9.02 Create and interpret circle graphs

Recently the Northern Lights, Aurora Borealis, were visible further south than usual. A survey was done of people who saw them and they were asked what color of Northern Lights was their favorite.

Complete the table.

For each of the following questions for the data cycle, determine whether or not the data can be well represented using a circle graph.

Are the following statements true or false?

The owner of a business wants to have a company-wide retreat in Virginia. He narrowed the list down to five cities, but he cannot decide which city to choose. He sends a survey to all 180 of his employees, asking them to choose the city in which the retreat should be held.

Would the following data displays be appropriate for the owner to use to analyze the results of the survey?

At different times of day, a sample of people were asked what they were doing at the park. Describe the probability that someone was there to go for a run using one of these words.

• Impossible

• Unlikely

• Equally likely

• Likely

• Certain

a

At 5 a.m.

b

At 10 a.m.

c

At 4 p.m.

d

At 7 p.m.

Edward surveyed a large group of people and asked for their favourite milkshake flavour. The results of the survey are in a circle graph.

a

What fraction of people chose chocolate?

b

What percentage of people chose chocolate?

c

What fraction of people chose strawberry?

d

What percentage of people chose strawberry?

Lucille formulates the question "What dairy products are the most popular for Americans?". She collects data from her classmates and makes Circle Graph A. Her friend DeShaun found data from a national survey of 10 \,000 people and summarized the results in Circle Graph B.

Circle Graph A

Circle Graph B

Manuela is an international student and is feeling homesick. She formulates the question, "How long are international students usually homesick for?" She does a survey of everyone currently on exchange through her program. She organizes the data in this table.

Construct a circle graph to represent this data.

A math teacher formulates the question "Which other subject would students like to see incorporated into math class more often?" She surveys 220 students to find their preference and needs to construct a circle graph to display the data. The survey results are shown in the following table:

A physiotherapist is doing a study with 1080 volunteers who have knee pain. He is trying a new technique and after six weeks asking the patients how they are feeling.

Bob asked his students to choose their favorite toy. 35\% students picked cars, 10\% of the students picked planes, 30\% picked balls and 25\% picked video games.

The following circle graphs show the number of students registered for different types of courses at a university.

This question is being explored with the data cycle: "What activities do students do after school? Does it vary by school level?"

Random samples of students were taken at several elementary schools, middle schools, and high schools. Students were asked about the first activity they do after school.

These circle graphs summarize the data:

a

What conclusions can we make that are true for all three groups?

b

What are some of the difference between the different groups?

c

If all of the data was grouped together, we get this circle graph. Is this a good overall summary, or is it better to have the graphs separate?

d

Formulate another question that is related to after school activities.

The given circle graph about the school election was displayed on poster:

a

Describe two mathematical errors with this circle graph.

b

Which of the following images better represents the same information?

A

B

c

After looking at the data, a student concludes that the majority of people would vote for each of the three candidates. Which of the following is not an explanation for how this is possible?

A

The three candidates are running for different positions in government.

B

Three different samples were surveyed.

C

The survey questions said, "Would you vote for Grylls if they ran for class president? Would you vote for McGill if they ran for class president? Would you vote for Flanders if they ran for class president?

D

The survey question said, "If Grylls, McGill, and Flanders run for class president, who would you vote for?"

Emil was at his auntie's house and noticed that she used a desktop computer. He had only ever seen gamers use them. He is now curious about what proportion of internet traffic comes from desktops/laptops, mobile phones, tablets, and consoles.