Grade by Grade
D. Data · Data Literacy and Probability

Analysing Circle Graphs and Misleading Graphs

D1.6 D1.3 A1About 55 minutes
Learning goals
  • I can ask and answer questions about data shown in circle graphs and other graphs.
  • I can spot ways a circle graph or other graph can mislead readers.
  • I can use data to challenge a preconceived notion.
  • I can make a convincing argument and an informed decision using data.

Words to know

misleading graph
A graph that gives a wrong impression, by accident or on purpose.
preconceived notion
An idea you have before looking at the evidence.
claim
A statement you want to convince others is true.
evidence
Facts and numbers from the data that support a claim.
informed decision
A choice made after looking carefully at the evidence.

Remember from Grade 6

You caught misleading bar and broken-line graphs: scales that don't start at 0, uneven scales and missing labels. You also challenged preconceived notions and made arguments with data. Now you'll do the same with circle graphs, which can mislead in their own ways.

Asking good questions

When you see a graph, become a detective. Ask:

  • What is the graph about? (Title, labels, legend.)
  • Who was asked, and how many? (Source, total, sample.)
  • What stands out? The biggest and smallest parts, parts that combine to more than half.
  • What doesn't fit? Percentages that don't add to 100%, sectors that look the wrong size.
  • What can I conclude, and what can't I conclude?

How circle graphs can mislead

  1. Percentages that don't add to 100%. Maybe a category is missing, or people could choose more than one answer. Either way, a circle graph doesn't fit.
  2. Sectors not drawn to size. A 20% sector drawn as big as a quarter makes that category look more important. Check with benchmarks: 25% should be a right angle.
  3. 3-D or tilted circle graphs. Tilting the circle makes the sectors at the front look bigger than the ones at the back.
  4. A pulled-out or brightly highlighted sector draws your eye and can make it seem more important than it is.
  5. No total or a tiny sample. "80% prefer our cereal!" might mean 4 out of 5 people.
  6. Comparing two circle graphs with different totals. A smaller sector can stand for more people if its whole is bigger.
Way to School at Two SchoolsSchool A (100 students)50%30%20%School B (800 students)45%20%35%WalkBusCarSource: sample data for this lesson
School A: walk 50%, bus 30%, car 20%. School B: walk 45%, bus 20%, car 35%. The bus sector is smaller at School B, but it stands for more students.
Worked example

Example 1: Comparing two circle graphs

Look at the two circle graphs. Mia says, "Fewer students take the bus at School B, because the bus sector is smaller." Is she right?

  1. School A bus: 30% of 100 = 30 students.
  2. School B bus: 20% of 800 = 160 students.
  3. School B's bus sector is a smaller percentage, but School B is 8 times as big.

Mia is wrong about the number of students. More students take the bus at School B (160 vs 30). A smaller share of School B's students ride the bus. Circle graphs compare shares, not counts.

Challenging a preconceived notion

A common idea is: "Kids spend most of their free time on screens." Let's test it with data. A class of 30 students tracked their free time for one week and found the percentage of free time spent on each activity.

How We Spend Our Free Time30%25%20%15%10%Screens 30%Outdoor play 25%Sports 20%Other 15%Reading 10%Source: 30 Grade 7 students, one week (sample data)
Screens 30%, outdoor play 25%, sports 20%, other 15%, reading 10%.
Worked example

Example 2: Testing the idea

Does the free-time graph support the idea that kids spend most of their free time on screens?

  1. "Most" means more than half, more than 50%.
  2. Screens are the largest sector, but only 30%, less than a third of the circle.
  3. Active time (outdoor play + sports) is 25% + 20% = 45%, more than screens.
  4. Limits: this is one class for one week. A different class or season might be different.

No. For this class, screens are the biggest single category (30%), but not most of free time. Active play and sports together (45%) take up more. The data challenges the preconceived notion.

Worked example

Example 3: A convincing argument

The class wants the principal to add a winter outdoor games club. Use the graph to make a convincing argument.

  1. Claim: Our school should start a winter outdoor games club.
  2. Evidence: In our class survey of 30 students, outdoor play and sports together make up 45% of our free time, more than screens (30%).
  3. Reasoning: Students already choose active play, so a club would likely get good attendance and support healthy habits all winter.
  4. Limits and next step: Our data comes from one class in one week. We could survey a random sample from every grade to make the argument stronger.

A convincing argument has a claim, evidence (with numbers and the source), reasoning, and is honest about limits.

