Pie charts

Pie charts


This lesson will explain pie charts.

See More
Introduction to Statistics

Get a load of these stats.
Our Intro to Stats course is only $329.

Sophia's online courses not only save you money, but also are eligible for credit transfer to over 2,000 colleges and universities.*
Start a free trial now.


Pie Charts

What's Covered

This tutorial is going to teach you to create and interpret pie charts. You will learn about:

  1. Pie charts
  2. Sectors

1. Pie Charts

Qualitative data can be displayed in a couple of different ways. One way is to display it in a bar graph, which you can see in another tutorial. Another way that this tutorial is going to deal with is called a pie chart.

Term to Know

Pie Chart/Circle Graph

A distribution of qualitative data that shows the relative frequency of each category as a sector of a circle.

A pie chart 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 there 321 Economics majors, 445 Biology majors, 127 Chemistry majors, etc., at this particular college. In order to make a pie chart, the first thing to do is to calculate relative frequencies. Relative frequency is the percent of the values that are in each category. How do you calculate relative frequency?

Try It

Take each number, like the 321, and divide by the total, which ends up being 2,070. Divide each frequency by 2,070 to obtain a relative frequency, which is a percent.

Now what you might notice here is that 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, but it's not a huge deal. This is mainly due to how we rounded the percents. This can happen when you deal with relative frequencies and it's not that big of a deal.

Step by Step

Now for your pie chart, you need to construct a circle. What you’re going to do then is, from the center of the circle, divide based on some central angle that you’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.

Make a central angle of about 58 degrees that corresponds to Economics and then do the same thing with all of the categories. 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, these actually add up to 363.6 degrees, but it's not a huge deal because it only results in 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.

2. Sectors

Once you have determined the relative frequency of each category, you can create the sectors of your pie chart. These are the sectors.

But which sector corresponds to which category? You could write the words inside each sector, labeling each with the names of the majors. It's pretty clear that the biggest slice is Biology. But which ones are the rest? You 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. You can do the same for each of the sectors.


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.

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. You can also fix this issue by rounding your values more precisely.

Thank you and good luck!


  • Pie Chart/Circle Graph

    A distribution of qualitative data that shows the relative frequency of each category as a sector of a circle.