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Spotting misleading statistics and graphs

9th grade (Year 10 in England) · 16 questions · Common Core: RI.9-10.7, RI.9-10.8 · England: GCSE English Language Paper 2, SAT Reading and Writing (Command of Evidence: Quantitative), GCSE Maths (statistics)

Name

Date

Score/ 16

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. neither relevant nor sufficient, because pilots are always wrong
    • B. completely sufficient, because twelve is a large number
    • C. irrelevant, because attendance has nothing to do with school
    • D. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  1. Question 2

    Is the proposed answer correct? 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? → the cut-off axis exaggerates a small change

    • A. yes, it is correct
    • B. no, it is not correct

  2. Question 3

    Read the question and choose. "The average salary at our company is £60,000!" But the boss earns £1 million and most staff earn £25,000. What's misleading?

    • A. £60,000 is too low
    • B. one huge value pulls the mean up, so it doesn't show a typical salary
    • C. the boss's salary is illegal
    • D. averages are always accurate

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 4

    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. completely sufficient, because twelve is a large number
    • B. irrelevant, because attendance has nothing to do with school
    • C. neither relevant nor sufficient, because pilots are always wrong
    • D. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  1. Question 5

    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? → a control group

    • A. yes, it is correct
    • B. no, it is not correct

  2. Question 6

    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 scores are wrong
    • B. graphs should never use numbers
    • C. the change is actually a fall
    • D. the cut-off axis exaggerates a small change

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 7

    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. irrelevant, because attendance has nothing to do with school
    • B. neither relevant nor sufficient, because pilots are always wrong
    • C. relevant, but one pilot in twelve schools is not enough to prove it works everywhere
    • D. completely sufficient, because twelve is a large number

  1. Question 8

    Is the proposed answer correct? 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

    • A. yes, it is correct
    • B. no, it is not correct

  2. Question 9

    Read the question and choose. "Towns with more ice-cream shops have more sunburn cases. So ice cream causes sunburn!" What's wrong?

    • A. both are linked to hot, sunny weather; correlation doesn't prove cause
    • B. there are too many shops
    • C. ice cream does cause sunburn
    • D. the numbers must be made up

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 10

    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. completely sufficient, because twelve is a large number
    • C. neither relevant nor sufficient, because pilots are always wrong
    • D. irrelevant, because attendance has nothing to do with school

  1. Question 11

    Is the proposed answer correct? "Since the new road opened, house prices have risen 10%." Why can't we say the road caused it? → house prices can't rise

    • A. yes, it is correct
    • B. no, it is not correct

  2. Question 12

    Read the question and choose. "Crime fell by 50%!" It went from 2 incidents to 1 in a small village. What's the issue?

    • A. 50% is calculated wrongly
    • B. a big percentage can hide a tiny real change
    • C. villages don't have crime
    • D. crime actually rose

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 13

    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. irrelevant, because attendance has nothing to do with school
    • C. neither relevant nor sufficient, because pilots are always wrong
    • D. completely sufficient, because twelve is a large number

  1. Question 14

    Is the proposed answer correct? "Crime fell by 50%!" It went from 2 incidents to 1 in a small village. What's the issue? → villages don't have crime

    • A. yes, it is correct
    • B. no, it is not correct

  2. Question 15

    Read the question and choose. A company shows only the three months when its sales rose and leaves out the nine months when they fell. What is this called?

    • A. a control group
    • B. a random sample
    • C. a fair summary
    • D. cherry-picking data

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 16

    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. irrelevant, because attendance has nothing to do with school
    • C. completely sufficient, because twelve is a large number
    • D. neither relevant nor sufficient, because pilots are always wrong

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Answer key: Spotting misleading statistics and graphs

  1. 1. D. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  2. 2. A. yes, it is correct

  3. 3. B. one huge value pulls the mean up, so it doesn't show a typical salary

  4. 4. D. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  5. 5. B. no, it is not correct

  6. 6. D. the cut-off axis exaggerates a small change

  7. 7. C. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  8. 8. B. no, it is not correct

  9. 9. A. both are linked to hot, sunny weather; correlation doesn't prove cause

  10. 10. A. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  11. 11. B. no, it is not correct

  12. 12. B. a big percentage can hide a tiny real change

  13. 13. A. relevant, but one pilot in twelve schools is not enough to prove it works everywhere

  14. 14. B. no, it is not correct

  15. 15. D. cherry-picking data

  16. 16. A. relevant, but one pilot in twelve schools is not enough to prove it works everywhere