A stem-and-leaf diagram is a way to organize data to make it easier to interpret. It helps to visualize a list of numbers by separating them into “stems” and “leaves”. The stem is typically the tens digit, and the leaf is the unit digit. For example, in the number 43:
- The stem is 4 (representing the tens place).
- The leaf is 3 (representing the unit place).
How to Construct a Stem-and-Leaf Diagram
Example 1:
Construct a stem-and-leaf diagram by using the ages of students:
11, 17, 20, 21, 24, 27, 30, 31, 34, 34, 37
Arrange data in ascending order
12, 18, 21, 22, 25, 28, 31, 32, 35, 35, 38
Identify the stems and leaves
For each number, the tens digit becomes the stem, and the unit digit becomes the leaf.
- Numbers in the 10s: Stems are 1 (leaves are 2, 8)
- Numbers in the 20s: Stems are 2 (leaves are 1, 2, 5, 8)
- Numbers in the 30s: Stems are 3 (leaves are 1, 2, 5, 5, 8)
Create the stem-and-leaf diagram
The stems are on the left, and the corresponding leaves are on the right.
1 | 2 8
2 | 1 2 5 8
3 | 1 2 5 5 8
This is how the data is displayed:
- The “1 | 2 8” represents numbers 12 and 18.
- The “2 | 1 2 5 8” represents numbers 21, 22, 25, and 28.
- The “3 | 1 2 5 5 8” represents numbers 31, 32, 35, 35, and 38.
Add a key to understand the diagram
To understand the diagram, add a key that explains how to read the stem and leaf.
For example:
Key: 1 | 2 means 12
Why do we use a stem-and-leaf diagram?
- Easy to interpret: It visually shows the distribution of the data.
- Keeps the original data: Unlike bar charts or pie charts, the stem-and-leaf diagram shows the data points.
- Organizes data into groups: It shows how data points are distributed across tens, hundreds, etc.
Example 2:
Create a stem-and-leaf diagram from the following data set of test scores:
45, 48, 52, 55, 59, 61, 67, 72, 75, 79
- Stems are: 4, 5, 6, 7
- Leaves for stem 4: 5, 8
- Leaves for stem 5: 2, 5, 9
- Leaves for stem 6: 1, 7
- Leaves for stem 7: 2, 5, 9
The stem-and-leaf diagram looks like this:
4 | 5 8
5 | 2 5 9
6 | 1 7
7 | 2 5 9
And the key:
Key: 4 | 5 = 45
Let’s practice more on stem-and-leaf diagram questions
0580/12/02/03/24/11a
Organize data in ascending order
28, 45, 46, 49, 50, 54, 58, 64, 65, 68, 70, 71, 72, 77
Steps:
Stem represents the tens digit
Leaf represents the unit digit
