Five-number summary

In the ordered list, users can see the numerical detail about the distribution of each dimension in an orderly manner. The numerical detail includes the five-number summary of each dimension and the mean and the standard deviation. The numerical score values are also shown at the third column whose background is color coded using the same color mapping as in the score overview. 

The box-and-whisker plot, accompanied by a numerical scale, is a graphical representation of the five-number summary, i.e. the data set is described by its extremes, its lower and upper quartiles, and its median. The plot shows at a glance the spread and the symmetry of the data. 

As in the previous example, the data as presented convey very little, but the use of two box-and-whisker plots or five-number summaries is very revealing. The five-number summaries are ... 

Five-Number Summary Also denoted as 5-number summary, an abbreviated representation or summary of a data set which states the lower limit, the first quartile, the median, the third quartile, and the upper limit. The five-number summary is often displayed using a box-and-whisker plot. 

One of the milestone references for EDA is the comprehensive book by Tukey [1]. Tukey, in his work, aimed to create a data analysis framework where the visual examination of data sets, by means of statistically significant representations, plays the pivotal role to aid the analyst to formulate hypotheses that could be tested on new data sets. The stress on two concepts such as dynamic experimenting on data (e.g. evaluating the results on different subsets of a same data set, under different data-preprocessing conditions) and exhaustive visualization capabilities offers researchers the possibility to identify outliers, trends and patterns in data, upon which new theories and hypothesis can be built. Tukey s first view on EDA was based on robust and nonparametric statistical concepts such as the assessment of data by means of empirical distributions, hence the use of the so-called five-number summary of data (range extremes, median and quartiles), which led to one of his most known graphical tools for EDA, the box plot. 

Before addressing the question of the health impacts of radon and its decay products, the levels that have been found in indoor air will be reviewed. During the past decade, there has been an increasing number of surveys on the concentrations of airborne radioactivity in homes and other structures. A number of systematic national surveys have been conducted during the past five years so that there is substantial information available on radon concentrations in many European countries and Canada. A summary of these studies is presented in Table II. 

In summary, researchers have found a number of methods for avoiding p-oxo dimer formation and preserving a five-coordinate Fe(II) in iron-containing model compounds, through ... 

A summary of the analyses of these five instruments is given in Table 6.5. The figure in brackets gives the total number of separate parts of the instrument analysed (the denominator), and the number of analyses included in the average figure (the numerator). 

There are a variety of liquid phases available for both packed and capillary columns. In packed columns, these are coated onto a solid support in capillary columns they are coated onto the capillary column wall. At the height of packed column use, there were over 200 liquid phases in common use. With the much higher separating power of capillary columns, this number has dropped to five most common liquid phases with perhaps two dozen specialty materials. A summary of common liquid phases and their application is shown in Table 14.5. The capillary column and instrument vendors also have extensive information on how to properly use packed and capillary columns and on applications available in their literature and on their WWW-sites. ... 

Table I presents a summary of some of the literature pertinent to the phase behavior of a number of the lighter components of petroleum, listing publications. In this table the specific references for each subject are identified by an index number applicable to an American Documentation Institute reference 59). The large number of entries involved does not permit the inclusion of the specific references as part of this discussion. The marked increase in publication found in the past five years appears typical of the general growth of research activities, although in part it may result from a more complete literature search in this period.

Summaries of the work in tetrahydrofuran polymerizations (7, 2, 3) have appeared as late as 1963. However, in the last four to five years the number of publications has been so numerous and the advances in the understanding of tetrahydrofuran polymerizations have been so rapid that it is worth reviewing again at this time. New catalysts have been reported, significant studies with old catalysts have been made, and a number of papers on the physical properties of polytetrahydrofuran have appeared. We will emphasize this new work and attempt to point out some areas where new investigations or a reinvestigation of earlier studies would be helpful. 

Of these 86, 47 were fieldworker reentry incidents (Table I). Nine states reported incidents. California had the highest number with 34 incidents, followed by North Carolina with 3. Sulfur led with 9 cases and parathion was involved in 6. All the sulfur cases were from California, usually involving eye irritation. Twenty-five different pesticides, covering all pesticide classes, were implicated in these reported incidents (Table II). But this summary must be judged incomplete as the... 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

SCAN gives a printout or summary of the quality of the data in a contig. The quality of the data depends on the number of times it has been sequenced and the particular uncertainty codes used in each gel reading. It divides the data into five categories and the quality codes are described below ... 

In summary, the number and the positional substitution of chlorine atoms determines the pathway and the susceptibility to PCB metabolism. PCB congeners with 2,5-dichloro- or 2,3,6-trichloro-substituted phenyl rings form persistent MeS02-substituted metabolites, but also hydroxylated metabolites. These MeS02-PCBs are accumulated in adipose tissue and/or selectively retained in tissues. PCB congeners that are less susceptible to metabolism, possess five or more chlorine atoms and no adjacent, chlorine-unsubstituted meta-para-positions, can be metabolized to hydroxylated metabolites that may be retained in blood. 

Table 1 shows a summary of the iterations. In this example, even thought the number o independent variables is five, the bounds of at least three of them are very close improving the performance of the algorithm. Therefore it is not strange that in the first iteration, the results are very close the optimal solution. The second iteration assures that the kriging errors are inside the tolerance. 

Fig. 8. A summary of garnet zoning profiles for the five structural domains of the Isua Greenstone Belt. The data are presented for fe-number, as an indicator of the thermal history of the grains, and show the generations of garnet in each domain, identified on the basis of their morphological, compositional and chemical-zonation differences.

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