Home >> Science & Nature >> Science

What Is a Box & Whisker Graph?

A box and whisker plot, also known as a box plot, is a statistical graph for describing a single quantitative variable, such as weight, although there are variations that include a categorical variable as well. Box plots are extremely useful when there are more than about 100 subjects. With smaller sample sizes, a strip plot may be better. Box plots were invented by John W. Tukey, one of the pre-eminent statisticians of the 20th century.

The Box
- The basic box and whisker plot consists of a box and whiskers, and there may be dots for outliers as well. The box has an upper limit and a lower limit and a line in the middle. The upper limit of the box is the third quartile, or 75th percentile, it is the value that is higher than 75% of all the values. The lower limit is the first quartile, or 25th percentile and the middle line is the median, or 50th percentile.
The Whiskers and Outliers
- The whiskers in a box and whisker plot are thin lines extending out from the box. The length of the whiskers is 1.5 times the interquartile range. The interquartie range is the difference between the third quartile and the first quartile. Any points that are beyond the whiskers are marked with dots, as outliers.
Variation: Parallel Box Plots
- One variation on the box plot is good for comparing groups of subjects; for example, you might want to compare the weights of people from different regions of the United States. In this variation, you make a box plot for each group, and put them next to each other so they can be compared.
Variation: Violin Plots
- It is possible to add more information to a box plot. One way to do this is the violin plot. In a violin plot, the rectangular box of the box plot is replaced by an irregular shape whose width is proportional to the density of the variable at that point. Parallel violin plots are also possible.

Science