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Topic: Geometric standard deviation

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Lognormal distribution

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	Geometric standard deviation - Wikipedia, the free encyclopedia
		In probability theory and statistics, the geometric standard deviation describes how spread out are a set of numbers whose preferred average is the geometric mean.
		The geometric standard deviation is related to the log-normal distribution.
		As such, the geometric mean and the geometric standard deviation of a sample of data from a log-normally distributed population may be used to find the bounds of confidence intervals analogously to the way the arithmetic mean and standard deviation are used to bound confidence intervals for a normal distribution.
	en.wikipedia.org /wiki/Geometric_standard_deviation (289 words)

	Log-normal distribution - Wikipedia, the free encyclopedia
		The log-normal distribution, the geometric mean, and the geometric standard deviation are related.
		In this case, the geometric mean is equal to exp(μ) and the geometric standard deviation is equal to exp(σ).
		If a sample of data is determined to come from a log-normally distributed population, the geometric mean and the geometric standard deviation may be used to estimate confidence intervals akin to the way the arithmetic mean and standard deviation are used to estimate confidence intervals for a normally distributed sample of data.
	en.wikipedia.org /wiki/Log-normal_distribution (390 words)

	Arithmetic vs. Geometric Mean
		The arithmetic standard deviation is a quantity. Multiples of that quantity are added to (or subtracted from) the arithmetic mean to determine the set of values that lie within a given range of dispersion. To determine the value that lies n standard deviations from the mean, we must multiply the arithmetic standard deviation by n.
		The arithmetic mean and arithmetic standard deviation are sum-based values. As such, they are appropriate for additive processes. But earnings growth is not additive; it is multiplicative. The appropriate measures for EPS growth factors are the geometric mean and geometric standard deviation, which are product-based values.
		The antilog of the logs' arithmetic standard deviation is the geometric standard deviation of the growth factors.
	thinkingapplied.com.webserver.natasha.asdf456.com /means_folder/deceptive_means.htm (1917 words)

	Intro to Environmental Stats: Mod 3 Transcript
		And the geometric standard deviation or the slope is E to the 0.5542 power.
		Geometric standard deviation of E to the 0.5542 or 1.74.
		The geometric mean from Excel was 10.6, from the hand plot 10.8; geometric standard deviation from Excel was 1.74; from the hand plot, 1.72.
	www.uic.edu /sph/eohs_webcasts/transcripts/envstats_3_transcript.htm (10382 words)

	[No title]
		The geometric mean of a set of positive numbers is the exponential of the arthmetic mean of their logarithms.
		The geometric mean of a lognormal distribution is the exponential of the mean of the associated normal distribution.
		Standard mortality ratio is the ratio of the disease or accident mortality rate in a certain specific population compared with that in a standard population.
	www.gwu.edu /~nsarchiv/radiation/dir/mstreet/commeet/meet2/brief2/br2c1.txt (2731 words)

	Archives of Environmental Health: Exposure to Benzene in Fuel Distribution Installations: Monitoring and Prevention (Site not responding. Last check: 2007-10-08)
		The estimated geometric mean exposures of fillers and nonfillers during different conditions (controlled for period effect) are shown in Table 3.
		The geometric standard deviations between workers and within workers during the 8 y of follow up are presented in 3 hierarchical mixed-effects models.
		In all models the geometric standard deviation components were at least borderline significantly different from 1 (i.e., variances were different from 0).
	www.findarticles.com /p/articles/mi_m0907/is_6_55/ai_68642256/pg_2 (1012 words)

	Environmental Protection Agency > Basic Concepts in Environmental Sciences > Module 3: Size Distribution
		The geometric mass mean diameter is the diameter of a particle that has the logarithmic mean for the size distribution.
		The geometric mass mean diameter is equivalent to the mass median diameter for lognormal graphs due to the bell-shaped symmetrical curve produced.
		The geometric standard deviation of a lognormal distribution is determined by dividing the mass median particle diameter by the particle size at the 15.78 percent probability or by dividing the particle size at the 84.13 percent probability by the mass median particle diameter.
	www.epa.gov /eogapti1/module3/distribu/distribu.htm (883 words)

