box-and-whisker plot

box-and-whisker plot, graph that summarizes numerical data based on quartiles, which divide a data set into fourths. The box-and-whisker plot is useful for revealing the central tendency and variability of a data set, the distribution (particularly symmetry or skewness) of the data, and the presence of outliers. It is also a powerful graphical technique for comparing samples from two or more different treatments or populations. It was invented in the 1970s by American statistician John Wilder Tukey.

A box-and-whisker plot typically consists of a line (vertical or horizontal) extending from the minimum value to the maximum value and a box, the end lines of which depict the first quartile (Q₁) and the third quartile (Q₃) and a central line within which depicts the second quartile (Q₂; also called the median). (The first quartile represents the 25th percentile, the second quartile represents the 50th percentile, and the third quartile represents the 75th percentile.) Outliers are plotted as individual data points.