7.6: StemandLeaf Plots
What is the average age of a US president when he is sworn into office? If you collected the ages of all the US presidents during their inaugurations how could you organize and graph the data at the same time?
Watch This
First watch this video to learn about stem and leaf plots.
CK12 Foundation: Chapter7StemandLeafPlotsA
Then watch this video to see some examples.
CK12 Foundation: Chapter7StemandLeafPlotsB
Watch this video for more help.
Khan Academy Stem and Leaf Plots
Guidance
In statistics, data is represented in tables, charts, and graphs. One disadvantage of representing data in these ways is that the actual data values are often not retained. One way to ensure that the data values are kept intact is to graph the values in a stemandleaf plot. A stemandleaf plot is a method of organizing the data that includes sorting the data and graphing it at the same time. This type of graph uses a stem as the leading part of a data value and a leaf as the remaining part of the value. The result is a graph that displays the sorted data in groups, or classes. A stemandleaf plot is used most when the number of data values is large, and it allows you to easily calculate the mode and the median of a data set.
Example A
Construct a stemandleaf plot for the following data values:
The stemandleaf plot can be constructed as follows. We will first create the stemandleaf plot, and then we will organize the values of the leaves.
Example B
The following numbers represent the growth (in centimeters) of some plants after 25 days.
Construct a stemandleaf plot to represent the data, and list 3 facts that you know about the growth of the plants.
Note that there are no leaves for the second stem. If there are no values in a class, do not enter a value in the leaf just leave it blank.
As for 3 facts that you know about the growth of the plants, answers will vary, but the following are some possible responses:
 From the stemandleaf plot, the growth of the plants ranged from a minimum of 10 cm to a maximum of 61 cm.
 The median of the data set is the value in the position, which is 41 cm.
 There was no growth recorded in the class of 20 cm, so there is no number in the leaf row.
 The data set is multimodal.
Example C
The following stemandleaf plot represents the ages of 23 people waiting in line at Tim Horton’s. What is the mode and the median of the ages? How many people are older than 32?
The mode is the value that appears the most often, and here it is 32. As for the median, since there are 23 data values, the median is the value that appears in the position. From the stemandleaf plot, it's clear that this value is 32, so the median of the data set is 32 as well. Finally, to find the number of people older than 32, count the number of all the digits after the number 2 in the row that has 3 as its stem. There are a total of 11 digits, so 11 people are older than 32.
Guided Practice
At a local veterinarian school, the number of animals treated each day over a period of 20 days was recorded. Construct a stemandleaf plot for the data set, which is as follows:
What is the mode and the median of the data set?
Answer:
Step 1: Create the stemandleaf plot.
Some people prefer to arrange the data in order before the stems and leaves are created. This will ensure that the values of the leaves are in order. However, this is not necessary and can take a great deal of time if the data set is large.
The leading digit of a data value is used as the stem, and the trailing digit is used as the leaf. The numbers in the stem column should be consecutive numbers that begin with the smallest class and continue to the largest class.
Step 2: Organize the values in each leaf row.
Now that the graph has been constructed, there is a great deal of information that can be learned from it.
The number of values in the leaf column should equal the number of data values that were given in the table. The value that appears the most often in the same leaf row is the trailing digit of the mode of the data set. The mode of this data set is 35. For 7 of the 20 days, the number of animals receiving treatment was between 34 and 39. The veterinarian school treated a minimum of 5 animals and a maximum of 60 animals on any one day. The median of the data can be quickly calculated by using the values in the leaf column to locate the value in the middle position. In this stem and leaf plot, the median is the mean of the sum of the numbers represented by the and the leaves: .
Practice

The following stemandleaf plot shows the cholesterol levels of a random number of students. These values range from 2.3 to 8.9. What percentage of the students have levels between 5.0 and 7.1, inclusive?
 6 %
 20%
 24%
 28%
 Just like Presidents of the United States, Canadian Prime Ministers must be sworn into office. The following data represents the ages of 22 Canadian Prime Ministers when they were sworn into office. Construct a stemandleaf plot to represent the ages, and list 4 facts that you know from the graph.
Use the stemandleaf plot below to answer the following questions:
 What is the mode of the data set?
 What is the median of the data set?
 What is the minimum of the data set?
 What is the maximum of the data set?
Use the stemandleaf plot below to answer the following questions:
 What is the mode of the data set?
 What is the median of the data set?
 How many of the data values are greater than 40?
 What percentage of the data values are less than 40?
frequency distribution table
A table showing the number of times a particular category appears in a data set is a frequency distribution.histogram
A histogram is a bar chart that describes a frequency distribution.stemandleaf plot
A method of organizing data that includes sorting the data and graphing it at the same time. This type of graph uses the stem as the leading part of the data value and the leaf as the remaining part of the value.Image Attributions
Description
Learning Objectives
Here you'll learn how to construct stemandleaf plots and the importance of stemandleaf plots in statistics.