Minds On

Which graph works best?

Not every graph can be used to accurately display all data sets. Keep that in mind as you investigate the following scenario.

Grade 7 data project

While working on a data project, a group of Grade 7 students conducted a survey. They created two different graphs to represent the survey results. As you investigate the two graphs, think about why one graph might be a better representation of the data than the other. What might be misleading?

Questions

Throughout this learning activity, you can record your ideas digitally, orally, or in print.

What do you notice when you explore these graphs? What makes it difficult to understand this data?

Press ‘Hint’ to reveal some helpful advice.

Consider the missing elements:

  • title
  • labels
  • source
  • scale

One of these graphs is an inappropriate choice for the data. Do you know which one it is?

Press ‘Hint’ to reveal some helpful advice.

Closely examine the circle graph.

  • A circle graph shows different parts of data in relation to the whole number.
  • When you’re using percent, the whole is 100%
  • The circle graph may have been an inappropriate choice for representing this set of data

Action

Avoid creating misleading graphs

The various elements of a graph are important. They ensure that the data reflects what is really happening.

Activity 1: Comparing bar graphs

The following two bar graphs display the same data. However, there is something different about them. Investigate the details of the graphs.

Brainstorm

What’s been changed?

  • What changes have been made to the way the data is presented?
  • Is the scale of the y-axis important?
  • Why might the change in scale have happened?
  • What are two conclusions you can make about the graphs?
  • How does the change in scale affect the interpretation of the data?

Press ‘Hint’ for some useful information.

Think about the scale and y-axis. These elements can be altered, changing how the data is interpreted.

Activity 2: Clean up that garbage!

Examine the following broken line graph. It records the amount of garbage cleaned up by an environmental company.

Questions

What conclusion can you make from the graph about the amount of garbage collected by the environmental program?

  • What evidence supports this conclusion?
  • Is this data misleading? Why or why not?

Press ‘Hint’ for some helpful advice.

The data can be modified by removing important pieces or misrepresenting how many pieces of data were collected.

Same data, new representations

Consider the following table and graph. How well do they display the same data that was represented on the previous graph?

Examine the following data table:

Annual Garbage Clean-Up (in metric tonnes)

Month

Amount of garbage

January

7.5

February

7.8

March

6.9

April

8.0

May

18.5

June

20.8

July

21.9

August

23.4

September

19.2

October

12.1

November

10.3

December

8.2

Examine the following broken line graph:

Brainstorm

What’s the effect of new information?

You have now explored a data table and a second broken line graph.

  • What conclusions can you make from this additional information about the company’s garbage clean-up?
  • What evidence supports this conclusion?
  • Has the new information affected your previous thinking?
  • Is this data misleading? Why or why not?
  • Which data representation is most accurate?
  • Compare the three data representations. How do the arguments and conclusions you make about the data change based on how the data is represented?

Record your thinking using a method of your choice.

Consolidation

What about the data?

Do we want that community centre?

A land developer is trying to persuade the local town council to allow their company to build a new community centre. The developer claims that the community supports the development plan and that they have data to support this claim.

Best to be cautious…

To determine whether the developer’s claim is valid, what questions might you consider about the data?

Select the correct answer, then press ‘Check Answer’ to check how you did.

The land developer supplies the following circle graph:

Test Your Skills!

Evaluate the circle graph

Record your ideas using the method of your choice.

  • What are some questions you have as you analyze the graph?
  • What are some things that this data does not explain?
  • Based on the data in the graph, explain the conclusion you can make about the community opinion of the development.
  • Is this data misleading?
  • What would be your recommendation to the town council?

Thinking about your learning

What are some ways that the data can be changed or modified?

Press ‘Hint’ for some suggestions.

Methods of changing data include the following:

  • using an inappropriate graph
  • modifying the data by removing pieces of information
  • changing the scale of the graph and manipulating the y-axis
  • misrepresenting how many pieces of data were collected
  • using a survey technique that favours your position

Brainstorm

The big picture

Use the method of your choice to record your ideas about the following questions:

  • Why is it important to understand how to make informed decisions about a graph?
  • When might misleading data serve a purpose?

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel…

Now, expand on your ideas by recording your thoughts using a voice recorder, text-to-speech, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

Press ‘Discover More’ to extend your skills.

  1. Create a set of data that represents one story.
  2. Change the data using one or more of the techniques you learned about in this learning activity. Discuss how you modified your data table or graph. Use the method of your choice to record your ideas.

Reminder: You can change data by…

  • using an inappropriate graph
  • modifying the data by removing pieces of information
  • changing the scale of the graph and manipulating the y-axis
  • misrepresenting how many pieces of data were collected
  • using a survey technique that favours your position

Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

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