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D1.6 · Critique circle graphs and misleading displays before drawing conclusions

Learn to critique circle graphs and misleading displays before drawing conclusions through clear examples and targeted practice.

Ontario Grade 7 Mathematics

Data

Critique the display before deciding what the data mean

A circle graph divides one whole into parts. Each part stands for a category, such as a way to travel to school. The size of a part should match the share of the whole that the category represents. A graph may look polished and still give a confusing or unfair impression. Before drawing a conclusion, check its title, labels, values, and source. In this lesson, all survey examples are hypothetical. They are practice data, not reports of real students.

What you will learn

Explain what a circle graph shows and how its parts relate to the whole.
Check whether categories and values in a circle graph are clear and complete.
Compare a circle graph with stated values to spot misleading displays.
State conclusions supported by the data, and avoid conclusions that are not.

Start with the whole

A fraction describes part of a whole. For example, if 4 of 10 equal counters are blue, the blue share is

\frac{4}{10}

. The total number of counters is the whole. A circle graph uses the same idea: the full circle represents the whole group, and each slice represents one category's share.

A percentage describes a share out of 100. In a complete circle graph, the category shares add to 100%. If a graph shows categories from one survey, its labels should account for the whole group. A missing category or a total that does not make sense is a reason to pause.

A circle graph is useful when you want to compare parts of one whole. It can be harder to compare slices that are close in size than to compare clearly written values. Read both the picture and the numbers, when numbers are provided.

category shares add to 100%

The full circle represents the whole.
Each slice represents a category's share of that whole.
For a complete circle graph, the category shares add to 100%.

Check the display before you compare

Begin with the title. It should tell you what the data are about. Next, check the labels. Each slice should have a category name or a clear key that matches the slices. If a label is missing or hard to match, readers may assign a slice to the wrong category.

Look for the values and the group being described. Ask what was counted, who was included, and whether the whole group is clear. If the graph gives no source or does not say whether the data are real or hypothetical, you cannot check where the numbers came from. Say what is missing instead of guessing.

Then compare the slice sizes with the values. A larger share should have a larger slice. If values are shown, use them to check the picture. If values are not shown, do not claim an exact difference from a small visual gap. A display is misleading when its design or missing information could lead readers to a wrong impression.

Check the title, category labels, values, group, and source.
Slice sizes should match the shares they represent.
Describe missing information instead of filling it in with a guess.

Make careful comparisons

A conclusion is a statement based on the data. A careful conclusion names the group and the measure being compared. For example, “In this hypothetical survey, 40% chose walking” is supported if the graph clearly shows that value and identifies the survey group.

Do not turn a share into a claim about a different group. A graph about one class does not tell you what all students in a city chose. Do not treat a larger slice as proof that a choice is better, safer, or more popular everywhere. The graph only reports the categories and group it actually describes.

When a graph seems unclear, return to the values or the data table. A table lists categories and counts or shares in rows. It can make exact comparisons easier. If the graph and table disagree, point out the mismatch and avoid choosing whichever display seems more convincing.

A conclusion must stay within the group and data shown.
A graph describes the data; it does not explain every cause or prove what is best.
Use the values or table to check close visual comparisons.

Use a simple critique routine

Use four questions before drawing a conclusion. First, what is the whole? Second, are all categories labelled and included? Third, do the stated shares add to 100% and match the slice sizes? Fourth, what conclusion is supported, and what information is still missing?

You can practise the routine with hypothetical values. If a circle graph labels three categories as 50%, 30%, and 20%, the shares make a complete whole because

50+30+20=100

. But that check alone does not prove the display is clear. You still need a title, labels, the group being described, and information about the data source.

Keep your critique specific. Instead of saying “This graph is bad,” name the issue: “The title does not say which group was surveyed,” or “The values add to 110%, so they cannot describe the full circle as stated.” Then explain why the issue matters to a reader.

Check the whole, labels, values, and supported conclusion.
A correct total does not fix unclear labels or missing context.
Name the problem and explain how it could affect a conclusion.

A quick critique routine

Check	Ask yourself
Whole	What group or total does the full circle represent?
Labels	Can I identify every category?
Values and slices	Do the shares add to 100%, and do the slice sizes match?
Conclusion	What does the graph support, and what is missing?

Worked example

Check a complete circle graph

A hypothetical class survey asks students to choose one favourite reading activity. The results are: graphic novels, 40%; mystery books, 35%; and poetry, 25%. Check the total and state one conclusion that stays within the data.

Hypothetical reading choices

Practice data for one hypothetical class survey. The slices represent 40%, 35%, and 25% of the whole.

