Geometric median

Using the same data, compute a geometric median size and geometric standard deviation. What would be the numerical value of the geometric standard deviation if the particles were all the same size ... 

If the particle size distribution is normal or log normal, then the data can be linearized by plotting the particle frequency as a function of particle rize on arithmetic or logarithmic probability graph p r respectively. The 50% value of sudi plots yields the geometric median diameter and the geometric standard deviation is the ratio of the 84.1% m the 50% values. 

The distribution in a log-normal representation can be completely specified by two parameters, the geometric median particle size (dg) and the standard deviation in the geometric mean (particle size pertaining to the 50% value in the cumulative distribution, and is calculated using ... 

Although the distribution in the log-normal representation is completely specified by the geometric median particle size and the geometric mean standard deviation, a number of other average values have been derived to define useful properties. These are especially useful when the physical significance of the geometric median particle size is not clear. The arithmetic mean (d v) particle size is defined as the sum of all particle diameters divided by the total number of particles, and is calculated using ... 

In many cases, the particle size distribution of a real sample turns out to be adequately represented by a log-normal distribution. In that case, the distribution can be specified by the geometric median particle size (d and the geometric mean standard deviation (cumulative distribution, and consequently, the geometric median particle size is often referred to as the dso value. The value of <7g is obtained by... 

For some runs we also included a similar scheme of reactions on the sub-micrometre mode of marine aerosol. Typical background aerosol concentration, 1.1 X 10 m (liquid) per m (air), size distribution (volume geometric median radius of 0.1 pm), and chemical composition (mainly NH4HSO4, (NH4)2S04 and water) are taken from MBL measurements [25]. Scavenging of HOBr, HCl and HBr on the additional surface of the submicrometre sulphate aerosol in combination with reactions (1) and (2) also leads to efficient conversion of CF and Br into BrCl and Br2. 

We have implemented all segmentation techniques described above, in an interactive software. The operator can chose and adapt the appropriate segmentation technique with the desired parameters. Some geometrical features can be extracted using a contour following such as length, width, surface, form, median axes of the selected defect. The selection is easy and can be done interactively using the mouse. 

Raw data are collected observations that have not been organized numerically. An average is a value that is typical or representative of a set of data. Several averages can be defined, the most common being the arithmetic mean (or briefly, the mean), the median, the mode, and the 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. 

In general, air quality data are classified as a function of time, location, and magnitude. Several statistical parameters may be used to characterize a group of air pollution concentrations, including the arithmetic mean, the median, and the geometric mean. These parameters may be determined over averaging times of up to 1 year. In addition to these three parameters, a measure of the variability of a data set, such as the standard deviation... 

FIGURE 5.28 Estimated overall airway deposition as a function of initial particle size and particle hygroscopicity for particles with mass median aerodynamic diameters (MMAD) between 0.1 and 10 p.m. ° Geometric dispersion, a measure of particle size distribution, principally affects only smaller MMAD,... 

The size of inhaled particles varies markedly. The size distribution approximates a log-normal distribution that can be described by the median or the geometric mean, and by the geometric standard deviation. For fibers, both... 

The values of a and Dmx are characteristic constants for a given size distribution. If a material follows a log-probability distribution on one basis (x), it also does on any other basis (y) - with the same value of the standard geometric deviation (a) but a different value of median size (Dmx) corresponding to the new basis (y). This is a unique property of log-propability distribution (See Eq 2) ... 

The median diameter is a measure of the general size level, whereas the standard geometric deviation is a measure of the degree of uniformity. A completely uniform material (all particles the same size) would show up as a horizontal line in Fig 3 and have a standard geometric deviation of 1,0. A completely heterogeneous material would be represented by a vertical line which would have a standard geometric deviation of infinity... 

AMAD = activity median aerodynamic GSD = geometric standard deviation... 

In case of unsymmetric distributions both geometric mean and median are smaller than the arithmetic mean. In the same way as the distribution converges towards a normal one, geometric mean and median turn into the arithmetic mean. 

Other means like the median (see Eq. (4.22)) or the geometrical mean (see Eq. (4.18)) etc. have to be reported in a similar way together with the belonging uncertainty interval, e.g.,... 

Table I. Numbers, Arithmetic Means and S.D.s, Geometric Means, Medians and Ranges of Rn Measurements for Dwellings in Different areas...

Figure 4. Cumulative frequency distributions of radon concentration for dwellings with different house constructions traditional wooden, ferro-concrete and prefabricated. Numbers, arithmetic means and S.D.s, geometric means, medians, and ranges of radon measurements are also indicated at the bottom of the figure.

Theoretical calculations of unattached fractions of radon progeny require prediction of an attachment coefficient. Average attachment coefficients for aerosols of various count median diameters, CMD, and geometric standard deviations, ag, are calculated using four different theories. These theories are ... 

Theoretical calculations of unattached fractions of radon or thoron progeny involve four important parameters, namely, 1) the count median diameter of the aerosol, 2) the geometric standard deviation of the particle size distribution, 3) the aerosol concentration, and 4) the age of the air. All of these parameters have a significant effect on the theoretical calculation of the unattached fraction and should be reported with theoretical or experimental values of the unattached fraction. 

Figures 3 and 4 show the variation of the attachment coefficient with count median diameter for the diffusion, kinetic, hybrid and kinetic-diffusion theory for geometric standard deviations of 2 and 3 respectively.

In Figs. 6 and 7 the attachment coefficient is plotted against the geometric standard deviation using the four theories, for count median diameters of 0.2 ym and 0.3 ym respectively. 

An aerosol size distribution can, therefore, be described in terms of the count median diameter, d, and the geometric standard deviation, a These parameters were obtained from experimental data using a diffusion battery method (Busigin et al., 1980). A diffusion battery is an assembly of a number of cylindrical or rectangular channels. The relative penetration of aerosols through different sizes of diffusion batteries at specified flow rates allows the aerosol size distribution to be calculated. 

Table IV. Activity and Aerosol Size Distributions, Count Median Diameter (CMD) and the Geometric Standard Deviation (indicated in brackets)...

Table II. Summary of Mean Monthly Activity Median Aerodynamic Diameters (AMAD) and Geometric Standard Deviations (tfg) of Radon and Thoron Daughter Size Distributions in Ambient Aerosols...

Table III. Median Aerodynamic Diameters (MAD) and Geometric Standard Deviations (Og) of Pb-210 and Be-7 Based on Radioactivity and SO Measured with High-Volume Cascade Impactors...

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