Overview of the Stem-and-Leaf Plot

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Data can be shown in a variety of ways including graphs, charts, and tables. A stem-and-leaf plot is a type of graph that is similar to a histogram but shows more information by summarizing the shape of a set of data (the distribution) and providing extra detail regarding individual values. This data is arranged by place value where the digits in the largest place are referred to as the stem, while the digits in the smallest value or values are referred to as the leaf or leaves, which are displayed to the right of the stem on the diagram.

Stem-and-leaf plots are great organizers for large amounts of information. However, it is also helpful to have an understanding of the mean, median, and mode of data sets in general, so be sure to review these concepts prior to beginning work with stem-and-leaf plots. 

Using Stem-and-Leaf Plot Diagrams

Stem-and-leaf plot graphs are usually used when there are large amounts of numbers to analyze. Some examples of common uses of these graphs are to track a series of scores on sports teams, a series of temperatures or rainfall over a period of time, or a series of classroom test scores. Check out this example of test scores:

Test Scores Out of 100
 Stem Leaf
9 2 2 6 8
83 5
7 2 4 6 8 8 9
61 4 4 7 8
5 0 0 2 8 8

The Stem shows the tens column and the leaf. At a glance, you can see that four students got a mark in the 90s on their test out of 100. Two students received the same mark of 92, and no students received marks that fell below 50 or reached 100.

When you count the total number of leaves, you know how many students took the test. Stem-and-leaf plots provide an at-a-glance tool for specific information in large sets of data. Otherwise, you would have a long list of marks to sift through and analyze.

You can use this form of data analysis to find medians, determine totals, and define the modes of data sets, providing valuable insight into trends and patterns in large data sets.

In this instance, a teacher would need to ensure that the 16 students who scored below 80 truly understood the concepts on the test. Because 10 of those students failed the test, which accounts for almost half of the class of 22 students, the teacher might need to try a different method that the failing group of students could understand.

Using Stem-and-Leaf Graphs for Multiple Sets of Data

To compare two sets of data, you can use a back-to-back stem-and-leaf plot. For instance, if you want to compare the scores of two sports teams, you can use the following stem-and-leaf plot:

 Scores
 LeafStemLeaf
Tigers Sharks
0 3 7 932 2
 2 843 5 5
1 3 9 754 6 8 8 9

The tens column is now in the middle column, and the ones column is to the right and left of the stem column. You can see that the Sharks had more games with a higher score than the Tigers because the Sharks only had two games with a score of 32, while the Tigers had four games—a 30, 33, 37 and a 39. You can also see that the Sharks and the Tigers tied for the highest score: a 59.

Sports fans often use these stem-and-leaf graphs to represent their teams' scores to compare success. Sometimes, when the record for wins is tied within a football league, the higher-ranked team will be determined by examining data sets that are more easily observable, including the median and mean of the two teams' scores.

Practice Using Stem-and-Leaf Plots

Try your own stem-and-leaf plot with the following temperatures for June. Then, determine the median for the temperatures:

77 80 82 68 65 59 61
57 50 62 61 70 69 64
67 70 62 65 65 73 76
87 80 82 83 79 79 71
80 77

Once you've sorted the data by value and grouped them by the tens digit, put them into a graph called "Temperatures." Label the left column (the stem) as "Tens" and the right column as "Ones," then fill in the corresponding temperatures as they occur above.

How to Solve to Practice Problem

Now that you've had a chance to try this problem on your own, read on to see an example of the correct way to format this data set as a stem-and-leaf plot graph.

Temperatures
TensOnes
50 7 9
61 1 2 2 4 5 5 5  7 8 9
70 0 1 3 6 7 7 9  9
80 0 0 2 2 3 7

You should always begin with the lowest number, or in this case temperature: 50.

Since 50 was the lowest temperature of the month, enter a 5 in the tens column and a 0 in the ones column, then observe the data set for the next lowest temperature: 57. As before, write a 7 in the ones column to indicate that one instance of 57 occurred, then proceed to the next-lowest temperature of 59 and write a 9 in the ones column.

Find all of the temperatures that were in the 60s, 70s, and 80s and write each temperature's corresponding ones value in the ones column. If you've done it correctly, it should yield a stem-and-leaf plot graph that looks like the one in this section.

To find the median, count all the days in the month, which in the case of June is 30. Divide 30 by two, yielding 15, count either up from the lowest temperature of 50 or down from the highest temperature of 87 until you get to the 15th number in the data set, which in this case is 70. This is your median value in the data set.