	Nonmandatory Protocol for Biological Monitoring - 1910.1027 App F (Site not responding. Last check: 2007-10-08)
		Standard Deviation: A measure of the distribution or spread of a data set about the mean; the standard deviation is equal to the positive square root of the variance, and is expressed in the same units as the original measurements in the data set.
		Standards of at least three different values are to be used for calibration, and should be constructed from at least 2 different sources.
		For studies reporting either an arithmetic or geometric standard deviation along with a mean, the lower and upper 95th percentile for the distribution also were derived and reported in the table.
	www.osha.gov /pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=10041 (15434 words)

	Summary Statistics: Location & Spread
		The geometric mean is the antilog of the mean of the logged data--that is, the data are logged, the mean of the logs is calculated, and the anti-log of the mean is obtained.
		The presence of geometric means indicates the analysis was done in the log scale, but the results were transformed back to the original scale for the convenience of the reader.
		Therefore, the geometric mean (anti-log of the mean) will be approximately equal to the anti-log of the median, which is the median in the original scale.
	www.tufts.edu /~gdallal/summary.htm (2909 words)

	Plug-flow process for the nucleation of silver halide crystals - Patent 5104786
		The geometric standard deviation of the residence time distribution of the silver halide crystals during said nucleating is less than 1.30.
		The geometric standard deviation of the residence times of all particles through the system is a measure of the width of that peak, and thus, is an indicator of the degree of plug-flow behavior of the system.
		Since a geometric standard deviation is dimensionless, it allows valid comparison between systems with different mixing patterns and mean residence times.
	www.freepatentsonline.com /5104786.html (3772 words)

	eBMJ -- Statistics at Square One: 2. Mean and standard deviation (Site not responding. Last check: 2007-10-08)
		The standard deviation is a summary measure of the differences of each observation from the mean.
		This procedure illustrates the structure of the standard deviation, in particular that the two extreme values 0.1 and 3.2 contribute most to the sum of the differences squared.
		Obtain the mean and standard deviation of the data in and an approximate 95% range.
	bmj.bmjjournals.com /collections/statsbk/2.shtml (2546 words)

	Research Abstract: 1990-03 Survey of Residential Indoor and Outdoor Radon Concentrations in California
		When the whole-house value was calculated by averaging the concentrations in the bedroom and living room, the geometric mean was 0.85 pCi/l and the geometric standard deviation was 1.91.
		The geometric mean of the concentrations in the 27 basements measured was 2.17 pCi/l, which was significantly higher than that of whole-house concentrations.
		The geometric mean of annual average outdoor radon concentrations was 0.55 pCi/l for the pretest area, 0.42 pCi/l for the statewide survey, and 0.66 pCi/l for the southern Sierra foothill area.
	www.arb.ca.gov /research/abstracts/a6-194-53.htm (408 words)

	Descriptive Statistics
		The average deviation or mean absolute deviation is calculated in a similar manner as standard deviation, except here you subtract the median from each data item producing a list of deviations from the median.
		With the usual standard deviation you add or subtract the standard deviation from the mean in order to test for fractions of included data; with the log standard deviation, you multiply or divide.
		The standard deviation of the counts in the repeated experiments should be close to the square root of 1000 (31.6).
	www.physics.csbsju.edu /stats/descriptive2.html (1632 words)

	Blood Lead Slope Factor Models for Adults: Comparisons of Observations and Predictions
		The geometric standard deviation (the antilog of the arithmetic standard deviation of the log-transformed data) is a measure of the range, or spread, in PbB levels for a group of people.
		To account for the tendency for site-specific geometric standard deviations to be smaller than geometric standard deviations for populations living over a broad geographic area, we assume that values from 1.7 to 1.9 are a reasonable range for the GSD for women of childbearing age.
		Table 9 considers alternative assumptions for several parameters, including: the geometric standard deviation, exposure frequency, the possibility that some fraction of soil ingested is comprised of dust, the soil ingestion rate, and the fraction of soluble lead that is absorbed.
	ehp.niehs.nih.gov /members/1998/Suppl-6/1569-1576bowers/bowers-full.html (6274 words)

