When looking at qualitative data, sometimes we just care more about the percentages across categories as opposed to the frequencies. This is especially true when we're looking at how the categories relate back to the total as opposed to how they relate to each other. When that's the case, a pie chart is a great option for displaying the data because pie charts show the percentage of responses in each category as opposed to the frequencies. In this video, we're gonna be taking a closer look at pie charts by creating our own and using one to answer some questions. I think you'll see that they're pretty straightforward.
Pie charts start with just a circle here, and we divide the circle into wedges, one wedge for each category. The size of the wedge depends entirely on the percentage of that category. So for example, 40% is our biggest percentage, and it's also inside of our largest wedge. We see our smallest percentage, 15%, inside of our smallest wedge. It is absolutely true that larger percentages do imply larger wedges of the pie.
Now pie charts are all about percentages, but in most problems, we might be given the frequency across categories and have to compute the percentages for ourselves. Don't worry, though. That's not too bad. In fact, we can use a formula that's already pretty familiar to us.
To compute the category percentages, we can just calculate the relative frequency of each category. As a reminder, the relative frequency of a category can be found by taking the category total f, dividing it by the total number of responses n, and then multiplying that by % to just put it into a percent. Let's take a peek at our example to see how this works. In our example, we're given data about hair colors in two classrooms. For classroom A, we're given the data in a table, and we wanna use it to create a pie chart.
We'll then use that pie chart and the pie chart for classroom B to answer questions a and b over here. Let's get started. I can see in my table that I have four different hair colors, which means I'm going to need four wedges in my pie chart. I can also see that I have all of my category frequencies, but I'm missing two of my relative frequencies for black hair and for red hair. So I am gonna have to use our relative frequency formula to find them.
Now I have my f's. Those are all set. I have each of my category frequencies, but I actually don't yet know the total number of responses. So that's something I'm gonna have to find. To find the total number of responses, I can just add together all of my f's.
I can add together all of my category totals, and that should get me my total number of responses. So I'm gonna do 6+4+5+5=20. In this example, then n will be 20 because I have 20 responses. Let's compute the relative frequency for black hair. Now, again, my category frequency f is 6.
My total number of responses n is 20, and I'm gonna multiply that by %. 6/20=0.3×%, and you'll get 30%. For red hair, I'm basically just going to do the exact same thing. The only thing that changes is that my category frequency is 4 now, but I still have 20 as my total number of responses, and I'm still gonna multiply by %.
4/20=0.2×% is 20%. We have the other two relative frequencies already computed for us, but feel free to pause the video and check them using the formula. Alright. Now let's start adding wedges. Looking at my table, I think I'm actually gonna start with my brown-haired wedge because I noticed the relative frequency is 25%.
That's just a quarter, so it's gonna be pretty easy to section out a quarter of the circle. I'm gonna label it with a relative frequency. I'm gonna shade it in so I can see it nice and clearly, and I'm also gonna label it with the hair color it represents so I know what that wedge is; it represents brown. Now blonde has the exact same relative frequency, so I'm gonna do the exact same thing. I'm gonna section out a quarter of the circle.
I'm gonna label it with its relative frequency, 25%. I'm going to shade in that wedge and also label it for the hair color blonde. And I'm just gonna do the same thing for my last two relative frequencies, my last two hair colors. Now I noticed for black hair, I have 30%, so I am gonna have to kinda eyeball it. And it's okay if these wedges aren't perfect.
I'm just gonna make sure that it takes up more than 25% so that I can clearly see that there's a higher percentage of black-haired students. I'm gonna label it with 30% here. I'm just gonna shade it in. And, of course, I'm gonna label black hair. My final wedge represents my red-haired students.
It's 20%. I'm gonna shade it in and label it for red hair. And now we finish the pie chart. Great work. Let's answer questions a and b.
In question a, I'm asked to find the difference in the percentage of students with red hair in class A versus classroom B. Now I see here in my finished pie chart here for classroom A that the percentage of red-haired students is 20%. So let's write that down. For classroom B, I can see that that wedge is 15%.
So let's write 15% for class B. Obviously, when I compare 20 and 15%, the difference is 5%. But what does that mean? Well, I can say that the percentage of students with red hair in classroom A is five percentage points higher than the percentage of red-haired students in classroom B. Be careful.
These are not frequencies, so I can't say that there are more red-haired students in classroom A, but I do know the percentage is higher. Awesome. For question b, I'm told that class B has 20 students, and I wanna figure out how many of them have brown hair. So I'm gonna come over to my pie chart, and I notice that my wedge for brown hair is 40%. So I know that 40% of my students in class B of those 20 students have brown hair.
To find 40% of 20, I'm gonna write 40% as a decimal 0.40 and multiply that by 20 to get 8. There are 8 students with brown hair in classroom B. Awesome job. If you're feeling ready, why don't you head on over to the examples and practice and give them a try?
