We have used pictograph, bar graphs, and dot plots to represent categorical and countable numerical data. We will now look at another display.

Students were asked what they favorite style of boardgame was. The information was recorded in this data display.

What do you notice?

What do you wonder?

What type of boardgame do you think is the most popular? Explain.

What type of boardgame do you think is the least popular? Explain.

A **circle graph** is different from a bar chart or line plot, because it does not show the count or frequency of each category. Instead it shows the **proportion** of the data that is in a category as parts of a whole.

A circle graph is sometimes called a pie chart because each sector could be a piece of pie.

Fraction of total | Percentage | |
---|---|---|

Orange | \dfrac{1}{8} | 12.5\% |

Red | \dfrac{1}{2} | 50\% |

Blue | \dfrac{1}{4} | 25\% |

Yellow | \dfrac{1}{8} | 12.5\% |

We often label the percentages on each sector, so that we can compare more easily and do calculations. For example:

Sometimes, we will show the number labels instead of percentages, for example, if 300 people were surveyed, this circle graph shows the same information as the one before:

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.

Circle graphs are not helpful for representing data with large numbers of categories because they get hard to read with too many sectors.

We can use circle graphs in the "Organize and Represent" stage of the data cycle. They can be helpful for questions that ask about a relationship of the parts of a whole.

Circle graphs can show us the probability of the events they represent. Recall that \text{Probability of an event}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

In a circle graph the favorable outcomes are represented by sectors of the graph and the total outcomes are the entire circle. So the percentage of the circle that the sector(s) makes up is the probability of that event occurring. Probabilities of an event can be described as:

Impossible - if no sectors represent that event

Unlikely - if the sector(s) for that event make up much less than half of circle

Equally likely - if the sector(s) for the event make up half of the circle

Likely - if the sector(s) for the event make up much more than half of the circle

Certain - if the sector(s) for the event make up the entire circle

For each of the following questions for the data cycle, determine if the data can be well represented using a circle graph. If yes, explain why. If not, suggest a different type of display and explain why you chose it.

a

How much time do students spend on homework, in hours?

Worked Solution

b

What was the most and least popular kind of candy that was sold at the school fair?

Worked Solution

c

Which Neapolitan ice cream flavors (chocolate, vanilla, or strawberry) do most students like?

Worked Solution

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

a

Which was the most popular food?

A

Burgers

B

Pizza

C

Nuggets

D

Noodles

Worked Solution

b

Which two foods were equally popular?

A

Burgers

B

Pizza

C

Nuggets

D

Noodles

Worked Solution

Every student in 6\text{th} grade was surveyed on their favorite subject, and the results are displayed in this circle graph:

a

Which was the most popular subject?

A

Phys. Ed

B

Math

C

History

D

Languages

E

Science

F

English

Worked Solution

b

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

A

50\%

B

75\%

C

3\%

D

25\%

Worked Solution

c

You later find out that there are 200 students in 6th grade. Approximately how many students selected Science as their favorite subject.

Worked Solution

Idea summary

**Circle graphs** represent the data as parts of a whole. Each sector of a circle graph represents a different category. The larger the sector, the larger the percentage of data in that category.

A circle graph should include:

A title to explain what the graph is about

A key to explain how to read the graph

Percents or number labels for each category

Circle graphs are good for representing categorical or countable numerical data with only a few categories.

Circle graphs can be created by hand or using technology. Some programs like Excel or Google Sheets refer to circle graphs as pie charts.

Using technology, we can:

Enter the data as a list or a frequency table

Highlight the data

Insert a chart and select pie chart or circle graph

Season | Number of students |
---|---|

\text{Winter} | 5 |

\text{Spring} | 15 |

\text{Summer} | 30 |

\text{Fall} | 10 |

Season | Number of students | Fraction | Percent |
---|---|---|---|

\text{Winter} | 5 | \dfrac{5}{60}=\dfrac{1}{12} | 8.\overline{3}\% |

\text{Spring} | 15 | \dfrac{15}{60}=\dfrac{1}{4} | 25\% |

\text{Summer} | 30 | \dfrac{30}{60}=\dfrac{1}{2} | 50\% |

\text{Fall} | 10 | \dfrac{10}{60}=\dfrac{1}{6} | 16.\overline{6}\% |

Then we can divide up the circle by first cutting it in half, then splitting one half into two quarters, then splitting one quarter into twelfth.

One half of the circle represents summer

One quarter of the circle represents spring

We can split the remain quarter into three pieces that will each represent \dfrac{1}{12}

\,\,\,\,\,\,\,\,\,\dfrac{1}{12} represents winter and \dfrac{2}{12}=\dfrac{1}{6} represents fall

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{Brand A} | 2051 |

\text{Brand B} | 967 |

\text{Brand C } | 531 |

\text{Other} | 451 |

a

Which circle graph most accurately represents this data?

A

B

C

D

Worked Solution

b

Write a conclusion that the marketing company could make based on the data and representation.

Worked Solution

Idea summary

To create a circle graph, we can use technology, or create it by hand. To make it by hand, we can:

Create a table with the categories, their count, fraction, and percentage

Draw a circle

Divide the circle into segments that match the proportions for each category

Check that the proportions add up to 1 or 100\%