Descriptive quartiles

Detailed instructions are provided for the calculation of the mean, median and SD (but not quartiles) using Microsoft Excel. Readers are referred to the accompanying web site for detailed instructions on generating all these descriptive statistics (including quartiles) using Minitab or SPSS. Generalized instructions that should be relevant to most statistical packages are provided in the book. 

The early chapters (1-5) are fairly basic. They cover data description (mean, median, mode, standard deviation and quartile values) and introduce the problem of describing uncertainty due to sampling error (SEM and 95 per cent confidence interval for the mean). In theory, much of this should be familiar from secondary education, but in the author s experience, the reality is that many new students cannot (for example) calculate the median for a small data set. These chapters are therefore relevant to level 1 students, for either teaching or revision purposes. 

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. 

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. 

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