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Math Foundations

You will construct a stem-and-leaf plot and interpret the data the plot represents.

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After completing this tutorial, you will be able to complete the following:

- Construct stem-and-leaf plots.
- Interpret stem-and-leaf plots.

Stem-and-leaf plots are a type of graphical display.

A stem-and-leaf plot is a method of organizing numerical data in order of place value. The leaf is the digit on the far right in the number. The stem is the digit or digits in the number that remain when the leaf is dropped. The total number of data items in a stem-and-leaf plot is equal to the number of leaves in the plot.

For example, suppose you have the following list of values:

12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41

Start the stem-and-leaf plot by creating a table with two columns. The "stem" is the left-hand column, which contains the tens digits. The "leaf" is the right-hand column, which contains the ones digits.

For instance, the first value in the list, 12, is written as a "1" under the stem column and as a "2" under the leaf column. The second row in this stem-and-leaf plot represents the numbers 21 and 27.

Use a stem-and-leaf plot to help analyze data.

For example, suppose the following scores were earned for a recent test:

42, 67, 73, 78, 82, 84, 86, 91, 94, 99

The stem-and-leaf plot for this data would look like this:

Notice that the 8 and 9 stems have the most leaves. This means that most of the students scored between 82 and 99 on this test. Because most of the data clusters occur here, we can say that the students generally performed well on this test.

Stem-and-leaf plots can be constructed with numbers other than whole numbers.

Data used to construct a stem-and-leaf plot is not always made up of whole numbers. Often, values with only one decimal place are used. The stem-and-leaf plot only looks at the last digit (for the leaves) and all the digits before (for the stem). Because of this, it is very important to always include a key with the plot to show what the numbers represent.

For example:

Students were timed while completing a certain task. Construct a stem-and-leaf plot for the following list of times:

7.6, 8.1, 9.2, 6.8, 5.9, 6.2, 6.1, 5.8, 7.3, 8.1, 8.8, 7.4, 7.7, 8.2

First, let's reorder the list:

5.8, 5.9, 6.1, 6.2, 6.8, 7.3, 7.4, 7.6, 7.7, 8.1, 8.1, 8.2, 8.8, 9.2

Next, we construct the plot along with a key to describe the meaning of the stems and leaves.

In this Activity Object, the data used will include decimal numbers.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should be familiar with place value and stem-and-leaf plots. |

Course | Math Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | 3D, stem-and-leaf plot, |