Spotting misleading statistics and graphs

Reading Comprehension

CCSS RI.9-10.7CCSS RI.9-10.8England: GCSE English Language Paper 2England: SAT Reading and Writing (Command of Evidence: Quantitative)England: GCSE Maths (statistics)

Objective and success criteria

Students will: Spotting misleading statistics and graphs.

I can answer questions on today's skill on my own, without help.
I can explain each step and say why it works.
I can check my answer and spot a mistake.

Before and after

Needs first: Checking claims online: lateral reading and tracing sources; Is the evidence relevant and sufficient?

Leads to: Bias and loaded language in reporting; Does the study design support the claim?

Materials: A short text or extract (one copy each), Highlighters, Question cards, Mini whiteboards, A short model text on the board, Printed student sheet (below).

Warm-up · 5 min

Quick retrieval from earlier learning (Checking claims online: lateral reading and tracing sources; Is the evidence relevant and sufficient?). Students answer on mini whiteboards.
Show answers together and note who needs support in the main task.

Is the proposed answer correct? A post says "A study proves X" but gives no link. What is the best next step? → share it so experts can check (yes, it is correct / no, it is not correct) → no, it is not correctPrompt: Good checkers leave the page and see what other reliable sources say.
Read the question and choose. You find a website about a health claim. You've never heard of the organisation behind it. What should you do first? (open a new tab and search for what reliable sources say about that organisation / trust its 'About us' page / read the whole site carefully before checking anything else / judge it by how professional it looks) → open a new tab and search for what reliable sources say about that organisationPrompt: Good checkers leave the page and see what other reliable sources say.
Is the proposed answer correct? You find a website about a health claim. You've never heard of the organisation behind it. What should you do first? → judge it by how professional it looks (yes, it is correct / no, it is not correct) → no, it is not correctPrompt: Good checkers leave the page and see what other reliable sources say.

Hook · 5 min

Read the first lines of a short text aloud and ask what students predict will happen and why.
Share the objective: Spotting misleading statistics and graphs. Read the success criteria together.

I do: model it · 10 min

Work through the example out loud, saying why you do each step, not just what you do.
Example: Read the question and choose. "9 out of 10 users loved our app!" The survey asked 10 people. What's the main problem?
Step 1: Numbers can mislead through small or biased samples, cherry-picking, distorted graphs, misleading averages and confusing correlation with causation.
Step 2: So the answer is: the sample is far too small to generalise
Answer: the sample is far too small to generalise
Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

Do these together. Students try each step on whiteboards before you reveal it.
Use the hints as prompts rather than giving the answer.

Is the proposed answer correct? "9 out of 10 users loved our app!" The survey asked 10 people. What's the main problem? → 9 out of 10 is a bad score (yes, it is correct / no, it is not correct) → no, it is not correctPrompt: Ask: how many people or cases is this based on, and who was asked?
Read the question and choose. "Towns with more ice-cream shops have more sunburn cases. So ice cream causes sunburn!" What's wrong? (ice cream does cause sunburn / there are too many shops / the numbers must be made up / both are linked to hot, sunny weather; correlation doesn't prove cause) → both are linked to hot, sunny weather; correlation doesn't prove causePrompt: Ask: how many people or cases is this based on, and who was asked?

You do: independent practice · 10 min

Students work on the student sheet. Circulate and check the first two answers of every student early.
Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

Is the proposed answer correct? "The average salary at our company is £60,000!" But the boss earns £1 million and most staff earn £25,000. What's misleading? → one huge value pulls the mean up, so it doesn't show a typical salary (yes, it is correct / no, it is not correct) → yes, it is correctPrompt: Ask: how many people or cases is this based on, and who was asked?
Read the question and choose. A graph of test scores has a vertical axis starting at 78 instead of 0, so a rise from 80 to 82 looks huge. What is misleading? (graphs should never use numbers / the change is actually a fall / the cut-off axis exaggerates a small change / the scores are wrong) → the cut-off axis exaggerates a small changePrompt: Ask: how many people or cases is this based on, and who was asked?

