Source: Train Schedule; Creative Commons: https://pperfectsquares.wordpress.com/category/math-lessons/statistics/
This tutorial talks about stem and leaf plots. Here's an example of what one is. On the left side, these numbers here are the stems. And on the right side, these are the leaves. So the number on the left side is combined with one of the leaves to tell us what value we have in our data set.
So for example, this 2 isn't a 2, but a 32. And this 7 is really 47. This 0 right here is on the stem for the 6, so it's really 60.
Now you might notice that right here on the 9, there is nothing written. So even though our data set doesn't have anything between 90 and 99, we still leave a spot for it on our stem and leaf chart so we can see the distribution of the data.
Now, from looking at our example, you can tell most of these facts already. A stem and leaf plot displays quantitative data. The data is broken into intervals of equal width, which become the stems.
So before, each stem represented 10 from 20 up to 29. The 3 was from 30 up to 39. So every stem has equal width.
The reason that's important is because a stem and leaf plot is providing a visual of the distribution. With this visual, the individual values are the leaves, and even though in the last example, we were using 10s for the stems, you could use numbers of any size. You just round to two significant digits. So if you wanted to represent 100s, you would round to two significant digits, and you'd have a key to let you know that the stem 2 actually represented 200.
Now one disadvantage to a stem an leaf plot is that when you have a very large data set, it's unwieldy. The data set is too large to give that visual distribution, and it's no longer useful.
So here's how we could create a stem and leaf plot. This one is going to be for the number of registered vehicles stolen for the selected cities. Now if we look across our data set, we start with 38 and end at 80. So it would be appropriate to do a stem and leaf plot where the stems were at the 10s.
So first, we would have a stem of 3 for the 30. And then the only leaf would be an 8. For the 4, the only leaf would be a 1. For the 5, we'd start to get more stems. We'd have two 0s for the 50, 52, 53, 53, 56, 58, 59. Then for the 6, we would have the 66, 68, 69, 69. For the 7 stem, we would have 70, 70, 73, 74, 75, as well as 78. And for the 80 stem, you just have the 0.
Now typically, you see a stem and leaf plot written with a line of some sort breaking the stems and the leaves. And when we've done this, we've chosen to have the stems be represented with 10s. You can include a key if you want, but you don't necessarily need to.
Here's a real world example of what a stem and leaf plot might look like. When you're looking at a train departure schedule, we have the stems being the hours, and the times being the leaves. In this case, because we're telling time and people are trying to read it, the leaves aren't one digit, but rather two for both of the minutes.
But you can see how the stem and leaf plot can help to organize data as well as give that distributional information. You can see that there's fewer times that are offered in the early morning and the late evening, and then most of the times in the middle of the day.
One other thing you can do with a stem and leaf plot is create a back-to-back stem and leaf plot. With this, you're comparing two sets of data because you're combining two stem and leaf plots together.
Now, this example shows the weights of middle school students. And on one side we have the girls, and on the other side we have the boys. One thing to notice is this is an unordered stem and leaf plot. Typically they're ordered with the smaller digits being first, out to the larger digits. And on the other side, it would be again, the same thing with the smaller digits being towards the leaves and the larger digits heading out. This one, the digits are not arranged in the leaves. They're kind of in any order. You could choose to order it, but sometimes you're going to see it in an unordered fashion.
Now with this, we read it just the same way we read a regular stem and leaf plot. This 6 represents 106, this 9 represents 149. On the girl side, it's a little bit backwards. We still have the stem of 12, except now our leaves are on the other side of it. So this 3 represents 123.
Now what this does is it lets us compare the data sets pretty easily. We can see that the girls have more of these middle values here on the 11 for the 110, but they have no one really in that upper range of the 140 pounds, and very few people in the 130 range. The boys, on the other hand, have some very lightweight boys, and some of the heavier boys, but their distribution looks different than the girls. So back to back stem and leaf plots let us do that kind of comparison. This has been your tutorial on stem and leaf plots.