Check the whole
Add the three stated shares. They total 100%, so the values account for a complete circle.
$40+35+25=100$
Compare the categories
Graphic novels have the largest stated share. That comparison is supported by the values, not by a guess about why students chose them.
$40\%>35\%>25\%$
State a careful conclusion
A supported conclusion is: In this hypothetical class survey, graphic novels were selected most often. The result does not tell us what students in other groups prefer.

Answer: The shares total 100%. In this hypothetical class survey, graphic novels were selected most often.

Check: The conclusion names the surveyed group and does not claim that the same result applies elsewhere.

Worked example

Find what is missing

A circle graph is titled “How Students Travel.” It has slices labelled walking, car, and bus, but gives no values, school or group name, or data source. What can a reader fairly conclude, and what should be questioned?

Identify the information shown
The title and slice labels name a topic and three categories. They do not identify the group or say where the data came from.
Limit the conclusion
Without values, a reader may describe only which slice looks largest, if the slices are clear. The reader cannot give an exact percentage or say how many students chose each category.
Explain the concern
The missing group and source make it hard to know whom the graph describes or whether the information can be checked. Ask for the values, group, and source before making a broader claim.

Answer: The graph names three travel categories, but it does not show who was included or where the data came from. Without values, exact shares cannot be stated. A reader should request the group, values, and source before drawing a broad conclusion.

Check: Do not invent a school, a sample size, or a percentage that the graph does not provide.

Worked example

Compare the graph with its values

A hypothetical display says that a club has 45% members who chose art, 35% who chose music, and 30% who chose drama. Its circle graph also makes the art slice look smaller than the drama slice. Identify both problems and explain what to do before drawing a conclusion.

Check the total
The three stated shares add to more than 100%, so they cannot describe non-overlapping parts of one complete circle as presented.
$45+35+30=110$
Check the picture
The stated art share is larger than the drama share. A circle graph should not draw the art slice smaller than the drama slice if those values are meant to describe the same whole.
$45\%>30\%$
Pause before concluding
There are two conflicts: the shares do not make a complete whole, and the slice sizes do not match the values. Ask for corrected data or a corrected display. Do not decide which club choice was most common from this inconsistent graph.

Answer: The values total 110%, and the slice sizes contradict the stated values. The display is inconsistent. Ask for clarification or corrected information before comparing the choices.

Check: Both the total and the picture need checking; fixing only one problem would not resolve the other.

Common mistakes and how to avoid them

Assuming a circle graph is reliable because it looks neat.

Correction: Check the labels, values, whole, and source. A neat design can still be unclear or inconsistent.

Treating a slice that looks a little larger as an exact measured difference.

Correction: Use stated values for exact comparisons. If values are absent, describe the visual cautiously.

Using a result from one group to make a claim about everyone.

Correction: Name only the group the data describe. Do not extend the conclusion beyond that group.

Ignoring a total that is not 100%.

Correction: For a complete circle graph of parts of one whole, check whether the shares add to 100%. If they do not, question the display.

Lesson summary

A circle graph shows parts of one whole.
In a complete circle graph, category shares add to 100%.
Check the title, labels, values, group, source, and slice sizes.
When information is missing or inconsistent, say so and pause before drawing a conclusion.
Keep conclusions within the group and information the graph actually shows.

Check your understanding

Question 1

A hypothetical circle graph gives shares of 20%, 45%, and 35%. Which statement is correct?

The shares total 100%, so they account for one complete circle.
The shares total 90%, so one category must be missing.
The shares total 110%, so the largest share must be removed.
The shares cannot be checked unless the graph has a source.

Show answer and explanation

The shares total 100%, so they account for one complete circle.

Adding the values gives 100%. A source is still useful for checking context, but it does not change this total.

Question 2

A graph shows travel choices for one hypothetical class but has no values. What is the safest conclusion?

The largest-looking slice is exactly 50%.
The whole city makes the same travel choices.
The graph does not provide exact shares, so do not state exact percentages.
The category with the shortest label is least common.

Show answer and explanation

The graph does not provide exact shares, so do not state exact percentages.

Without values, exact shares are not given. The graph also describes only the class named, not a whole city.

Question 3

A graph states three category shares of 40%, 40%, and 30%. What should you do first?

Conclude that the first two categories are tied.
Check the total and question the display because the values add to 110%.
Change the last value to 20% without asking.
Ignore the values and trust the slice sizes.

Show answer and explanation

Check the total and question the display because the values add to 110%.

The stated values total 110%, so they do not describe a complete circle as presented. Do not alter data without evidence.

Key terms

Whole: The complete group or amount being represented.
Category: A named group or choice in the data, such as walking or bus.
Share: The part of the whole that belongs to a category.
Percentage: A way to describe a share out of 100.
Conclusion: A statement made from information in the data.
Misleading display: A graph or chart whose design or missing information may give readers a wrong impression.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation D1.6. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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