	ASA Southeast Asia
		Standardized procedures for particle size determination have been developed (American Society of Agricultural Engineers, 1983) and determination of particle size of grains is a fairly simple procedure (Behnke, 1983).
		The average particle size of the sample is then determined by standard formulas and given as geometric mean diameter (GMD, expressed as microns or µ).
		Particle size uniformity is described by geometric standard deviation (GSD), a small GSD representing higher uniformity.
	www.asasea.com /po34_97.html (2507 words)

	Assessing Risks of Exposure to Plutonium
		The lung, liver, bone, and bone marrow are shown to be the principal organs of concern.
		Because the inhalation dose depends upon the particle size distribution of the plutonium aerosol inhaled, dose and risk coefficients are determined for three different particle size distributions (AMAD = 1 µm, 5 µm, 10 µm) each with a geometric standard deviation of 2.5.
		A median inhalation dose coefficient of 9 µGy Bq for 1-µm AMAD plutonium oxide aerosol is determined with a geometric standard deviation of 3.
	www.racteam.com /Experience/Publications/PuAbstract.htm (635 words)

	Environmental Protection Agency > Basic Concepts in Environmental Sciences > Practice Problems (Size ...
		The mass median diameter and the geometric mean diameter are equivalent because the graph is lognormal.
		Determine the mass median particle diameter and the geometric standard deviation.
		The geometric standard deviation can be determined by using either the 15.87 or 84.13 probability values.
	www.epa.gov /eogapti1/module3/distribu/pp_answer/p_answer.htm (363 words)

	Geometric Standard Deviation
		Compute the geometric standard deviation for a variable.
		is a parameter where the computed geometric standard deviation is stored;
		GEOMETRIC SD is a synonym for GEOMETRIC STANDARD DEVIATION.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/geomsd.htm (81 words)

	Optimization of the Pelletization Process in a Fluid-Bed Rotor Granulator Using Experimental Design
		This study examined the effect of rotor speed, amount of water sprayed, and atomizing air pressure on the geometric mean diameter and geometric standard deviation of pellets produced in a fluid-bed rotor granulator using a 2
		None of the 3 factors significantly affected the geometric standard deviation of the pellets.
		Because the geometric SD of the pellets was not statistically significantly affected by the selected factors, the study further focused only on pellet size.
	www.aapspharmscitech.org /view.asp?art=pt010435&pdf=yes (2508 words)

	How High Are Exposures in The U.S. Population? - 1999 NIEHS Report on Health Effects from Exposure to Power-Line ...
		Therefore, the central tendency of the values is better represented as a geometric mean (log-weighted average) and the variation around that mean given as a geometric standard deviation.
		Another measure commonly used is the median, which denotes the estimate of exposure for which 50% of the population have smaller exposures and 50% have larger exposures.
		This report presents averages as geometric means with geometric standard deviations given in parenthesis beside the average estimate.
	www.niehs.nih.gov /emfrapid/html/EMF_DIR_RPT/Howhigh.HTM (1077 words)

	CTPL Home (Site not responding. Last check: 2007-10-08)
		Results indicate that particle formation and growth is mixing limited in this study and the mean particle diameter and geometric standard deviation increase as the concentration level of the initial reactants increases.
		In general, a high a geometric standard deviation corresponds to a large particle size.
		Additionally, the simulations produced strong spatial variation in the geometrical standard deviation, with rather large values.
	www.menet.umn.edu /~guanghai/Research.html (393 words)

	Particle Seperation Efficiency of a Uniflow Deduster with Different Types of Dusts
		The count mean diameter of the swine building dust was 2.28 µm with geometric standard deviation of 2.1 µm.
		The mass mean diameter of the commercial dust was 9.1 µm with geometric standard deviation of 2.32 µm.
		The standard deviation is shown as the vertical bar across the data point.
	www.age.uiuc.edu /bee/research/Deduster/dedpaper2.html (3377 words)

