9.02 Interpret circle graphs

What makes a circle graph so different 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.

Consider the circle graph below:

We can see from the circle graph (using the legend to check our categories) that the red sector takes up half the circle, while the blue sector takes up a quarter and the yellow and orange sectors both take up one eighth.

The fraction of the circle taken up by each sector indicates what fraction of the total fish are that colour. So, in this case, half the fish are red since the red sector takes up half the circle. We can also write this as a percentage: 50\% of the fish are red.

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.

There is a 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\% 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\% so this circle graph is valid.

Examples

Example 1

The pie chart below shows the results of a class survey where students were asked to nominate their favourite food:

a

Which was the most popular food?

A

Burgers

B

Pizza

C

Nuggets

D

Noodles

Worked Solution

Create a strategy

Choose the largest section in the graph.

Apply the idea

The most popular food was pizza, because it largest section in the graph. So the correct answer is option B.

Watch question walkthrough

b

Which two foods were equally popular?

A

Burgers

B

Pizza

C

Nuggets

D

Noodles

Worked Solution

Create a strategy

Choose the food with the same size section.

Apply the idea

Noodles and nuggets have the same size section, so nuggets are as popular as noodles. So the correct answers is options C and D.

Watch question walkthrough

Example 2

A marketing company conducted a survey to determine the market share of smartphone manufacturers. They surveyed 4000 people, and the results are given in the table below:

Manufacturer	Responses
\text{Apple}	2051
\text{Samsung}	967
\text{Huawei}	531
\text{Other}	451

Which pie chart most accurately represents this data?

A

B

C

D

Worked Solution

Create a strategy

Determine the percentage of market share for each manufacturer by dividing the number of responses for each manufacturer by the total number of responses and multiply the decimal by 100.

Apply the idea

Let's start by looking at the market share of Apple. \dfrac{2051}{4000} \times 100 \approx 51\%

51\% is more than half of 4000, so the sector corresponding to Apple should take up more than half the circle.

For Samsung, we have \dfrac{967}{4000} \times 100 \approx 24\% which is a little under a quarter of a circle.

For Huawei, \dfrac{531}{4000} \times 100 \approx 13\%For others we have \dfrac{451}{4000} \times 100 \approx 11\%So the the sector for Huawei and the others should be about the same size.

Here is the pie chart that most accurately represents the data would look like .

So the correct answer is option C.

Watch question walkthrough

Example 3

Every student in year 8 was surveyed on their favourite subject, and the results are displayed in this pie chart:

a

Which was the most popular subject?

A

Phys. Ed

B

Math

C

History

D

Languages

E

Science

F

English

Worked Solution

Create a strategy

Check which subject matches the largest sector.

Apply the idea

Based on the pie chart, English has the largest sector. So the correct answer is option F.

Watch question walkthrough

b

What percentage of the class selected History, Phys. Ed., or Languages?

A

50\%

B

30\%

C

3\%

D

25\%

Worked Solution

Create a strategy

Together these subjects take up one quarter of the circle.

Apply the idea

We know that one quarter is 25\% in percentage. So the correct answer is option D.

Watch question walkthrough

c

You later find out that 32 students selected Science. How many students are there in year 8?

Worked Solution

Create a strategy

Since the Science sector takes up a quarter of the circle, we can multiply the number of Science students by 4.

Apply the idea

\displaystyle \text{Total students}	\displaystyle =	\displaystyle 32 \times 4	Multiply 32 by 4
	\displaystyle =	\displaystyle 128	Evaluate

Watch question walkthrough