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While these graphs, known as stem-and-leaf plots, have a funny name, they actually serve a useful purpose and are very versatile.
Many quantitative data sets can be displayed in stem-and-leaf plots, such as the one below:
95 | 95 | 87 | 76 | 70 | 81 | 43 | 90 | 84 | 55 |
84 | 81 | 84 | 83 | 75 | 76 | 85 | 89 | 84 | 81 |
56 | 80 | 52 | 80 | 63 | 89 | 73 | 56 | 62 | 72 |
91 | 96 | 82 | 80 | 73 | 86 | 81 | 87 | 55 | 82 |
74 | 79 | 89 | 92 | 87 | 85 | 77 | 75 | 88 | 82 |
This data set represents the 50 states in the United States, and these numbers are the percent of college students in each state that are enrolled in public colleges. For example, in one state, 95% of its college students are in public schools, whereas in another state, only 52% are enrolled in public colleges.
To create a stem-and-leaf plot, follow these steps:
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9 | 0 | 1 | 2 | 5 | 5 | 6 | |||||||||||||||||||
8 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 7 | 7 | 7 | 8 | 9 | 9 | 9 |
7 | 0 | 2 | 3 | 3 | 4 | 5 | 5 | 6 | 6 | 7 | 9 | ||||||||||||||
6 | 2 | 3 | |||||||||||||||||||||||
5 | 2 | 5 | 5 | 6 | 6 | ||||||||||||||||||||
4 | 3 |
9 | 0 | 1 | 2 | 5 | 5 | 6 | |||||||||||||||||||
8 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 7 | 7 | 7 | 8 | 9 | 9 | 9 |
7 | 0 | 2 | 3 | 3 | 4 | 5 | 5 | 6 | 6 | 7 | 9 | ||||||||||||||
6 | 2 | 3 | |||||||||||||||||||||||
5 | 2 | 5 | 5 | 6 | 6 | Key: means 43% | |||||||||||||||||||
4 | 3 |
There is more than one way to display data on a stem-and-leaf plot. Other variations include:
In our previous graph, the 80's had more than any other grouping. In fact, they had more than twice as much as any other single grouping, which looked a little strange. Is there anything we can do about that?
Suppose that you decided that tens were too wide of a bin. Instead, you could break it down by fives, and then write two 8's--a low 8 and a high 8, or 85 to 89 for the high, and 80 to 84 for the low. Note, though, that if you’re going to split one bucket, you need to split them all.
9 | 5 | 5 | 6 | ||||||||||||||||
9 | 0 | 1 | 2 | ||||||||||||||||
8 | 5 | 5 | 6 | 7 | 7 | 7 | 8 | 9 | 9 | 9 | |||||||||
8 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | ||||
7 | 5 | 5 | 6 | 6 | 7 | 9 | |||||||||||||
7 | 0 | 2 | 3 | 3 | 4 | ||||||||||||||
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6 | 2 | 3 | |||||||||||||||||
5 | 5 | 5 | 6 | 6 | |||||||||||||||
5 | 2 | Key: means 43% | |||||||||||||||||
4 | |||||||||||||||||||
4 | 3 |
If you split the stems into lows and highs, the graph will look like the one above. Because this separates the stems so that no one stem has so much more data than any other, this is a more of an appropriate visual than the first one.
Take a look at this set of high school GPAs for this group of students. Make a stem-and-leaf plot of these GPAs.
Student | GPA |
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Amy | 2.95 |
Blake | 3.55 |
Holly | 3.75 |
Isaiah | 1.94 |
Jenny | 2.23 |
Jesse | 3.41 |
Jim | 1.96 |
Johnathan | 2.25 |
Katherine | 2.56 |
Kelly | 2.89 |
Ryan | 3.24 |
Sherry | 3.61 |
Teri | 4.00 |
Todd | 2.78 |
Tyler | 3.12 |
In this option, we can round the GPAs, which is a legitimate thing to do. Take Jim, for example. His GPA is 1.96, which would round to 2.0. Isaiah's GPA of 1.94 would round down to 1.9, Amy's GPA of 2.95 would round to 3.0.
4 | 0 | |||||||||||
3 | 0 | 1 | 2 | 4 | 6 | 6 | 8 | |||||
2 | 0 | 2 | 3 | 6 | 8 | 9 | Key: means GPA rounds to 2.0 | |||||
1 | 9 |
The graphs says “2 bar 0 means the GPA rounds to 2.0.” That refers to Jim, whose GPA rounds to 2.0.
In the same GPA example as above, we can leave the numbers as is and not round. This is also a completely legitimate way to represent this data as long as you visually separate these numbers.
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3 | 12 | 24 | 41 | 55 | 61 | 75 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
2 | 23 | 25 | 56 | 78 | 89 | 95 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1 | 94 | 96 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Key: means GPA is 2.23 |
The graph’s key says, “2 bar 23 means a GPA of 2.23.” For example, Tyler's GPA of 3.12 would be represented by the stem 3 and leaf 12.
Again, using the same GPA data from above, suppose you are interested in the differences between girls' GPAs, like Amy, Holly, Jenny, Katherine, etc., and the boys' GPAs.
You could compare those by putting one group of leaves to the right of the stem and another group of leaves to the left of the stem. This is known as a back-to-back stem-and-leaf plot, and it would look like this:
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Boys | |||||||||||
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8 | 6 | 0 | 3 | 1 | 2 | 4 | 6 | ||||||
9 | 6 | 2 | 2 | 0 | 3 | 8 | Key: means GPA rounds to 3.1 | ||||||
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1 | 9 |
This graph rounds the numbers again, saying that “3 bar 1 means the GPA rounds to 3.1.” Here, the girls' GPAs are on the left. The boys' GPAs are on the right. This allows you to compare the distributions of boys' GPAs to girls' GPAs, illustrating that the girls' GPAs are typically a little bit higher.
Why use a stem-and-leaf plot instead of other graphical displays, like histograms or dot plots? Stem-and-leaf plots have a couple of advantages:
Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.