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This course, we've seen that histograms are great options for displaying quantitative data, but they don't actually allow us to see the specific values in our dataset, which might be a disadvantage depending on what types of questions we've been asked about our data. That's why we want other options for displaying numerical data, including the stemplot, which does display quantitative data by showing both trends and the specific values in our dataset. In this video, we're gonna talk about how to go from a data table to a stemplot, and I think you'll see that they're pretty straightforward. Let's dive right into the example to see how they work. We've been given a table showing the weekly study time for different students in the class, and we wanna follow the steps here to take that table and create a stemplot.

Now our first step is to write the data in increasing order. That's a very important step because it makes our jobs much easier for some of the later steps. We can see in our table that the data is already in increasing order, but if it wasn't, you just start by locating the smallest value in your dataset, writing it down, crossing it off, and then just going in that pattern until you had every data point written down. Whenever you write out your dataset, you always wanna make sure you have the right number of points because it's super easy to accidentally miss one or do one twice. Let's check this off because step one is already done.

Now we wanna do step two, which is draw a vertical line. This will be the foundation for our stemplot. So I'm just gonna draw my vertical line here. Now we wanna divide our data points into stems and leaves. The leaf is always just the rightmost digit.

It's always one digit no matter how many digits our data point has. The stem is always everything else. So it's the digit or digits to the left of the leaf. Let's practice dividing some numbers into stems and leaves before we do it with our dataset. And let's start with:

• 20 : The rightmost digit is 0 . And so that rightmost digit is going to be my leaf. Now everything else is just the 2. So my stem is going to be a 2.
• 105 : I'm still just gonna take one digit as my rightmost digit, that 5 , and that's gonna be my leaf. Everything else is this 10 here. So my 10 is going to be the stem.

Awesome. Now we're ready to try breaking our data points into stems and leaves. I really want my stems to pop, so I'm going to underline each of my stems. For:

• 20 , I have a stem of 2.
• 31 , I have a stem of 3.
• 33 and 35 , I have a stem of 3.
• 40, 42, 45, 45 : I have a stem of 4.
• 50, 56 : I have a stem of 5.
• 65, 67 : I have a stem of 6.
• 105 , I have a stem of 10. .

Now that I have all my stems identified, I want to list my stems in the left column, so on the left side of that line in ascending order. So I want them to get bigger as I go down. I'm also only going to list each stem once even if it's the stem of multiple data points. So I'm gonna list:

1. 2,
2. 3,
3. 4,
4. 5,
5. 6,
6. And finally,
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Welcome to the stemplot practice. In this problem, we're given the test scores of two classes shown in the stemplots here, and we wanna use that data to answer questions a, b, and c. Before we dive in, let's do a quick refresher on how to read stemplots. We know that the rightmost digit of each data point is on the right side of the vertical line. And for test scores, that rightmost digit is gonna be the ones.

We know that our leftmost digits or stems are going to appear on the left side of the line. And in the case of test scores, those are gonna be tens. Putting a ones digit with its tens digit is going to create each test score we see in our dataset. Alright. Let's dive right in.

So question a asks us to find the highest and lowest score in each class. So let's start with our highest scores. Well, I'm gonna start by looking in my tens column, and I noticed that I have scores in the sixties, seventies, eighties, and nineties. Obviously, the highest score is then going to be in the nineties. Then I'm gonna take my highest ones digit in that row, which in this case is 8, meaning for class a, my highest score is 98.

I can do the same thing for class b. I'm gonna look in that bottom row. It's also for the nineties, and I'm gonna look for that highest leaf, which in this case is 6. So it looks like in class b, my highest score is 96. For the lowest score, I'm actually gonna do something very similar.

But instead of looking at my highest tens row, I'm gonna look at my lowest tens row. And instead of looking for my highest leaf, I'm gonna look for my smallest leaf. In this case, I can see that the lowest score in my class a stemplot is actually 67. I'm gonna do the same thing for class b. I'm gonna look in that top row, and I'm gonna look for the smallest leaf.

And I noticed that my lowest score is 63. Let's take a peek at question b. So I know that if a student scores in the seventies, between 70 and 79, they get a c. And I wanna figure out which class has more students that get a c. So I'm gonna take a peek at the seventies row in each of my stem plots.

I'm gonna figure out which stem plot has more leaves or scores in the seventies. For class a, it looks like we have 1, 2, 3, 4, 5, 6 leaves, meaning that there are 6 students that score in the seventies. For class b, it looks like we have 1, 2, 3, 4, 5, 6, 7, 8 leaves. So in class b, there are 8 students that score in the seventies. Eight is obviously bigger than six, meaning that there are more students in class b who score in the seventies or receive a c.

Let's take a peek at our final question. Our final question asks us to compare the distributions of test scores and asks us what we notice. Now this can seem like a pretty vague question, but we wanna compare certain things. We wanna see maybe did one class seem to score lower, and what does it mean to score lower? Well, maybe they have a lower minimum score, or maybe they have a lower maximum score, or maybe they have more scores that are in the lowest tens value.

So maybe they have more scores in the sixties or seventies as opposed to scores in the eighties or nineties. We also might wanna see what is the most popular letter grade, or were there the most students that score in the seventies, the nineties? Those are some things we wanna look for. So let's take some notes, and I'm just gonna start over here because I want plenty of room. So if I'm looking for the most popular tens or the most popular letter grade in both of my classes, I actually noticed that for both of them, they're in the eighties.

That's because I have the most leaves in my eighties row, and that's something I can see quickly, but I also could count my leaves in each row to compare. So I can say that the most popular range for both classes is 80 to 89. But another observation I can make is that class b did worse overall than class a. Now why is that? I'm going to look for some evidence in my stem plots to back that statement up.

And I think some evidence comes from question a. I know that class b has the lowest minimum score. Right? Because 63 is smaller than 67. I also know that class b has the lowest maximum score.

When I looked at the highest scores, I noticed that class b had a 96 and class a had a 98. 98 obviously is higher. I can also see here that there are more leaves in my sixties row in class b than class a, and I can notice the same thing in my seventies rows. So I can say that class b had more students get sixties and seventies scores. Whereas I can see that my nineties row is longer in my class a stemplot.

So I can say that class a had more nineties. So for these types of questions, I'm just looking for general patterns. I might wanna look for both of them to see, hey, which scores were most popular? But I also wanna compare, hey, do I see more scores on the lower end or in the higher end, and how do their maximums and minimums compare when I'm asked general questions about comparing the distribution. Awesome work.