A stemplot also referred to as a stem-and-leaf display, functions to provide in graphical form the shape and spread associated with a set of quantitative data. Stemplots provide a useful method for presenting small data sets without their being any loss of detailed or valuable information. Commonly there is a loss of detailed information when data is graphed or tallied in a summary table.
For example, consider a frequency distribution. When you record the tallies counted for each of the class frequencies, you unfortunately lose some the information regarding the values of the numbers which are part of the tally. When using a stemplot, you can avoid this loss of information. Stemplots allow the digits of each class to be recorded.
For example, pretend that you are an eighth grade math teacher and you want to observe the range of scores received by your class. The scores are as follows: 58, 63, 78, 98, 100, 98, 84, 84, 75, 64, 67, 56, 88, 78, 78, 89, 86, 92, 90. The first step here is to order these values in order from smallest to largest.
Order: 56, 58, 63, 64, 67, 75, 78, 78, 78, 84, 84, 86, 88, 89, 90, 92, 98, 98, 100.
The second step involves the actual construction of the figure. In a stemplot, the left-side which is the stem, records the tens digits (50, 60, 70 and so on). The right-hand side, which is known as the leaves, represents the 1.0 units.
Figure 1. This is a stemplot for the math scores of an eighth grade math class.
As can be seen in Figure 1, stemplots clearly display the full range and spread of the values associated with a data set. Additionally, when working with small data sets, or essentially any data set, a stemplot ensures that there is no loss of information.