Minds On

Ways to present data

Brainstorm

Get that data across!

What are some effective ways to present, share, and/or represent data? Throughout this learning activity, you can record your ideas digitally, orally, or in print.

Press ‘Hint’ to reveal some suggestions.

Graphs and tables are great ways to share data. Here are some types:

  • broken line graph
  • circle graph
  • frequency table
  • stem-and-leaf plot
  • histogram
  • bar graph
  • double bar graph

Graphs

Let's review various types of graphs.

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

Tables

You have explored frequency tables and tally tables in this course, but there are also other types of tables. For example, a stem-and-leaf plot is an organization of quantitative data that is represented in a t-table. Each data value is split into two components – a “stem” and a “leaf.” Stems are listed vertically, and their leaves are listed beside them. In the following stem-and-leaf plot, the stem records the first digit of the number (tens) and is indicated in the left column. The leaf is the last digit of the number (ones) and is listed in the right column. The leaves are listed in ascending order in the plot.

A t-chart with the left column labeled "Stem" and the right column labeled "Leaf." In the stem column are seven rows numbered 4 to 10. Row 4 has the numbers 4, 6, 7, and 9 in the leaf column. Row 5 has no numbers in the leaf column. Row 6 has the numbers 3, 4, 6, and 8 in the leaf column. Row 7 has the numbers 2, 2, 5, and 6 in the leaf column. Row 8 has the numbers 1, 4, and 8 in the leaf column. Row 9 has no numbers in the leaf column. Row 10 has the number 6 in the leaf column.

Brainstorm

To answer your question…

There are diverse types of questions that can be considered and answered about data representations. Consider the data representations presented in the previous activity: broken line graph, circle graph, histogram, bar graph, double bar graph, frequency table, stem-and-leaf plot.

  • Record your ideas about what each data representation would effectively present.
  • Think of question that would be suitable for each of these data representations.

Action

Analyzing data

All data shares a story. We analyze this story to understand what the data represents.

You will now analyze two different types of graph.

Graph 1: Circle graph

Examine the following graph:

Source: Statistics Canada. (CATSnet, March 2018)


Complete Analysis: Circle Graph in your notebook or use the following fillable and printable document. If you prefer, use another method to record your ideas.

Analysis: Circle Graph

What is the source of this information and what time period does it represent?

What story does this graph tell about its topic?

List at least four facts that you learn by examining the data in this circle graph.

Fact 1:

Fact 2:

Fact 3:

Fact 4:

Bonus fact:

Bonus fact:

List at least three questions that cannot be answered by analyzing this graph.

Question 1:

Question 2:

Question 3:

If you were a fruit grower in Ontario, what are some questions you might have?

Press the ‘Activity’ button to access Analysis: Circle Graph. 

Activity(Open PDF in a new window)

Press ‘Completed Table’ to compare your answers with some suggestions.

Analysis: Circle Graph (completed)

What is the source of this information and what time period does it represent?

The source of the information is Statistics Canada and the data is from 2019.

What story does this graph tell us about its topic?

This circle graph displays the top five destinations for Canadian fruit exports in 2019.

List at least four facts that you learn by examining the data in this circle graph.

Fact 1:

The U.S. represents about two-thirds of the export market.

Fact 2:

Of the countries identified, Netherlands represents the smallest percent of the export market.

Fact 3:

China, Japan, and Germany each represent about the same percent of the export market.

Fact 4:

“Others” represents roughly the same share of the market as China, Japan, and Germany together.

List at least three questions that cannot be answered by analyzing this graph.

Question 1: What percent of fruit grown in Canada does this represent?

Question 2: Which countries are in “Others”?

Question 3: Why is the U.S. the destination that receives so much (66%) of fruit exported?

If you were a fruit grower in Ontario, what are some questions you might have?

What fruits does this represent?

Are certain fruits exported more than others?

From where in Canada is most of the fruit exported?

Graph 2: Double bar graph

Examine the following graph:

Source: Statistics Canada, EnviroStats (16-002-X).


Double bar graph comparing how households disposed of unwanted cellphones in 2011 and 2013.

Disposal method

2011

2013

Garbage

5

5

Depot

25

24

Returned to retailer/provider

19

18

Donated or gave away

8

9

Repaired/Sold

too unreliable to be published

2

Other

2

1

Still had at time of interview

44

44

Complete Analysis: Double Bar Graph in your notebook or use the following fillable and printable document. If you prefer, use another method to record your ideas.

Analysis: Double Bar Graph

What is the source of this information and what time period does it represent?

What story does this graph tell us about its topic?

List at least four facts that you learn by examining the data in this double bar graph.

Fact 1:

Fact 2:

Fact 3:

Fact 4:

Bonus fact:

Bonus fact:

List at least three questions that cannot be answered by analyzing this graph.

