4.04 Circle graphs

If you've ever seen a poll or a popularity survey, you might be familiar with graphs that look something like this:

In terms of representing data in a visually appealing and digestible manner, a very common tool is circle graph or pie chart.

Circle graphs and the whole

What makes a circle graph so different from other types of displays is that it represents the data as parts of a whole. In a circle graph, all the data is combined to make a single whole with the different sectors representing different categories. The larger the sector, the larger percentage of the data points that category represents.

Notice that the sum of our percentages is $100%$100%. This is consistent with the fact that a circle graph represents $100%$100% of the data, one whole, split up into different category sectors.

 

Worked Example

Question 1

Consider the circle graph below.

Complete: If there were $3$3 orange fish, how many of each color would there be? Fill in the table below.

Color of fish	Number
Orange	$3$3
Yellow
Blue
Red

Think: The ratio of Orange:Yellow = $1:1$1:1, the ratio of Orange:Blue=$1:2$1:2, and the ratio of Orange:Red = $1:4$1:4. We can use our proportional reasoning to solve for the number of yellow, blue and red fish.

Do: 

Color of fish	Number	Reasoning
Orange	$3$3	Given
Yellow	$3$3	Ratio of $1:1$1:1 means the same
Blue	$6$6	Ratio of $1:2$1:2 means the double
Red	$12$12	Ratio of $1:4$1:4 means four times

 

Question 2

Pie charts with additional information

A notable drawback of the circle graph is that it doesn't necessarily tell us how many data points belong to each category. This means that, without any additional information, the circle graph can only show us which categories are more or less popular and roughly by how much.

It is for this reason that we will often add some additional information to our circle graphs so that we can show (or at least calculate) the number of data points in each category. There are two main ways to add information to a circle graph:

• Reveal the total number of data points
• Reveal the number of data points for each sector

By revealing the total number of data points, we can use the percentages represented by the sector sizes to calculate how many data points each sector represents.

Aside from these two ways to add extra information to a circle graph, there is also the case where the percentage taken up by each sector is shown on the circle graph.

This will often look something like this:

This is very useful as it does a lot of the calculations for us. However, it is important that we always check that the percentages on the graph add up to $100%$100% since a circle graph always represents the whole of the data points, no more and no less.

In this particular case, the percentages do in fact add up to $100%$100% so this circle graph is valid.