What Is a Box-and-Whisker Plot?

The box-and-whisker plot is a technique in statistics that graphically shows the distribution of a set of data involving the minimum and maximum values, as well as the first, second and third quartiles. The plot is typically drawn using a number line.

The interpretation of a set of data can be made simpler and easier by devising measures of location, which is either a computed value, such as averages, or a probability distribution of a sample statistic. The three commonly used measures in statistics are the mean, mode and median. The mean is the common average, where all values are added up and then divided by how many data values there are in a sample. The mode is the most repeated value in the data set. When the values are arranged in increasing order, the middle value is called the median.

The way a set of data is clustered or distributed can be illustrated by dividing the data into four parts, known as quartiles. The median is also referred to as the second quartile. The first and third quartiles are the medians of the lower and upper half of the data set, respectively. In a box-and-whisker plot, the first and third quartiles form the ends of the box, with the median in the interior of the box. The highest and lowest values represent the whiskers.