A variety of graphic displays can be used to give an effective visual summary of key descriptive statistics for a data set. One of these is a box plot, which is also called a box-and-whisker plot.

A box plot shows the smallest and largest values of a data set, the first and third quartiles and the median. By presenting these key descriptive statitsics, the box plot also shows the range and interquartile range.

Diagram
 Minimum        Median                              Maximum
   |              |                                    |
   |     First    |          Third                     |
   |     quartile |          quartile                  |
   |       |      |            |                       |
   |      \|/    \|/          \|/                      |
   |        ___________________                        |
  \|/      |      |            |                      \|/
   ._______|      |            |_______________________.
           |      |            |
           |______|____________|

           |___________________|
                     |
            Interquartile range

   |___________________________________________________|
                               |
                             Range


The above diagram shows a prototype box plot (as best depicted within a HTML environment). The plot has been displayed horizontally but it could also be displayed vertically.

  • The extremeties of the plot (the ends of the whiskers) correspond to the smallest and largest observations in the data set, the distance between these represents the range.

  • The ends of the box are positioned at the first and third quartiles of the data set, hence the length of the box represents the interquartile range.

  • The partitioning line within the box is drawn at the median of the data set.
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