How a Chart Can Mislead · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Read the numbers, not the ink

Mathematics · Data & Statistics · ages 11-13
Name ______________________   Date ____________

  1. Bars show 48 and 52 with an axis starting at 40. How many times taller does the 52 bar look? Give your answer as a decimal.

    Answer: ______________

  2. A bar chart of 48 vs 52 uses an axis from 40, so the 52 bar looks far taller. What is the honest fix?

    • Make both bars red
    • Start the axis at zero
    • Remove the taller bar
    • Double both bars

  3. An honest bar chart must start its axis at what?

    • 40
    • Zero
    • The biggest value

  4. A bar twice as tall always means twice as much.

    Circle one:   True   False

  5. A pictogram uses 4 football icons for Team A and 8 for Team B. How many times as many icons does Team B have?

    Answer: ______________

  6. One chart repeats 4 fixed fish icons, another 8. How should you read it?

    • Measure icon sizes
    • Count the icons: double the fish
    • Admire the colours

  7. Which feature exaggerates a difference?

    • A truncated axis starting near the values
    • An axis that starts at zero
    • Equal bar widths
    • A clear title

  8. After redrawing with an axis from zero, the 48 and 52 bars look almost equal. Dan says the new chart hides a real difference. Is Dan right?

    Circle one:   True   False

  9. A news chart draws 48 and 52 from 40, shouting a boom. What is wrong?

    • Nothing, ink never lies
    • The cut axis turns an 8 percent gap into 50 percent more ink
    • Fish cannot be counted

  10. Charts P (axis from 0) and Q (axis from 190) show the same 200 vs 210 data. How do they differ?

    • P makes the gap look far bigger
    • They look identical
    • Q makes the gap look far bigger
    • Q swaps which value is bigger
LightMySky · lightmysky.comW1-mt_z7yMoRWipf-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Read the numbers, not the ink W1-mt_z7yMoRWipf-s1

  1. 1.5 · Visible heights are 12 and 8, and 12 / 8 = 1.5.
  2. Start the axis at zero · A zero baseline restores true proportions: 52 is only slightly taller than 48.
  3. Zero · Zero keeps bar heights proportional to the numbers.
  4. False · That holds only when the axis starts at zero.
  5. 2 · 8 / 4 = 2: Team B has twice as many icons.
  6. Count the icons: double the fish · Fixed icons keep area honest, so counting tells the truth.
  7. A truncated axis starting near the values · Truncation hides the shared base, so small gaps fill the frame.
  8. False · Dan is wrong: the zero-based chart shows the true 8 percent gap; nothing is hidden.
  9. The cut axis turns an 8 percent gap into 50 percent more ink · Redrawn from zero, the bars stand nearly level.
  10. Q makes the gap look far bigger · Q shows 20 vs 10 units of ink (double!) for a 10-in-200 gap; P shows honest 210 vs 200.
Worksheet · LightMySky