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Particle Characterization and Dynamics
Published in Wen-Ching Yang, Handbook of Fluidization and Fluid-Particle Systems, 2003
The geometric mean is the logarithmic equivalent of the arithmetic mean. Being a logarithmic average, the geometric mean is always smaller than the arithmetic mean. d‾g=dpln1dp2n2⋯dpnnnnd‾g=∑inilogdpi∑ini
Research Methods and Statistics
Published in Monica Martinussen, David R. Hunter, Aviation Psychology and Human Factors, 2017
Monica Martinussen, David R. Hunter
In addition to a measure of the most typical value in the distribution, it is also important to have a measure of variation. If we have calculated the arithmetic mean, it is common to use the standard deviation as a measure of variation. Formulated a little imprecisely, the standard deviation is the average deviation from the mean. If results are normally distributed—that is, bell shaped—and we inspect the distribution and move one standard deviation above and one standard deviation below the average, then about two-thirds of the observations fall within that range. Including two standard deviations on both sides of the mean, then about 95% of the observations will be included. The formulas for calculating the arithmetic mean and standard deviation are X¯=∑i=1NXiNSD=∑i=1N(Xi−X¯)2N−1 where N is the sample size, Xi is the test score, and X¯ is the mean score.
Noise
Published in Martin B., S.Z., of Industrial Hygiene, 2018
Arithmetic mean is used as the measure of the central tendency of the measured distribution, and the standard deviation is the measure of dispersion about the mean. The calculated confidence limits measure the degree of certainty of the calculated mean. This will provide the range within which the noise exposure should fall 90% to 95% of the time, depending upon the degree of confidence that one wishes to use.
Beyond descriptive statistics: using additional analyses to determine the technological feasibility of meeting a new exposure limit
Published in Journal of Occupational and Environmental Hygiene, 2021
Benjamin Roberts, Taylor Tarpey, Nicole Zoghby, Thomas Slavin
In most cases, OSHA used a geometric mean analysis to characterize the exposure data, believing that the geometric mean is better suited than the arithmetic mean to finding an average where exposure levels cluster around one point and have only one or a few "outliers" at higher exposures. In these situations, taking an arithmetic mean would result in an average closer to the outliers, which would not be representative of the majority of exposure levels. To determine feasibility, OSHA decided it was most important to know what level was being met most of the time (the cluster of exposure levels), and it therefore concluded that the geometric mean, which is a logarithmic average and tends to fall within the cluster, would better characterize the entire exposure level distribution (American Iron Steel Institute v. OSHA 1991).
Workers’ exposure to electric fields during the task ‘maintenance of an operating device of circuit breaker from a service platform’ at 110-kV substations
Published in International Journal of Occupational Safety and Ergonomics, 2019
Leena Korpinen, Rauno Pääkkönen
At 16 substations, we conducted 255 measurements. Table 1 presents the measured maximum electric fields, the means and the standard deviations of electric fields at different substations. In this case, the mean is the arithmetic mean of the measured values. In addition, the table also presents the quartiles (25th, 50th and 75th percentiles) and the 95th percentile when the number of measurements at the same substation was over 20. The heights of the service platforms varied. The figures show some examples of the different service platforms: in the photograph in Figure 1 the height of the platform was 0.6 m, and in the photograph in Figure 5 the height of the portable service platform was 1.2 m. In some substations there were handrails around the platform, but not in all. In some substations, we used different measurement methods because service platforms were not always present in the working area. Therefore, we could measure exposure situations without platforms. Moreover, at substation 15 we employed two portable service platforms: Suomi-Tikas (Suomi-Tikas, Finland) (Figure 5) and ZARGES (ZARGES, Germany) (Figure 6). We also measured electric fields without platforms (Figures 3 and 4). However, we conducted only about 20 measurements, which were too few to perform a statistically significant analysis and compare the exposure in different situations (with and without platforms).
Very Fast C4.5 Decision Tree Algorithm
Published in Applied Artificial Intelligence, 2018
Anis Cherfi, Kaouther Nouira, Ahmed Ferchichi
Mean or average is the representative value of the whole group of data. The arithmetic can take any value not observed in the original set of data, which can improve the generalization ability of a cut point (Lewis 2012). In this setting, using the mean as a threshold value will improve the classification of unseen cases. The median is also widely used as a measure of central tendency, and it is the central value in the set of data. It divides the data into two equal halves. This measure is affected by the number of values observed in the distribution (Rubin 2012). As shown in Eq. (6), the arithmetic mean involves both distribution values () and number of observations (). That is why the mean is sensitive to the outlier values in a dataset, in such a case, the mean cannot deliver a relevant cut point. Whereas, as can be seen from Eq. (7), the median value is affected only by the number of observations (), it is not sensitive to outlier values. The presence of outlier data values or the shape of frequency distribution has a dramatic impact on mean value (Sharma 2012), that is why, in such cases arithmetic mean could be replaced by the median (Reimann, Filzmoser, and Garrett 2005).