Question 1:

Question 2:

Question 3:

Press the ‘Activity’ button to access Analysis: Double Bar Graph. 

Activity(Open PDF in a new window)

Press ‘Completed Table’ to compare your answers with some suggestions.

Analysis: Double Bar Graph (Completed)

What is the source of this information and what time period does it represent?

The source of this information is Statistics Canada and the time period represented is 2011-2013.

What story does this graph tell us about its topic?

This graph tells the story of what people do with their unwanted cellphones.

List at least four facts that you learn by examining the data in this double bar graph.

Fact 1:

Almost half the people included in the data still have an unwanted cellphone.

Fact 2:

The data hasn’t changed a lot over the two years.

Fact 3:

Three main things are done with unwanted cell phones: “brought to the depot,” “returned to the retailer,” and “still had at time of interview.”

Fact 4:

“Garbage” and “Still had at time of interview” are the two options that haven’t changed at all over the two years.

List at least three questions that cannot be answered by analyzing this graph.

Question 1: What was done with the cellphones in the “Other” category?

Question 2: Why do almost half the people still have their unwanted cellphones at home?

Question 3: What is the ideal way to dispose of an unwanted cellphone?

Brainstorm

That raises another question…

Sometimes when we analyze data, we come up with more questions that require further collection, representation, and data analysis.

Can you think of any questions that might be raised from the data analysis of Graph 1 and Graph 2 that would require more data collection?

Press ‘Sample responses’ to reveal some suggestions.

Graph 1: Circle graph Graph 2: Double bar graph
Which countries are represented by “Others”? Were different populations surveyed both times? The data hasn’t changed much over the two years.
How does this data compare to data from five years earlier? Are there any major changes in the data? What information is available to households about disposal options in the community? How accessible are the options?
What fruits are exported to these destinations? Why do almost half the households still have the unwanted cell phones?
Did the number of cellphones that were unwanted change over the two years?

Consolidation

Analyzing data

You will now analyze a data table from Statistics Canada that breaks down Canadians’ overnight trips by purpose.

Student Tips

What’s a quarter (Q)?

In the table you’ll be examining, the calendar year is divided into four quarters:

  • The first quarter (Q1) is January, February, and March.
  • The second quarter (Q2) is April, May, and June.
  • The third quarter (Q3) is July, August, and September.
  • The fourth quarter (Q4) is October, November, and December.

Press 'Activity' to download the table Overnight Travel by Canadians by Trip Purpose (× 1,000), 2019.

Overnight travel by Canadians

Press the Activity button to access the Overnight Travel by Canadians by Trip Purpose (× 1,000), 2019.

Activity (Open PDF in a new tab)

Overnight Travel by Canadians by Trip Purpose (x 1,000), 2019

Source: Statistics Canada. Table 24-10-0045-01  Travel by Canadian residents in Canada and abroad by trip purpose (x 1,000)

Q1 2019

Q2 2019

Q3 2019

Q4 2019

Main trip purpose

Number of trips

Number of trips

Number of trips

Number of trips

Total, all trip purposes

16,605A

22,055A

35,603A

19,403A

Holiday, leisure or recreation

5,354A

7,669A

18,286A

5,719A

Visit friends or relatives

7,838A

10,015A

13,358A

10,060A

Personal conference, convention or trade show

272B

467B

491C

326C

Shopping, non-routine

180C

205C

291C

245B

Other personal reasons

891B

1,290B

1,411B

913B

Business conference, convention or trade show

943B

1,150B

728B

987B

Other business

1,127B

1,258B

1,038B

1,152B

Symbol legend

A data quality: excellent

B data quality: very good

C data quality: good

D data quality: acceptable


Complete Analysis: Travel Data Table in your notebook or use the following fillable and printable document. If you prefer, use another method to record your ideas.

Analysis: Travel Data Table

What time period does the table represent?

What does (x 1,000) mean in the title, how does this relate to the data?

List at least four facts that you learn by examining the data in this table.

Fact 1:

Fact 2:

Fact 3:

Fact 4:

What story does this table tell about its topic?

List at least three questions that cannot be answered by analyzing this graph.

Question 1:

Question 2:

Question 3:

New questions may arise as you analyze this data. List some questions that would require more data collection.

Press the ‘Activity’ button to access Analysis: Travel Data Table. 

Activity(Open PDF in a new window)

Why collect and analyze data?

Data is collected regularly by all levels of government, companies, organizations, and individuals for a wide variety of reasons. Reflect on your learning by answering the following questions. Use the method of your choice to record your ideas.

  • What are some reasons why governments collect data? List some specific topics and the level of government involved.
  • What are some reasons that businesses collect data? List some specific topics.
  • What are some reasons why students should be able to collect, represent, and analyze data? List some specific reasons.
  • Why might we want to ask questions about the data that we explore?

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.

Connect with a TVO Mathify tutor

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