Watch out for

Answering from memory or opinion instead of evidence in the text.
Copying a long quote without explaining what it shows.

Support and stretch

Support

Review first: Checking claims online: lateral reading and tracing sources.
Use concrete materials: a short text or extract (one copy each).
Give the first step of each question, or a partly worked example to finish.
Pair with a confident partner for the guided practice.

Stretch

Move on to: Bias and loaded language in reporting; Does the study design support the claim?.
Explain a common mistake in writing and how to fix it.
Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/english/grade-9.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Spotting misleading statistics and graphs

Name

Date

Score/ 8

Should Secondary Schools Try a Four-Day Week?

Imagine a school week that ends on Thursday afternoon. For students in a growing number of schools around the world, this is no longer a fantasy. I believe secondary schools should at least trial a four-day week. The strongest reason is wellbeing. Many teenagers report feeling exhausted by the end of the week, and a longer weekend could give them time to rest, exercise and pursue interests that school leaves no room for. Supporters also point to attendance. In one regional pilot involving twelve schools, attendance rose by three percentage points after the change. That may sound small, but across a year it adds up to thousands of extra lessons attended. Critics argue that working parents would struggle with childcare on the fifth day. This is a serious concern. However, schools could offer an optional supervised study day, run by staff and volunteers, so that no family is left without support. Others worry that students will learn less. Yet schools in the pilot lengthened each remaining day by forty minutes, so total teaching time hardly changed. A trial costs little and teaches us a lot. If it fails, we can change back. If it works, students will thank us for it.

1
Question 1
Read "Should Secondary Schools Try a Four-Day Week?". Is the attendance evidence relevant and sufficient on its own to prove four-day weeks work everywhere?
- A. relevant, but one pilot in twelve schools is not enough to prove it works everywhere
- B. neither relevant nor sufficient, because pilots are always wrong
- C. completely sufficient, because twelve is a large number
- D. irrelevant, because attendance has nothing to do with school

2
Question 2
Is the proposed answer correct? A company shows only the three months when its sales rose and leaves out the nine months when they fell. What is this called? → cherry-picking data
- A. yes, it is correct
- B. no, it is not correct
3
Question 3
Read the question and choose. A graph of test scores has a vertical axis starting at 78 instead of 0, so a rise from 80 to 82 looks huge. What is misleading?
- A. the change is actually a fall
- B. the cut-off axis exaggerates a small change
- C. graphs should never use numbers
- D. the scores are wrong
4
Question 4
Is the proposed answer correct? "9 out of 10 users loved our app!" The survey asked 10 people. What's the main problem? → the sample is far too small to generalise
- A. yes, it is correct
- B. no, it is not correct
5
Question 5
Read the question and choose. "Towns with more ice-cream shops have more sunburn cases. So ice cream causes sunburn!" What's wrong?
- A. ice cream does cause sunburn
- B. the numbers must be made up
- C. there are too many shops
- D. both are linked to hot, sunny weather; correlation doesn't prove cause
6
Question 6
Is the proposed answer correct? "Towns with more ice-cream shops have more sunburn cases. So ice cream causes sunburn!" What's wrong? → both are linked to hot, sunny weather; correlation doesn't prove cause
- A. yes, it is correct
- B. no, it is not correct
7
Question 7
Read the question and choose. "Since the new road opened, house prices have risen 10%." Why can't we say the road caused it?
- A. roads never affect prices
- B. house prices can't rise
- C. 10% is a small number
- D. prices may have risen everywhere for other reasons
8
Question 8
Is the proposed answer correct? An online poll on a cycling website finds 85% of people want more bike lanes. Why should we be careful? → the people answering are not representative of everyone
- A. yes, it is correct
- B. no, it is not correct

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Answer key: Spotting misleading statistics and graphs

1. A. relevant, but one pilot in twelve schools is not enough to prove it works everywhere
2. A. yes, it is correct
3. B. the cut-off axis exaggerates a small change
4. A. yes, it is correct
5. D. both are linked to hot, sunny weather; correlation doesn't prove cause
6. A. yes, it is correct
7. D. prices may have risen everywhere for other reasons
8. A. yes, it is correct