What is a stem-and-leaf plot?

This post is directed at content developers, elementary math. I would like you to develop a Voxitatis tutorial on this topic to help parents explain elementary school mathematics to their children. The tutorial, when developed, may also help students who are struggling with the content described.

The topic of the tutorial should be stem-and-leaf plots: what they show about data, how to make a stem-and-leaf plot, the importance of the key, etc.

When should you use a stem-and-leaf plot?

Teachers have sort of “invented” the idea of a stem-and-leaf plot as an alternative way to represent data. I don’t want to imply that they are useless, but they are “coined” representations of data that teach elementary students another way to represent data. That said, they are fairly useful if you want to get an overall view of how often values in certain ranges occur in the data, compared to the frequency of values in other ranges.

A stem-and-leaf plot represents integers, which as students will know by the time they get to stem-and-leaf plots, are whole numbers. Integers do not include fractions or decimal points. A set of integers is like this: { … , -4, -3, -2, -1, 0, 1, 2, 3, 4, … }.

Then a stem-and-leaf plot “groups” integers by tens. For example, all the numbers between 20 and 29 would be in one category, numbers between 30 and 39 in the next category, 40 to 49 in the next, and so on.

A typical problem students would be asked to solve is to be presented with a large set of data, all of which are integers, and put them in a stem-and-leaf plot. The first step in that task is to group the integers by tens. In one science class, for example, students received the following scores on their chapter test:

We want to make a stem-and-leaf plot of these scores, and the first step is to group the scores by tens. How would you group these scores by tens?