Source: Table and pie chart created by author; Books, Public Domain http://commons.wikimedia.org/wiki/File:Alte_Buecher.JPG
This tutorial is going to teach you to create and interpret pie charts. Qualitative data can be displayed in a couple of different ways. One way is to display it in a bar graph. We showed you how to do that in another tutorial.
Another way that this tutorial is going to deal with is called a pie chart. And it displays relative frequencies for each category. That is, how do these categories relate to the whole?
So imagine this set of information here. These are courses taken by different majors. So 321 Economics majors, 445 for Biology majors, 127 Chemistry majors, et cetera at a particular college. What we're going to start by doing is calculating relative frequencies.
Now how do we calculate relative frequency? Relative frequency is the percent of the values that are in each category. So we're going to take each number, like the 321, and divide by the total. The total ends up being 2,070. We're going to divide each frequency by 2,070 to obtain a relative frequency, which is a percent.
Now what you might notice here that might be a little problematic is 16%, 21%, 6%, 13, 15, 12, 10, and 8 don't add up to 100% percent. In fact. They add up to 101%. This is a little problematic. It's not a huge deal. This is mainly due to how we rounded the percents. So know that this can happen when you deal with relative frequencies, and it's not that big of a deal.
Also, we need to, for our pie chart, construct a circle. What we're going to do then is, from the center of the circle, divide it based on some central angle that we're going to make. The central angle for Economics has to be 16 percent of the circle. You may recall there are 360 degrees in a circle.
So how do I set this up? I need 16% of 360 degrees. I multiply each percent by 360. Remember, when you multiply this out, it needs to be 0.16 because it's 16%. 0.16 times 360 gives you about 58 degrees. I'm going to make a central angle of about 58 degrees that corresponds to Economics. I'm going to do the same thing with all of the categories. I'm going to obtain angle measurements for each of these central angles.
There's only one small problem in that those don't add up to 360 degrees. Again, because of this 101, these actually add up to 363.6 degrees. It's not a huge deal. It's a couple of extra degrees in a circle. So long as everything is approximately relative to each other the right size, we're not going to worry about it too much.
These are the sectors. But which sector corresponds to which category? I could write the words in here, the names of the majors. It's pretty clear that this one, being the biggest slice, is Biology. But which ones are the rest? We need to create a key. So we'll add a key off to the side.
We can either have written the word Economics here in the blue sector, or we can create a blue square here and write Economics next to it. That shows that anything that's blue means Economics. And we'll do the same for all of them.
And so to recap, pie charts are visual displays, but they're only for qualitative data. What they do is they display the relative frequency or percent of each category by dividing a circle into sectors that relate those relative sizes. The biggest advantage to a pie chart over something like a bar graph is that it's possible to see how each category relates to the whole. And sometimes, because of rounding, much like in our example, the relative frequencies don't add up to 100%. They might add up to only 99% or 101%, as they did in our example. But as long as the relative sizes of each are in the right proportions, we're not going to make a huge deal out of it. Also, that issue of not adding to 100% can get fixed by rounding the values more precisely. And so we talked about pie charts, also called circle graphs. Good luck, and we'll see you next time.
A distribution of qualitative data that shows the relative frequency of each category as a sector of a circle.