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.