Respectful questioning

When you question someone's graph or idea, question the data, not the person. Say "I noticed the percentages add to 110%. Could you check them?" instead of "Your graph is wrong!" And be ready to change your own mind when the evidence says so. That's what good thinkers do.

Just for fun

Spotted in an ad: "100% of the people who tried our snack were surveyed!" Sounds impressive... until you notice it says nothing about whether anyone liked it.

Hands-on activity

Misleading graph hunt and fix

You need: flyers, newspapers or websites (look with a grown-up), paper, a protractor and a round lid.

  1. Find a circle graph or another graph. Check it with the detective questions: title, total, source, percentages add to 100%, sectors the right size?
  2. If you can't find a misleading graph, make one on purpose: draw a circle graph of 50%, 30%, 20%, but draw the 20% sector as big as a quarter. Show a family member. Do they notice?
  3. Redraw it correctly (180°, 108°, 72°).
  4. Think of a preconceived notion your family has, like "We eat out a lot" or "It always snows on the weekend". How could you collect data to test it?

Math talk: "Why might someone make a misleading graph on purpose? How can a reader protect themselves?"

Your turn

1

Use How We Spend Our Free Time (30 students). What percentage is reading? What is its central angle?

2

What percentage of free time is not screens?

3

A circle graph shows: yes 55%, no 40%, maybe 15%. What is wrong?

4

An ad says "9 out of 10 dentists recommend our toothpaste!" What questions should you ask?

5

Why can a 3-D tilted circle graph be misleading?

6

At School C (200 students), 40% bike. At School D (500 students), 20% bike. Which school has more bikers?

7

Turn this into a convincing argument: "We should have a skating party because lots of people like skating." Use the survey result: 35% of 40 students chose skating, the most of any activity.

More practice: warm-up

1

What should the percentages in a circle graph add to?

2

What is a preconceived notion?

3

Name the three main parts of a convincing argument.

4

A survey of 5 people says 80% like a new snack. How many people is that?

5

True or false: a bigger sector always means more people.

More practice: on your own

1

A circle graph labelled "Favourite Fruit" has a 25% sector that looks like a third of the circle. What angle should a 25% sector have? What angle is a third?

2

A company's graph shows 60% of people prefer its juice. The source says "Survey of our customers." Why could this be misleading?

3

Someone says, "Hardly anyone walks to School A." Use the School A circle graph to respond.

4

A store shows a circle graph of how its customers rate service, with only these sectors: excellent 60%, good 30%. What might be hidden?

5

Make an informed decision: the student council can afford one event. Survey of 80 students: dance 30%, movie 25%, games day 25%, talent show 20%. Which event, and why? Is the decision clear-cut?

Challenge

1

Two circle graphs show favourite sport. Town X (2 000 youth): hockey 40%. Town Y (5 000 youth): hockey 25%. A newspaper headline says "Hockey More Popular in Town X." Is the headline fair? Write a more accurate one.

2

A data set's percentages are 32.6%, 27.1%, 22.4% and 17.8%. They add to 99.9%. Is the graph misleading? Explain.

3

Write a convincing argument against a claim using data: "Our class spends too much free time reading" (use the free-time circle graph).

Check your understanding

Quiz

1.

A circle graph shows 45%, 35% and 30%. What is the problem?

2.

School P (100 students): 40% walk. School Q (600 students): 25% walk. Which is true?

3.

Why can a tilted 3-D circle graph be misleading?

4.

Which statement is best supported by a graph showing screens 30% of free time?

5.

Which is the strongest argument?

6.

An ad says "80% of people prefer our cereal!" What is the most important question to ask?

For parents and teachers

Big idea: D1.6 asks Grade 7 students to analyse data presented in various ways, including circle graphs and misleading graphs, by asking and answering questions, challenging preconceived notions and drawing conclusions, then making convincing arguments and informed decisions. Grade 6 covered misleading bar and line graphs; this lesson adds circle-graph traps.

Common difficulties:

  • Treating a bigger sector as more people when two graphs have different totals.
  • Saying "most" for the largest category even when it is less than half.
  • Arguments without numbers or sources.
  • Forgetting the limits of a small or biased sample.

How to help: Look at ads together and ask, "Out of how many? Who was asked?" Practise the claim, evidence, reasoning pattern for family decisions ("Which park should we go to?"). This lesson builds A1 skills: thinking critically, communicating respectfully, and being willing to change your mind.