2.5 Stem and leaf displays

A stem and leaf display is a graphical method of displaying data. It is particularly useful when your data arenot too numerous. In this section, we will explain how to construct and interpret this kind of graph.

As usual, an example will get us started. Consider . It shows the number of touchdown (TD) passes

A stem and leaf display of the data is shown in the below. The left portion of the table contains the stems. They are the numbers3, 2, 1, and 0, arranged as a column to the left of the bars. Think of these numbers as 10's digits. A stem of 3 (forexample) can be used to represent the 10's digit in any of the numbers from 30 to 39. The numbers to the right of the bar areleaves, and they represent the 1's digits. Every leaf in the graph therefore stands for the result of adding the leaf to 10times its stem.

To make this clear, let us examine this more closely. In the top row, the four leaves to the right of stem 3 are 2, 3, 3, and 7. Combinedwith the stem, these leaves represent the numbers 32, 33, 33, and 37, which are the numbers of TD passes for the first fourteams in the table. The next row has a stem of 2 and 12 leaves. Together, they represent 12 data points, namely, two occurrencesof 20 TD passes, three occurrences of 21 TD passes, three occurrences of 22 TD passes, one occurrence of 23 TD passes, twooccurrences of 28 TD passes, and one occurrence of 29 TD passes. We leave it to you to figure out what the third row represents.The fourth row has a stem of 0 and two leaves. It stands for the last two entries, namely 9 TD passes and 6 TD passes. (Thelatter two numbers may be thought of as 09 and 06.).

One purpose of a stem and leaf display is to clarify the shape of the distribution. You can see many facts about TD passesmore easily in than in the . For example, by looking at the stems and the shape of the plot, youcan tell that most of the teams had between 10 and 29 passing TDs, with a few having more and a few having less. The precisenumbers of TD passes can be determined by examining the leaves.

We can make our figure even more revealing by splitting each stem into two parts. The below shows how to do this. The top row is reserved for numbers from 35 to 39 and holds only the 37TD passes made by the first team in the . The second row is reserved for the numbers from 30 to 34 and holds the 32, 33, and 33 TD passesmade by the next three teams in the table. You can see for yourself what the other rows represent.