Let's take a look at stem and leaf plots and dot plots in this video. You're going to see that these are a little bit more basic, but you should know that there's never a bad way to display your data. And sometimes these can actually be really effective at showing just the shape that your data take on, the distribution of the data, while being able to see the data itself.
Okay, so let's start with stem and leaf plots. When we talk about stem and leaf plots, we take our numbers and we break them up into stems and leaves. So just to give you a real simple example, suppose I have two data points 142 and 147. What we do is we say the rightmost digit of these numbers are the leaves and then 14 or 1 and a 4 is in common to these two numbers and so we make 14 the stem.
And so in a stem and leaf setup it would look like this where you would have 14, you would draw a vertical line, and then you would have a 2 and a 7. So this represents 142 and 147. You should note that I am not separating the leaves with commas and you should also note that I am putting these leaves in here in increasing order. That's going to be an important part of a stem and leaf plot. Let me give you another example. Suppose we have 16.4 and 16.9.
Well in a case like this what's common to our data is the 16 in the front. And so our rightmost digit is what's after the decimal point. That's a 4 and that's a 9. So again in a stem and leaf setup it would look like this where we would have 16 as the stem and then 4 and 9 would be the leaves.
Notice that I'm not putting in here 0.4 and 0.9 but this actually represents 16.4 and 16.9 given the context that we're working within. So this is not 164 and 169, it's 16.4 and 16.9. So your stem and leaf plots are actually specific to the context of your data. Okay, so let's look at a bigger example.
Construct a stem and leaf plot for the reported ideal outdoor temperature of a statistics class. So we've got these 30 data points, and they range from the 50s all the way up into the 90s. And so I'm going to construct my stem and leaf plot with... the following stems.
I will have 5, 6, 7, 8, and 9. But before I simply start taking these numbers one at a time and just filling in like a 2 next to the 5 and filling in a 7 next to the 8 and then a 0, you can see right away with those two in particular, if I put in a 7 and then a 0, then I kind of break that rule that I mentioned above that suggests that these numbers need to be increasing. order as you move away from that stem. And so what's pivotal in these examples with stem and leaf plots is we need to sort the data.
So we must sort the data into the calculator. And so let's enter all of this data into the calculator and we can do that by pressing stat edit. You're going to get really comfortable with this.
This is something that we're going to be doing a lot in this module and also moving forward. So we say stat edit and you can see under list one I've got 52, 87, 80. I've entered all of the all of these data into L1 and when I do that I just plug in the number, press enter, all the way and then go all the way down. And if I want to sort that what I'm going to do is I'm going to go back to the stat button. Press stat. There we go.
And when I press stat, I'm going to go down to sort A. That is sort in ascending order. But then I need to tell the calculator that I want to sort list one in ascending order.
So I'm going to press second. That's up here. Number one to tell the calculator to sort list one in ascending order.
And it just says done here. Let me just write this down real quickly. So we're saying sort A.
List 1. So now if I go back into Stat Edit, there's my first list with all of my data in order. And watch how much easier this makes filling in the stem and leaf plot now. So in the 50s, I've got 52. In the 60s, I've got a 0, a 2, 1, 2, 3, 4, 5s. So let's do this. A 0, a 2, I said 4 5s.
And then we have a 7 and a 9. Okay, now let's scroll down to see our 70s. And so in the 70s, you can see that we have... Two zeros, let's get that down. We have two zeros, we have a 1, a 2, a 3, and then it looks like we have three 5s. Let's continue scrolling to see what else we have.
We have three 6s, a 7, and an 8, and a 9. So three 6s, a 7, 8, and 9. In the 80s, we have two zeros, a two, a four, a five, and a seven. So two zeros, a two, a four, a five, and a seven. And then we have 90. And so like I was saying, when you have the stem and leaf plot, a lot of times it gives you that nice looking shape of your data.
So we can kind of see how the data are distributed. And at the same time, we're observing what all of the data are. Now, one of the tricky things is with stem and leaf plots is there's all kinds of different types. So this is just a regular stem and leaf plot right here.
But sometimes what we'll do is we will make what's called a back to back stem and leaf plot or a split stem and leaf plot. And first, I'll talk about the split stem and leaf plot. So a split stem and leaf plot would look like the following. What we are going to do is we are going to split all of our stems so that we have the five stem twice, we have the sixth stem twice, we have the seventh stem twice, we have the eight stem twice, and then we have the nine stem twice. So it would look like this right here.
