In descriptive statistics, a boxplot or box plot (also known as a box-and-whisker diagram or plot) is a good way of graphically displaying groups of numerical data through their five-number summaries (minimum, first quartile (Q1), median, third quartile (Q3), and maximum). A boxplot may also indicate which observations, if any, might be considered outliers.

The space between the different parts of the box illustrate the spread and/or skewness in the data, and identify outliers. Boxplots can be drawn either horizontally or vertically.

 To make a boxplot:

Step 1) Find the five-number summary (minimum, first quartile, median, third quartile and the maximum) from all of the observations

Step 2) Draw a horizontal and a vertical axis. (*Note: boxplots can go either horizontally or vertically. In this example the boxplot will be vertical.)

Step 3) Label the vertical axis with uniform intervals beginning with a value equal to or less than the minimum at the bottom, and a value equal to or greater than the maximum at the top.

Step 4) Draw a short horizontal line at each of the data points from the five-number summary.

Step 5) Draw two short vertical lines (to make a "box") from the first and third quartiles. Finished.

Example: Make a boxplot from the following data: 75, 82, 62, 55, 95, 99, 76, 82, 81, 55, 62, 75, 76, 81, 82, 82, 95 and 99.

The five-number summary from this data is (55, 75, 81, 82, 99). Below is the boxplot.

Video example of how to make a boxplot.