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D1.3 · Select suitable graphs, including circle graphs

Learn to select suitable graphs, including circle graphs through clear examples and targeted practice.

Ontario Grade 7 Mathematics

Data

Show the parts of one complete whole

A circle graph is useful when categories are non-overlapping parts of one whole. Each sector should match its category share, and the percentages must add to 100. The title, labels, total, and source matter just as much as colour. Here we use a small hypothetical class survey only for practice; these are not observations from a real school. We compare a circle graph with a bar chart and decide which question each answers most clearly.

What you will learn

  • Check whether categories form one whole.
  • Verify circle-graph percentages total 100.
  • Choose a graph that suits the question.

Start with the question

A circle graph answers questions about shares of a single whole. A bar chart is often easier when the purpose is to compare exact counts across categories. A time series calls for a different display because time order matters.

Calculate each share

In a hypothetical group of 20, suppose 8 choose drawing, 6 choose music, 4 choose sport, and 2 choose reading. Divide each count by 20 and multiply by 100. The shares are 40%, 30%, 20%, and 10%.

Check the display

Add the shares: 40 + 30 + 20 + 10 = 100. Every student appears in one category only. A missing category, repeated person, or mismatched denominator would make a circle graph misleading. The displayed sectors are proportional to the stated percentages.

Worked example

A hypothetical activity survey

Twenty hypothetical students each choose one favourite activity: drawing 8, music 6, sport 4, reading 2. Is a circle graph suitable, and what share chose drawing?
One choice from 20 hypothetical students
One choice from 20 hypothetical studentsDrawing 40%, music 30%, sport 20%, and reading 10% total 100%; each sector is one exclusive category.Drawing: 40%Music: 30%Sport: 20%Reading: 10%Hypothetical classroom practice data

Drawing 40%, music 30%, sport 20%, and reading 10% total 100%; each sector is one exclusive category.

  1. Check the whole
    The counts 8 + 6 + 4 + 2 equal the 20 students.
  2. Compute the part
    Drawing is 8 of 20, or 8 ÷ 20 = 0.4 = 40%.
  3. Choose the display
    Each student selects exactly one category, so a circle graph can show the parts of this whole.
Answer: Yes. The categories form one whole, and drawing represents 40%.
Check: The remaining 30% + 20% + 10% equals 60%, completing 100%.

Common mistakes and how to avoid them

Using 8 as though it were 8% because the drawing category has eight students.
Correction: Eight is a count. Divide by the whole group of 20 before converting to a percent.

Lesson summary

  • Use circle graphs for exclusive parts of a whole.
  • Every sector needs a clear category and percent.
  • Check the total and label hypothetical data honestly.

Check your understanding

Question 1

What share of the hypothetical group chose music?
  1. 30%
  2. 6%
  3. 20%
  4. 60%
Show answer and explanation
30%
Six of twenty is 6 ÷ 20 = 0.30 = 30%.

Key terms

Circle graph
A circular display divided into sectors representing parts of one whole.
Percent
A ratio expressed out of 100.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation D1.3. It is a study resource, not an official curriculum publication.

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