Median and mean

The median (denoted by x) is the middle value when the data points are ordered from smallest to largest. The median can only be defined in this way when there 

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Typical levels of NO, N02, and NOy Figure 11.30 shows a summary of measurements of surface concentrations of NO, NO., and NO made at a variety of remote to rural sites in North America and Europe (Emmons et al., 1997). The bars encompass the central 90% of the values and the medians and means are... 

In venous blood samples eolleeted from 13 non-smokers and 14 cigarette smokers, the concentrations of ethylbenzene tended to be higher in smokers. The median and mean levels of ethylbenzene in non-smokers were 431 and 651 ng/L, respeetively (range, 175-2284 ng/L), compared with smokers with median and mean levels of 535 and 837 ng/L, respeetively (range, 378-2697 ng/L) (Hajimiragha et al., 1989). 

Spreadsheet 2.1. Calculation of mean, standard deviation, median, and mean absolute deviation of titration data with outlier, and after correction (shaded cells show the change from 11.02 to 10.02). 

Rimando et al., 2004 Sobolev and Cole, 1999 Tokusoglu et al., 2005]. In an adult Spanish cohort resveratrol and piceid, trans and czls-forms, were evaluated. Estimated median and mean of resveratrol and piceid were 100 and 933 pg/day, respectively, of which 98.4, 1.6, and less than 0.1% come from wines, grape and grape juice, and peanuts, pistachios, and berries, respectively [Zamora-Ros et al., 2008]. 

The median and mean are clearly different measures of location/center. The former is in the middle of the data in the sense that about half of the data are larger and about half are smaller. The latter is a kind of center of mass, and for asymmetrical data sets like that of Table 5.1 is usually pulled from the median in the direction of any skew present, that is, is pulled in the direction of extreme values. 

The median and mean value are given Indicates that the values are not well defined. 

The sidereal orbital period is the mean time for one revolution about the Sun relative to the fixed stars. The tropical orbital period is the mean time for one orbit from the same point to itself (such as equinox to equinox). The time between Venus-Earth oppositions. Retrograde rotation. Median radius = 6,051.64 km, mean radius = 6,051.84 km. Model-dependent constraint from Yoder (1997). The temperature and pressure at the median and mean radii are 738.4 K, 94.5 bar and 736.8 K, 93.3 bar, respectively. 

Estimation is the use of the sample data to make inferences about the population that the sample represents . With qualitative data, we would usually be interested in estimating the proportion or percentage of individuals in the population having some outcome or characteristic with ordinal data we would probably wish to estimate the population median, and with quantitative data the population mean. Although percentages, medians and means are most often of interest, it is possible to use any sample statistic to estimate the corresponding population value thus in Sections 7.3.1.3.3 and 7.3.1.3.4 we were interested in whether a sample gl or g2 was consistent with ffie true or population values being zero. 

ER Davies. The relative effects of median and mean filters on noisy signals. J. Modern Optics, 39 103-113, 1992. 

Figure 3. An example of the log-normal distribution function in normalized linear form for CMD = 1.0 and Og = 2.0, showing the mode, median and mean of the size distribution, the surface area distribution median and mean diameters, the mass distribution median and mean diameters, and the diameter of average mass. Reproduced with permission from Raabe OG (1970). Generation and characterization of aerosols. In Inhalation Carcinogenesis (MG Hanna, P Nettersheim and JR Gilbert, eds), pp. 123-172. Proceedings of a Biology Division, Oak Ridge National Laboratory Conference. Oak Ridge, TN, USA US Atomic Energy Commission...

The ambient concentrations of ammonia determined at Whiteface Mountain, New York, in 1982 ranged from approximately 0.3-5 ppb, with the hourly median and mean values both determined as 2.2 ppb (Kelly et al. 1984). Ammonia concentrations in mral Thurber, Nevada, ranged from approximately 0.5 to 2 ppb (Farmer and Dawson 1982). In the atmosphere over the world s oceans, ammonia concentrations ranged from approximately 0.28 to 5.6 ppb (Georgii and Gravenhorst 1977). 

Figure 12.1 A typical particle size reporting scheme showing mode, median and mean diameters...

Several standard expressions of a population that are used include mode, median, and mean differences (arithmetic, geometric, square, harmonic, etc.), as shown in Figure 9.10. 

Various statistical parameters such as median and mean size, deviation, skewness and kur-tosis can be calculated from data derived from cumulative curves. The median or mean size permits the determination of the grade of gravel, sand or silt, or their lithified equivalents. Deviation affords a measure of sorting. However, the latter can be quickly and simply estimated by visual examination of the curve in that the steeper it is, the more uniform the sorting of the sediment. 

Table 7.13 contains the distributions of experimental density and of descriptors for the size of molecules, i.e. number of atoms (A), molecular weight (MW), and van der Waals volume (y du)- Minimum, maximum, first and third quartile, median and mean are given for each quantity, for the library as a whole and for LS and TS separately. LS and TS are similar according to this information. Important predictors will be constructed from A, MW and... 

The mode, median, and mean of a particle size distribution. 

AU three types of location parameters— modes, medians and means—are fre-quentiy used in practice yet their meaning and robustness is not identical. 

Figure 2.4 The mode, median and mean of a size distribution...

Statistically, the particle size distribution can be characterized by three properties mode, median, and mean. The mode is the value that occurs most frequently. It is a value seldom used for describing particle size distribution. The average or arithmetic mean diameter, d, is affected by all values actually observed and thus is influenced greatly by extreme values. The median particle size, is the size that divides the frequency distribution into two equal areas. In practical application, the size distribution of a typical dust is typically skewed to the right, i.e., skewed to the larger particle size. The central tendency of a skewed frequency distribution is more adequately represented by the median rather than by the mean (see Fig. 9). Mathematically, the relationships among the mean, median, and mode diameter can be expressed as... 

It may seem a paradox, but they are very effective to identify gross errors for example, a huge difference between median and mean for a variable could be due to a misprinted number, or could suggest the need to transform variables (e.g. log transform) and help choosing the appropriate data pretreatment. 

For this distribution the mode, median and mean sizes are different. Using Eqs. (2.3.4) and (2.B.7) the mean particle size becomes ... 

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