	ATSDR - Health Consultation - Lawrence Livermore National Laboratory, Big Trees Park 1998 Sampling, Livermore, ...
		The standard deviation is the population standard deviation.
		Standard techniques were used for the other aspects of the statistical analysis.
		The geometric mean is used to measure the central tendency of a data set, especially if the data set is not evenly distributed.
	www.atsdr.cdc.gov /HAC/pha/lln/lln_p4.html (9451 words)

	Patent 6,805,853 (Site not responding. Last check: 2007-10-08)
		Typically, the geometric standard deviation around the mass median aerodynamic diameter of the aerosol particles is less than 3.0.
		Preferably, the geometric standard deviation is less than 2.5.
		The amount of active drug compound collected in the chamber is determined by extracting the chamber, conducting chromatographic analysis of the extract and comparing the results of the chromatographic analysis to those of a standard containing known amounts of drug.
	www.pharmcast.com /Patents100/Yr2004/Oct2004/101904/6805853_Diazepam101904.htm (3519 words)

	Fine Particle Software - Experts in Particle Technology - Classification of Particulate Materials (Site not responding. Last check: 2007-10-08)
		The feed particle size distribution is assumed to follow the log-normal law which requires only two parameters: the median size and the geometric standard deviation.
		The user is asked to enter the geometric standard deviation of the REDUCED grade efficiency curve for the classifier, the cut size x50 of the ACTUAL grade efficiency and the underflow by-pass Rf.
		The user enters the five input numbers and then the total efficiency, the reduced total efficiency and the reduced cut size are calculated and displayed; followed by a series of graphics screens, plotting first the reduced and actual grade efficiency curves (with the cut size marked).
	www.fortunecity.com /business/merger/767/software_classif.htm (401 words)

	Magnetic Fields on the Flight Deck
		For measurements taken during block time, harmonic geometric means ranged from 6.7 mG for the B-767-300ER (99 percent of harmonic measurements below 13.9 mG) to 12.7 mG for the B-737-200 (99 percent of harmonic measurements below 30.1 mG) (see Table III).
		The geometric harmonic means differed by less than 1 mG between captains and first officers on the same airplane type (see Table IV).
		Recalculating the harmonic geometric mean for all B-747-400 flights with bunk time removed produces a reduction in this group mean from 11.0 mG (geometric standard deviation 2.0) to 10.1 mG (geometric standard deviation 1.7).
	cf.alpa.org /internet/alp/2001/jan01p21.htm (1502 words)

	Mean-Variance Optimization and Modern Portfolio Theory
		The efficient frontier is conventionally plotted on a graph with the standard deviation (risk) on the horizontal axis, and the expected return on the vertical axis.
		Then elementary statistics tells us that the one standard deviation error in the value R as an estimate of the mean is the standard deviation divided by the square root of N. If N is not very large, then this error can distort the results of the MVO analysis considerably.
		Lastly, and most important, the weighted geometric mean does not represent any meaningful property of the rebalanced (or unrebalanced) portfolio with the given composition, while the weighted arithmetic mean does at least correctly represent the arithmetic mean return of the rebalanced portfolio.
	www.effisols.com /basics/MVO.htm (3161 words)

	JAWMA Paper: Health Risk Assessment of Fluctuating Concentrations Using Lognormal Models (Site not responding. Last check: 2007-10-08)
		One represents the geometric standard deviation of the con-centration distribution relative to that of the dose-response curve, and the other represents the distance between the geometric mean concentration and the concentration pro-ducing an adverse response in 50% of the exposed popu-lation.
		If the two parameters of the dose-response curve are known, the health risk of the concentration pattern may be calculated conveniently for any geometric mean and geometric standard deviation values.
		It also clari-fies exactly the adverse effects that may be expected for various geometric mean concentrations and geometric standard deviation values.
	www.awma.org /journal/ShowAbstract.asp?Year=1997&PaperID=431 (336 words)

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