Notice and wonder

Examine the following two graphs and their descriptions.

What do you notice about each graph?

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

Task 1: Misleading graphs

Graphs are visual representations of data that are used to display patterns, trends, and relationships in data. There are many different types of graphs, some of which can be misleading, just like the two graphs in the Minds On! We will revisit them later on.

Pause and consider…

Why do you think some graphs are created to misrepresent data?

How might a graph be misleading?

Record your ideas using a method of your choice.

Task 2: How do graphs misrepresent data?

There are various graph features you can consider in order to determine the accuracy of a graph.

Let’s explore how different features can be used to misrepresent data.

Consider the following features.

Titles

Does the title accurately reflect the data?

The data in the graph should also connect to the title. Without a title, it can be unclear what the graph is supposed to record.

It is also important that the title uses clear and concise language and explains as much about the graph as possible without providing a summary or interpretation of the data.

Labels

Is the graph or plot labelled properly?

A graph that is properly labelled has a title, data source, vertical axis title, horizontal axis title, category labels, and a scale. On a circle graph, all sections should be labelled.

Some graphs will also include data labels and if there are multiple sets of data, a key or legend.

You should also check if the labels make sense. The labels should help the data tell an accurate story. Graphs that are missing labels or use unclear labels can be misleading.

Source of data

Where did the data and/or graph come from? Is the information collected from primary-source data or secondary-source data?

The source indicates where the data was collected. It’s important to know where the information and data are coming from. This allows us to determine if the source is reliable.

Scale

What is the scale?

Check the following table and two corresponding bar graphs.

The scale on a graph affects the appearance of data and as a result, the conclusions someone might make about the data.

Stretching out or compressing the scale can change the impression of the differences in the data. This is why the data in the two graphs can be identical but can display two very different stories.

When it comes to scale, it’s important to consider if:

• the scale reflects the size of the greatest number in the data
• the scale starts at 0
• the scale is consistent and if the numbers are equally spaced on the scale

Keys and legends

If more than one data set is displayed on a single graph, there should be a key or legend to identify the individual data sets.

Without a key or legend, it is not possible to compare the data sets. As a result, the purpose of the graph has no value.

Consistent visuals

Do the symbols represent the data accurately?

In a pictograph, for example, each symbol should be the same size for each category. The symbols should also be spaced the same distance apart.

In bar graphs, the bars should all be the same width. If the area of a bar one bar is greater than the rest of the bars, it might suggest that one category is more significant than the other bars.

Task 3: Analyzing misleading graphs

Let’s revisit the graphs and their descriptions from the Minds On section.

Identify and explain how each graph is misleading. How does the misleading graph influence the conclusion you make about the data presented?

What are the reasons someone would have intentionally created each misleading graph?

Record your ideas using a method of your choice.

Creating misleading graphs

Choose one of the following two options:

Option 1: Changing misleading graphs to be more accurate

Select one of the misleading graphs from the Minds On section.

Then, recreate the graph to represent the data more accurately. You can create your graph on paper, or using a computer.

Once you have recreated the graph, describe how the graphs are different and the same. Record your responses to the prompts above using a method of your choice.

Option 2: Make a graph misleading

The following data set records the daily temperature (in Celsius) in Niagara Falls, Ontario for ten days.

• 17, 15.5, 14, 13, 9, 13.5, 14.5, 15.5, 15, 13

Create a misleading line graph that records a steep drop in temperature.

Then, create another line graph that depicts the decrease in temperature accurately.

• How are the graphs the same? How are they different?
• Which graph gives a more accurate representation of the daily temperatures for ten days? Explain your thinking.

You can create your graphs on paper, or using a computer. Record your reflections on the graphs using a method of your choice.

Reflect in your math journal

Use the following questions to reflect on your learning. You can record your responses using a method of your choice.

• How can you analyze a graph to decide whether or not its misleading?
• How can the scale on a graph affect someone’s understanding of the data displayed?
• When might it be to someone’s advantage to create a misleading graph?

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.

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.

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