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.
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
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
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
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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Pause the video here and see if you can create a stem-and-leaf display from Tess' work hours. How did you do? Does your stem-and-leaf display look like mine?
Stem-and-leaf display from hours Tess worked
Remember, if you have two of the same value, you still have to show those values on the stem-and-leaf display. That's why we have 2 twos in the second row. Also notice that we have a zero on the left side of the display. That's because for the times that Tess worked 5, 7, or 8 hours, we can only represent those values on the right side of the display. Also notice that we do not put zeros into the places that have no numbers. This is because the left side represents the tens place. If we put a zero into one of these places, then we would have 30 or 40 or 50 represented in the data set.
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.
Not only can we see the frequency of our data in a stem-and-leaf display, but we can also get each specific value from our data set. Remember the left side of the display represents the tens values, so first put the digits one through five on the left side of the display. On the right side of the display, put the ones place digits. You can see all of the values this way rather than a visual representation that just shows the big picture!
Following this lesson, you should have the ability to:
Explain what a stem-and-leaf display is and why it is useful
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