And what we do is with the split stem and leaf plot is we say that the first stem for all of these is getting the leaves 0 through 4 and then the second stem is going to get the leaves 5 through 9. Now that we have a regular stem and leaf plot though this is actually going to be pretty easy for us because we could see that the two would go here because that's between 0 and 4. With the data that we had in the 60s before the only ones that are going to go with the first six will be the 0 and the 2 and then The four fives, the seven and the nine are going to go with the second six because again when the leads are zero through four they go with the first stem and when the leads are five through nine they go with the second stem. In the seventies we're going to have zero, zero, one, two, three and then we have three fives, three sixes, seven, eight, nine. In the eighties we go with zero, zero, two, four. and then in the second one we have five and seven and then again in the 90s we have just a zero and so this just gives it kind of a finer glimpse of what that distribution is like just breaks it down a little bit more and that is known again as a split stem and leaf plot so we have a regular stem and leaf plot a split stem and leaf plot and as i mentioned we'll also take a look at a back-to-back stem and leaf plot so let's do that one right now and Whenever we talk about a back-to-back stem and leaf plot, that means that you would typically need two sets of data. And so a back-to-back stem and leaf plot is often comparing two groups.
So in this example, I said, let's pretend that I have a second class and they've also reported their ideal outdoor temperatures. So if I have a second class and I want to compare those temps to my first class, that what I'm going to do with my back-to-back stem and leaf plot is the following. I'm going to have five, six, seven, and eight, and nine, and I'll have my original stem and leaf plot on this right side, and then on the left side I'm going to have my second class. And so if I go back to my calculator here, you can see that we have, I have both of these lists in the calculator. Now, I need to sort my second list just as I sorted my first list because remember it's almost impossible to try to do this one at a time without having your data going in ascending order.
So let's do that. Let's say stat sort A and I'm going to sort list two and it says done so I can go back to stat. And now let's fill in our back to back stem and leaf plots.
So on this side, this is going to be my first class. And then this side over here is going to be the second class. Okay, so once again we had 52 for the first class and for the second class we have several values in the 50s.
We had 54, 55, 58, and 58. Now watch how I enter in the 4, 5, and 8 in the 8. I actually put it in like this where it's 4, 5, 8, 8. So as I move away from the stem, as I move away from the stem, my numbers are increasing. So in this direction, they're ascending as you move to the right, but in this direction, they're actually descending as you move to the right, but they're ascending as you move to the left. This is one of the trickiest things with these stem and leaf plots, in particular, these back-to-back stem and leaf plots. Let's do the 60s. So in the first data set, we had, again, 0, 2, we had 4, 5s, and then we had a 7 and a 9. And in the second data set in the 60s, we have two 2s, a 3, a 4. We also have two 5s and an 8. Let's scroll down now so that we can see some more of our data.
It takes a little bit of time here. And you can see that we had a second 68. with data set number two. As we get into the 70s for the first data set we had 0 0 1 2 3 and then as we continue there we had three fives and three sixes so let's get those three fives those three sixes and then also we had a seven and an eight and a nine. Okay, I don't want to miss something with the second data set here.
So we had a 7 and an 8 and a 9. With the second data set, we've got four 0s, four 70s. So 1, 2, 3, 4. We have a 1, two 2s. We have a 3, a 4, a 5. And let's scroll back down once again. And you can see that we've got a couple more fives. And we also have a six and a nine.
So I'm kind of running out of space here, but you would have a nine and a six also in that 70s row. Once again, notice that those numbers are descending as they go towards the stem on this side, but the numbers are increasing as you move away from the stem. Okay, let's go into the 80s. Now in this data set we have in the first one we had two zeros, a two and a four, and we also had a five and a seven, and then in the second data set we had zero, two, four, five, and that is just about it. We have the 90 in the first data set.
And so there you go. And so this just allows you to do a comparison now. When you have these back-to-back stem and leaf plots you could say you know what it almost looks like the the class that reported their ideal temps over here has a distribution that's you know in that 60s to 80s range a little bit more and maybe we have 50s to 70s a little bit more in that second data set and so that's the whole point of the back-to-back stem and leaf plot it allows you to draw certain comparisons.
Okay Now let's take a look at a dot plot real quickly. A dot plot is another very simple way of displaying your data, and it's probably even less work than what we just did with the stem and leaf plot. So in this example, I said let's construct a dot plot for the number of cavities reported by my last stats class.
And so here's a number of data points, and these just represent the number of cavities. And so what we would do is we would say, Okay, this is number of cavities, and I'm going to list out my possibilities. I had 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. And every time I see a number in this list, I'm just going to put a dot above the number that I have on my single axis.
So I... go to the number two, I put a dot. I go to ten, put a dot.
8, 4, 6, 3, another 2. So I'm putting another dot in that 2 column. And then 1, and then I've got two 0s. I've got another 1. I've got a 5, a 3, a couple more 2s, a couple more 1s, a couple more 0s.
and then a 7 and a 9 and a 12 and a 15 and an 8 and one final zero. And so again this is a another clear picture of the distribution of our data and you could look at this and you could say oh you know what most of your data is kind of clustered on one side and so I would describe this as being skewed to the right and so as I started this video there is no bad way to display your data even some of these very simple techniques like stem and leaf plots and dot plots can be very useful at times.