Median calculation

In order to tear a piece of paper into four equally wide strips, three tears must be made. One to tear the original paper in half and the other two to tear those halves in half again. A quartile is the mathematical equivalent of this to a range of ordered data. You should realize that the middle quartile (Q2 ) is, in effect, the median for the range. Similarly, the first quartile (Qi) is effectively the median of the lower half of the dataset and the third quartile (Q3) the median of the upper half. In the same way as for the median calculation, a quartile should be represented as the mean of two data points if it lies between them. 

Low-Pressure Impactor Data. Table I lists the count medians and geometric standard deviations from log-normal fits of the distributions obtained by SEM analyses of sample MKV-1, Listed also are the corresponding mass medians calculated from the count distributions. 

Figure 54-3 Concentration of chorionic gonadotropin (CG) in maternal serum as a function of gestational age. Lines represent the 2nd, 50th, and 97th percentiles.The maternal serum values from 14 to 25 weeks are medians calculated from 24,229 pregnancies from testing performed at ARUP Laboratories Inc, from January to October 1997, fRedrawn fromAshwood R. Evaluating health and maturation of the unborn the role of the clinical laboratory. Clin Chem 1992 38 1523-1529. Permission granted from Clin Chem.)...

Figure 54-12 Concentrations of alpha fetoprotein (AFP) in fetal and newborn serum, maternal serum, and amniotic fluid. The maternal serum values are medians calculated from 24,232 pregnancies and the amniotic fluid values are medians calculated from 1544 pregnancies from testing performed at ARUP Laboratories Inc. from January to October 1997.The fetal serum values are from Gitlan. The newborn serum values are from Wu et aU "...

Ingrid Pettersson and Tommy Li(jefors, Molecular Medianics Calculated Conformational Energies of Organic Molecules A Comparison of Force Fields. 

AVERAGE Calculates the mean of a series of numbers MEDIAN Calculates the median of a series of numbers... 

C. A. Croxton and R. P. Ferrier, Statistical medianical calculations of the surface properties of simple liquids III. Surface tension, J. Phys. C 4, 2433-2446 (1971). 

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. 

Acute toxicity studies are often dominated by consideration of lethaUty, including calculation of the median lethal dose. By routes other than inhalation, this is expressed as the LD q with 95% confidence limits. For inhalation experiments, it is convenient to calculate the atmospheric concentration of test material producing a 50% mortaUty over a specified period of time, usually 4 h ie, the 4-h LC q. It is desirable to know the nature, time to onset, dose—related severity, and reversibiUty of sublethal toxic effects. 

The probabihty-density function for the normal distribution cui ve calculated from Eq. (9-95) by using the values of a, b, and c obtained in Example 10 is also compared with precise values in Table 9-10. In such symmetrical cases the best fit is to be expected when the median or 50 percentile Xm is used in conjunction with the lower quartile or 25 percentile Xl or with the upper quartile or 75 percentile X[j. These statistics are frequently quoted, and determination of values of a, b, and c by using Xm with Xl and with Xu is an indication of the symmetry of the cui ve. When the agreement is reasonable, the mean v ues of o so determined should be used to calculate the corresponding value of a. 

The suitabihty of the Gompertz fit to the cui ve can be assessed by comparing the values olb calculated from Eqs. (9-97) and (9-98), and, if suitable, the average value of b may be used in Eq. (9-99) to calculate the corresponding value of a to ensure a fit at the median and reasonable accuracy over the more important practical range within a couple of standard deviations on either side of the median. 

Cone] (jj.M) Response Calculated Residual (0j)2 0j -median(0j) Weighting3... 

The most useful characteristic of the median is the small influence exerted on it by extreme values, that is, its robust nature. The median can thus serve as a check on the calculated mean. 

A wholly different approach is that of Huber, who orders the values according to size, and determines the median (cf. Section 1.1.1) then the absolute deviations jx, - x l are calculated and also ordered, the median absolute deviation (MAD) being found. MAD is then used as is Sx earlier, the coefficient k being chosen to be between 3 and 5. This algorithm is much more robust than the ones described before. 

Select a column from a data file and calculate mean, median, and standard deviation. Display the original data together with Xmean and mean i ... 

Calculate all deviations (jc(i) - jc ), and sort according to absolute size calculate the median average deviation MAD calculate cut-off limits for outliers according to Huber i by assuming the recommended value for Huber s k (3.5). Different values for this multiplier can be selected. Display the cut-off limits and the clipped data set. 

Results of the calculated reductions of actual exposure of the hands are plotted in Figure 2. As illustrated, there is a large variability among individual workers. The median reduction of the exposure was 95% for the applicators and 87% for the harvesters. Reduction of the dose showed even larger... 

Comparisons between observed data and model predictions must be made on a consistent basis, i.e., apples with apples and oranges with oranges. Since models provide a continuous timeseries, any type of statistic can be produced such as daily maximums, minimums, averages, medians, etc. However, observed data are usually collected on infrequent intervals so only certain statistics can be reliably estimated. Validation of aquatic chemical fate and transport models is often performed by comparing both simulated and observed concentration values and total chemical loadings obtained from multiplying the flow and the concentration values. Whereas the model supplies flow and concentration values in each time step, the calculated observed loads are usually based on values interpolated between actual flow and sample measurements. The frequency of sample collection will affect the validity of the resulting calculated load. Thus, the model user needs to be aware of how observed chemical loads are calculated in order to assess the veracity of the values. 

Another way is the robust parameter estimation on the basis of median statistics (see Sect. 4.1.2 Danzer [1989] Danzer and Currie [1998]). For this, all possible slopes between all the calibration points bij = (yj — yi)/(xj — X ) for j > i are calculated. After arranging the b j according to increasing values, the average slope can be estimated as the median by... 

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. 

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. 

The fraction of unattached daughters (fp), the equilibrium factor (F) and the activity median diameter (AMD) are plotted in Figure 6 for all the measurements. The AMD is derived from the aerosol measurements. These three parameters are important in the dosimetric models. At the top of Figure 6 the effective dose equivalent is plotted, computed with two models called the J-E (Jacobi-Eisfeld) and J-B (James-Birchall) models in the NEA-report (1983, table 2.9, linear interpolation between AMD=0.1 and 0.2 ym). The figure also shows the effective dose equivalent calculated from the equilibrium equivalent radon concentrations with the NEA dose conversion factor (NEA,1983, table 2.11). 

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