Boxplots display basic summary statistics of a data set in the form of a rectangular picture. You can gain an intuitive understanding of a data set from boxplots because they de-emphasize exact data points and display the data in a unique manner. The left plot in the following figure is an example of a boxplot. The rectangle represents where the center 50% of the data points lie. The horizontal line in the center rectangle represents the median of the data set. The long vertical lines are called whiskers. Whiskers have a length of 1.5 times the inner quartile spread, which is the difference between the upper quartile and the lower quartile. You measure whiskers from the median of the data. The whiskers are indirect plot indicators because you use other statistics to generate them. However, whiskers are useful because they display the distribution of the data in a clear manner. An X indicates a potential outlier, which is outside the range of the whiskers.
Boxplots are valuable because they quickly show the median, upper and lower quartiles, and potential outliers of the data set. Data that is skewed upward or downward on the range has a boxplot in which the median does not divide the box evenly. Although an evenly divided boxplot can give the impression of a normally distributed data set, the boxplot still suppresses the exact values of the data set. You can overcome this weakness in the boxplot by creating a stem-and-leaf display, shown as the right display in the previous figure.
Technically, stem-and-leaf displays are not plots because they are text-based. However, stem-and-leaf displays indicate every data point, which is useful for determining exact values and seeing the distribution of the data. You construct stem-and-leaf displays by dividing the data set in to ranges, or stems. Each stem has a number of leaves, or data points. A leaf is the least significant digit of the stem value. For example, in the previous figure, the first stem is the range from 2.23—2.27. This stem contains three leaves: 2.24, 2.26, and 2.27.
Boxplot and Stem-and-Leaf Display