calculate the arithmetic (d) geometric (dg) and harmonic (c/h) means. The derivation of optimal estimates is beyond the scope of this chapter but the interested reader can consult any good statistic book (1.9). The most commonly used averages are the arithmetic averages. The standard formulas for estimating the arithmetic or average diameter and the standard deviation are ... 

An aerosol rarely consists of particles that are the same size, and usually a distribution of sizes around a mean is observed. The observed data may be fitted by statistical approximation to a distribution. The number of particles in a size range when plotted against the logarithm of the particle diameters frequently exhibit a normal (Gaussian) distribution. This is known as a log-normal distribution and is described by a parameter known as the geometric standard deviation. Theoretically, a monodisperse aerosol will exhibit a geometric standard deviation of 1 in practice, however, an accepted limit is 1.2 [6]. 

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