Creating & Reading Stem & Leaf Displays

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  • 0:03 Stem-and-Leaf Displays
  • 1:28 Creating Displays
  • 3:38 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Every once in a while you will come across stem-and-leaf displays in statistics. These displays can be very useful in identifying all of the values in a data set while still visually representing the data.

Stem-and-Leaf Displays

Jamie is a musician. He is working hard to earn money to buy his first guitar. Right now, he has been borrowing his friend's to learn how to play and practice. Each week, Jamie works odd jobs, such as lawn mowing, house sitting, and cleaning out gutters to earn the money he needs for his guitar. We can use the money Jamie makes each week to create a data set. Here are the amounts Jamie has made over the past ten weeks:

25, 37, 44, 56, 32, 42, 28, 31, 47, 37

Jamie can use different visual representations to analyze and compare this data. Jamie could make a histogram like this:

Example of a histogram

This histogram shows how often Jamie earned money in each of the categories. Jamie can also make a frequency chart. Here is an example of a frequency chart and an interval frequency chart:

Example of an interval frequency chart and a frequency chart
frequency charts

The problem with these forms of visual representation of data is that the original amounts that Jamie earned have been lost. We can get an overall picture or idea of the data, but if we need to look at each specific value, a histogram or frequency table would not help us. In this case, we need to create a stem-and-leaf display. A stem-and-leaf display is a visual representation of data where the stem, the data on the left side of the chart, shows one part of the value, while the leaves, the data on the right side of the chart, show the other.

Creating Stem-and-Leaf Displays

Jamie can create a stem and leaf display by first ordering his data in ascending order like this:

25, 28, 31, 32, 37, 37, 42, 44, 47, 56

This is a stem-and-leaf display without the values:

Stem-and-leaf display without values
empty stem and leaf chart

The left side of the display represent the tens values, so first we need to put the digits one through five on the left side of the display. On the right side of the display, we put the ones place digits. So for 25, we put the 2 on the left side and the 5 on the right side. This is how our data looks on a completed stem-and-leaf display:

Completed stem-and-leaf display
completed stem and leaf display

Notice that there are two sevens on the ones place in the third row. That's because there are two 37s in our data set. Not only can we see the frequency of our data in this display, but we can also get each specific value from our data set.

Jamie's friend, Tess, is tracking how many hours she works each week at the local pizza dive. Here is the data set for Tess's past ten weeks of working:

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