What are Stem and Leaf Plots?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange and represent data so that it is simple to see how frequently various data values occur. It is a plot that displays ordered numerical data.
A stem and leaf plot is shown as a special table where the digits of a data value are divided into a stem (first few digits) and a leaf (usually the last digit). The symbol ‘|’ is used to split and illustrate the stem and leaf values. For instance, 105 is written as 10 on the stem and 5 on the leaf. This can be written as 10 | 5. Here, 10 | 5 = 105 is called the key. The key depicts the data value a stem and leaf represent.
How do we Construct a Stem and Leaf Plot?
Step 1: Classify the data values in terms of the number of digits in each value, such as 2 digit numbers or 3 digit numbers.
Step 2: Fix the key for the stem and leaf plot. For example, 2 | 5 = 25, 3 | 2 = 3.2 or 19 | 2 is 192.
Step 3: Consider the first digits as stems and the last digit as leaves.
Step 4: Find the range of the data, that is the lowest and the highest values among the data.
Step 5: Draw a vertical line. Place the stem on the left and the leaf on the right of the vertical line.
Step 6: List the stems in the stem column. Sort them in ascending order.
Step 7: List the leaf values in the column against the stem from lowest to the highest horizontally.
Explore More on Stem and Leaf Plot Through This Video
Rapid Recall
Key : 0 | 1 = 1
Solved Examples
Example 1:
The table below shows the duration of calls that Rosy makes each day. Represent the given data using a stem and leaf plot.
Solution:
Step 1: Sort the data (number of minutes).
2, 3, 5, 6, 10, 14, 19, 23, 23, 30, 36, 56
Step 2: Choose the stems and the leaves. Just because the data values range from 2 to 56, use the tens digit for the stem and the ones digit for the leaf. Also, include the key.
Step 3: Write down the stems on the left of the vertical line.
Step 4: Write down the leaves for each stem on the right of the vertical line.
Example 2
The stem-and-leaf plot below shows the quiz scores of students.
(a) Find the number of students who scored less than 9 points?
(b) Find the number of students who scored a minimum of 9 points?
Solution:
a) There are fourteen scores less than 9 points.
They are 6.6, 7.0, 7.5, 7.7, 7.8, 8.1, 8.1, 8.3, 8.4, 8.4, 8.6, 8.8, 8.8 and 8.9.
So, fourteen students scored less than 9 points.
b) There are two scores which are at least 9 points.
They are 9.0, 9.2, 9.9, and 10.0.
So, four students scored a minimum of 9 points.
Example 3:
Construct a stem-and-leaf plot for the data in the table.
Solution:
Step 1: Sort the data values: 1, 1, 1, 2, 2, 4, 5, 5, 7, 12, 20, 23, 27, 30, 32, 33, 38, 40, 44, 47
Step 2: Choose the stems and the leaves. As the data values range from 1 to 47, use the tens digits for the stems and the ones digits for the leaves. Be sure to include the key.
Step 3: Write the stems to the left of the vertical line from the top to bottom.
Step 4: Write the leaf values corresponding to each stem to the right of the vertical line.
Key : 0 | 1 = 1 cm
A stem and leaf plot is useful in displaying numerical data in a graphical and tabular style to visualize the shape of distribution.
The key in the stem and leaf plot splits the stem and leaf values and describes the data value for each stem-leaf set. It is denoted by ‘|’ as a symbol that is placed between particular stem and leaf values. For example: 2 | 1 = 21 or 12 | 2 = 122.
In math, the initial digit or digits of the data values are displayed in the ‘stem’, which is written on the left of the table from top to bottom.
The last digit of the data value is displayed in the ‘leaf’ column, which is written on the right of the table horizontally.