Grade by Grade
D. Data · Data and Probability

Spotting Misleading Graphs and Claims

D1.6 D1.3 A1About 45 minutes
Learning goals
  • I can explain how a scale that doesn't start at 0, or has unequal steps, can mislead.
  • I can spot other tricks, like a biased sample, missing labels and leaving out data.
  • I can fix a misleading graph.
  • I can question data claims respectfully.

Words to know

misleading graph
A graph that gives the wrong idea about the data, on purpose or by accident.
broken scale
A scale that starts at a number other than 0. It makes small differences look huge.
claim
A statement that someone says is true.
critical thinking
Asking careful questions before you believe something.

Same data, two graphs

Room 5 collected 52 cans for the food drive. Room 6 collected 56 cans. Room 6 made Graph A for the school newsletter. Look at both graphs. Which one makes Room 6 look like the big winner?

Graph A5052545658Room 5Room 6Graph B0102030405060Room 5Room 6Cans collected: same data, two graphs
Graph A: the scale starts at 50 and counts by 2s up to 58. Room 6's bar looks three times as tall as Room 5's. Graph B: the scale starts at 0 and counts by 10s up to 60. The bars look almost the same.

In Graph A, the scale starts at 50, not 0. Room 5's bar shows 2 steps above 50 and Room 6's shows 6 steps above 50, so Room 6's bar is three times as tall. But 56 is only 4 more than 52!

In Graph B, the scale starts at 0. The bars are almost the same height, which is the truth: the rooms collected almost the same number of cans.

Both graphs are drawn correctly for their scales. Graph A just tricks your eye.

Ways graphs and claims can mislead

  1. The scale doesn't start at 0. Small differences look huge.
  2. The steps on the scale are not equal, like 0, 5, 10, 50, 100.
  3. Pictures are different sizes. In a pictograph, a bigger picture looks like more, even when it stands for the same amount.
  4. Labels, a scale or a source are missing, so you can't check what the graph shows.
  5. The sample is biased or too small. "9 out of 10 kids love Crunch-O's!" might come from 10 kids at a Crunch-O's booth.
  6. Some data is left out. A graph that shows only the best months hides the others.
  7. Counts are compared when groups are different sizes. A big group can have more in a category without having a bigger share.
Worked example

Example 1: Is the claim fair?

A poster says: "9 out of 10 kids love Crunch-O's cereal!" The small print says 10 kids were asked at a Crunch-O's free-sample table. Is the claim convincing?

  1. How big is the sample? Only 10 kids. That's very small.
  2. How was it chosen? Kids at a free-sample table probably already like the cereal. The sample is biased.
  3. Who is "kids"? The poster talks about all kids, but only 10 were asked.

No. The sample is too small and biased. A fair test would ask a large random sample of kids.

Worked example

Example 2: Counts or shares?

"Room 7 is the best at reading! 18 Room 7 students finished the reading challenge, but only 15 in Room 8." Room 7 has 30 students. Room 8 has 20. Is the claim fair?

  1. Find the shares. Room 7: 18/30 = 6/10 = 0.6.
  2. Room 8: 15/20 = 75/100 = 0.75.
  3. A greater share of Room 8 finished.

Not fair. Room 7 had more finishers only because it has more students. Room 8 had the greater share (0.75 compared to 0.6).

Question respectfully

When a graph or claim seems wrong, it's good to ask questions, but be kind: "I wonder why the scale starts at 50?" or "How many people were asked?" Questioning ideas, not people, keeps everyone learning. Being open to changing your mind is a sign of a strong thinker.

Graph riddle

When is 56 three times as big as 52?

Only on a graph whose scale starts at 50!

Hands-on activity

Graph detective hunt

You need: flyers, a newspaper, magazines, or news websites (with a grown-up), plus paper and a pencil.

  1. Find two or three graphs or number claims ("4 out of 5...", "twice as many...").
  2. For each one, check: Does the scale start at 0? Are the steps equal? Is there a title, labels and a source? How many people were asked, and who?
  3. Give each graph a rating: fair, a bit misleading or very misleading. Explain why to your grown-up.
  4. Bonus: use the cans data (52 and 56) and draw your own fair graph and your own misleading graph. Which would you put in a newsletter?
Votes for New Equipment859095100SwingsWallSlideWall means climbing wall.
Use this graph for the Your turn questions. The scale starts at 85 and counts by 5s to 100. Swings 95 votes, climbing wall 100 votes, slide 90 votes.

Your turn

1

What number does the scale on the votes graph start at?

2

How many votes did each piece of equipment get?

3

The climbing wall's bar looks how many times as tall as the slide's bar?

4

How many more votes did the climbing wall really get than the slide?

5

How would you fix the votes graph?

6

A graph has no title, no labels and no source. Why is that a problem?

More practice: warm-up

1

Where should the scale on a bar graph usually start?

2

A scale goes 0, 10, 20, 50, 100. What's wrong?

3

True or false: a graph can be misleading even if every number on it is correct.

4

"Everyone I asked loves my lemonade!" Kai asked 3 people: his mom, his dad and his sister. What is the problem?

5

What does "leaving out data" mean?

More practice: on your own

1

A pictograph shows 1 maple leaf for each 10 trees planted. The leaves in one row are drawn twice as big as in the other. Why is that misleading?

2

A store's graph shows sales for only June, July and August, when sales were highest. What might the store be hiding?

3

Team A scored 40 goals and Team B scored 44. On a graph with the scale starting at 38, how many times as tall does Team B's bar look?

4

"Our school recycles more than Maple Park School! We recycled 400 kg and they recycled 300 kg." Our school has 800 students and Maple Park has 400. Is the claim fair?

5

Write a kind question you could ask about a graph whose scale starts at 50.

Challenge

1

Use the cans data (Room 5: 52, Room 6: 56). Room 6 wants their graph to make them look like big winners. Room 5 wants a graph that shows it was almost a tie. Describe each graph's scale. Which graph is fairer?

2

A survey says "Most families want school to start at 9:30." They asked 20 families at a coffee shop at 9:00 a.m. on a school day. Give two reasons to doubt the claim.

3

Make up your own misleading claim using counts when groups are different sizes. Then show why it's misleading.

Check your understanding

Quiz

1.

A bar graph's scale starts at 50 instead of 0. What does this usually do?

2.

Room 5 collected 52 cans and Room 6 collected 56. How many more did Room 6 collect?

3.

Which scale has unequal steps?

4.

"9 out of 10 kids love Crunch-O's!" The 10 kids were asked at a Crunch-O's free-sample table. What's the biggest problem?

5.

Room 7 (30 students) had 18 finish a challenge. Room 8 (20 students) had 15 finish. Which room had the greater share finish?

6.

What is the kindest way to question a misleading graph?

For parents and teachers

What this lesson teaches: analysing misleading graphs and claims (D1.6), including broken scales that don't start at 0, unequal intervals, different-sized pictures, missing labels or sources, biased or small samples, left-out data, and comparing counts for groups of different sizes. It connects to graph-making (D1.3). Questioning respectfully and keeping an open mind (A1) are built in.

How to help at home:

  • Do the graph detective hunt with flyers or news sites, and make it a habit: "Where does that scale start?"
  • When you hear an ad claim ("4 out of 5 dentists..."), ask: "Who was asked? How many?"
  • Model kind questioning: question the idea, not the person.

Common difficulties:

  • Judging by bar height alone without reading the scale.
  • Thinking a graph is fair because every number on it is correct.
  • Forgetting to compare shares when groups are different sizes.
  • Note: a scale that doesn't start at 0 isn't always used to trick people, but readers should notice it.