Introduction to Box Plots

An essential part of any Belt training, box plots provide an excellent visual summary of many important aspects of a distribution.

The box represents the middle 50% of the data; the whiskers the range. Q1 and Q3 are the quartiles. A scale is placed under the box plot to show the values indicated on the plot. Outliers are points that are more than 1.5 times the interquartile range above the third quartile or below the first quartile. The whiskers extend to the largest, and smallest, data values that are not outliers.

From Wikipedia:

Boxplots may seem more primitive than a histogram or probability density function (pdf) but they do have some advantages. Besides saving space on paper, boxplots are quicker to generate by hand. Histograms and probability density functions require assumptions of the statistical distribution. This assumption can be a major barrier because binning techniques can heavily influence the histogram and incorrect variance calculations will heavily affect the probability density function.

Some worked examples can be found here (with an unexpected application here) . You can also generate these plots in Excel.

However, beware! Although all box plots are interpreted in the same way, the actual values used for the quartiles, Q1 and Q3, differ in practice. There are three methods for obtaining the five number summaries, for example, Joseph M. Juran method, MINITAB method and the John Wilder Tukey method.

How do you use your boxplots?