The boxplot is a good graph for representing the median, interquartile range and extreme cases. Notice, however, that the graph does not necessarily represent the distribution of ranked data. It only represents above statistics within the distribution of scores of the variable of reference.
If the boxplot were to represent above statistics within the distribution of ranked data, then the boxplot would look the same for all distributions, with the median symmetrically centered in the middle of the box, the IQR extending symmetrically towards the 25th and 75th percentile, respectively, and no extreme cases or outliers.
What the typical boxplot actually does is to graph the above ordinal statistics on the scale the variable is expressed on (eg, interval or ratio). Because of this, the boxplot can be used to identify extreme cases and outliers, assess the skewness of the distribution, etc. Thus, it is a graph that although it represents ordinal statistics (ie, non-parametric ones), it actually informs about the distribution of scores on the natural scale of the variable (ie, parametric ones).
Want to know more?
- Khan Academy - Box-and-whisker plots
- Khan teaches about how to calculate the range in this video.
|Khan Academy (undated - embedded from YouTube on 29 April 2012)|