Stem-and-Leaf Plots

Stem and leaf plots are one way of representing data in a simple and efficient way to read. Stem and leaf plots have several advantages that make them especially useful for the purpose of analyzing large sets of data easily.

Stem and leaf plot definition

The stem and leaf plot is a graphical way of organizing data that makes it easy to notice the frequency of different values. Stem and leaf plots are pictorial representations of grouped data, but they can also be called modal representations. This is because, with a quick glance at the stem and leaf plot, we can easily determine the mode.

Data visualization

Statistics are often easier to read and understand when they are shown in a graphic format. There are many ways to represent statistical data graphically, such as bar graphs, histograms, line graphs, column charts, tree maps, and stem and leaf plots, among others.

Displaying statistical data visually, or data visualization is a useful way to provide accessible ways to analyze patterns and trends across a large set of data. These are used by governments, scientists, and climatologists to record data and present it graphically for easier access.

A basic understanding of different ways of data visualization is useful in all sorts of different fields. Stem and leaf plots organize data points by the place value of the leading digits.

When making a stem and leaf plot, each item of data is separated into two parts. The "stems" typically represent the digits in the highest place value of each data point. The "leaves" represent the remaining digits of each data point.

How to create a stem and leaf plot

Example 1

Suppose you are given the data set $\left\{35,37,24,23,27,31,33,49,34,41,35\right\}$ . The digits in the tens place would be the "stems" and the digits in the ones place would be the "leaves". The smallest digit in the tens place is 2 and the largest is 4. List them vertically on the left side. For each stem, list the corresponding leaves in increasing order on the right side.

Stem	Leaf
2	3 4 7
3	1 3 4 5 5 7
4	1 9

Note that there are two 5s in the second row because there are two 35s in the data set.

Making a stem and leaf plot for decimals

When making a stem and leaf plot for data that is in decimal form, you can forget about the decimals. You may break the stem and leaf apart at the point of the decimal or you may not, but on the plot itself, you do not represent the decimal points.

Example 2

Make a stem and leaf plot for the following data set:

$\left\{0.1325,0.1329,0.1331,0.1332,0.1332,0.1333,0.1337,0.1344,0.1348,0.1351\right\}$

Note that in this case, the data is already presented in ascending order. This will not usually be the case.

Since the digits 0.13 are common to all data points, you will arrange the 0.132, 0.133, 0.134, and 0.135 in the left column.

132	5 9
133	1 2 2 3 7
134	4 8
135	1

Be sure to include a "key" to show the place value that is meant. In this case, the key is:

$132|5=0.1325$

Using a stem and leaf plot to find the median, mode, and range of a data set

Use the previous stem and leaf plot to find the median, mode, and range of the data set.

Example 3

There are 10 elements in this set. Since this is an even number of elements, the median of the data is the mean of the 5th and 6th data points. Counting on the stem and leaf plot, we see that 133|2 and 133|3 are the 5th and 6th entries. So the median is:

$\frac{0.1332+0.1333}{2}=0.13325$

To find the mode, simply look for the leaf that is repeated the most times under a single stem. In this case, $133|2$ occurs twice, so the mode is 0.1332.

To find the range of the data set, subtract the least number from the greatest.

$0.1351-0.1325=0.0026$

The range is 0.0026

Practice using stem and leaf plots

Use the following set of data to create a stem and leaf plot. Then find the median, mode, and range of the data set.

$\left\{126,138,142,133,156,138,147,159,162,148,154,142,138,146\right\}$

First, arrange the data in ascending order:

$\left\{126,133,138,138,138,142,142,146,147,148,154,156,159,162\right\}$

Then create the stem and leaf plot.

12	6
13	3 8 8 8
14	2 2 6 7 8
15	4 6 9
16	2

There are 14 data points in this set, so the median will fall between the 7th and 8th data points, which are 142 and 146.

$\frac{142+146}{2}=144$

So the median is 144.

The mode is 138, as there are three data points with this number, more than any other data points.

To find the range, subtract 126 from 162.

$162-126=36$

The range is 36.

Topics related to the Stem-and-Leaf Plots

Frequency Distributions

Bar Graphs

Probability Distribution

Flashcards covering the Stem-and-Leaf Plots

Statistics Flashcards

Common Core: High School - Statistics and Probability Flashcards

Practice tests covering the Stem-and-Leaf Plots

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

Get help learning about stem and leaf plots

Stem and leaf plots can be fun to make, but they can be confusing at first. If your student is having difficulty understanding stem and leaf plots, connect them with a private tutor who can show them the step-by-step process to create and utilize these visual data representations. An expert tutor can work with your student using their learning styles so they understand the content even if it seemed confusing when the instructor presented it. Contact the Educational Directors at Varsity Tutors today to learn how tutoring can help your student master stem and leaf plots.