Graphics whisker plots

Another graphical description of the data is used when comparing the results of several trials is the box plot (also called box-and-whisker plot). A box represents the range of the middle 50% of the data, and whiskers extend to the maximum and minimum values. A line is drawn at the median value. A glance a this plot allows one to assess the symmetry and spread of the data. Figure 5.4 is a box plot for the carbonate data of figure 5.2. Specific plots, such as Youden two-sample plots for method performance studies, are discussed below. 

Detection of aberrant (outlier) or suspected values The Grubbs test is the statistical test used to identify if there are some aberrant (outlier) or suspected values, the risk taken is also 5% (Feinberg, 2001). Aberrant or suspected values can also be checked graphically through Box and Whiskers plots. 

The heights of the bars or columns usually represent the mean values for the various groups, and the T-shaped extension denotes the standard deviation (SD), or more commonly, the standard error of the mean (discussed in more detail in Section 7.3.2.3). Especially if the standard error of the mean is presented, this type of graph tells us very litde about the data - the only descriptive statistic is the mean. In contrast, consider the box and whisker plot (Figure 7.2) which was first presented in Tukey s book Exploratory Data Analysis. The ends of the whiskers are the maximum and minimum values. The horizontal line within the central box is the median, fhe value above and below which 50% of the individual values lie. The upper limit of the box is the upper or third quartile, the value above which 25% and below which 75% of fhe individual values lie. Finally, the lower limit of the box is the lower or first quartile, the values above which 75% and below which 25% of individual values lie. For descriptive purposes this graphical presentation is very informative in giving information about the distribution of the data. 

Descriptive Statistics Graphically Illustrated Box-and-Whisker Plots... 

Graphically, the most important details of descriptive statistics of data can be represented in a box-and-whisker plot or, for short, box plot (Figure 2.5). Along the variable axis, here the ordinate, a box is drawn, with the lower and upper quartile being the bottom and top of the box, respectively. The width of the box has no meaning. 

Characterize the data in Problem 1 graphically by a box-and-whisker plot. 

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. 

We now present and discuss some of the results of the benchmark. The benchmark exercise features aU of the techniques applied to each of the examples, but in the scope of this document we only can present a representative subset. Most of the graphics are shown in form of box plots derived from the 25 available runs per sample size. The box plots show the lower quartile, the median, and the upper quartile values. The whiskers in the plots are lines showing the data range. Outhers are detected using a multiple (here 3) of the inter-quartile range. 

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