Mathematics · Investigate

Two charts from the same invented table

Which display choices change an impression without changing the values?

Display the same fictional token counts with two labelled scales, and separate a visual impression from a numerical difference.

15–25 minutes, or one comparison for a first try. More time is optional.

Two equally tall bar-chart frames show A = 8, B = 10 and C = 12. The first count axis spans 0–12; the second spans 0–24, so corresponding bars are half as tall.
Invented table: 8, 10 and 12. Open full-size diagram ↗

Start here

Write this fictional table: token type A = 8, B = 10, C = 12. These are invented token counts, not responses from people.

Use your idea or the example below. Talk, write, draw, point or listen first. You can stop after one step.

Try it your way.

  1. Make the first display

    Draw a bar chart with three equal-width bars labelled A, B and C. Use equally spaced marks 0, 4, 8 and 12 on the count axis; all bars begin at zero.

  2. Change only the scale range

    Draw the same-size plotting area again. Use marks 0, 8, 16 and 24, still equally spaced and starting at zero. Plot the same three counts, keeping labels, bar widths and order unchanged.

  3. Read values before impressions

    Read each bar against its own scale. C exceeds A by 12 − 8 = 4 tokens in both charts. C is 12 ÷ 8 = 1.5 times A, regardless of the changed display range.

  4. Choose and explain

    Say which chart makes the values easier to read for your purpose, and why. A bar looks half as tall on the second scale, but its labelled count has not halved. Keep both scales visible.

One possible version

Invented table: 8, 10 and 12

This original comparison uses the same fictional data twice. Both count axes begin at zero; neither chart reports a survey.

  • Chart 1 ranges from 0 to 12; chart 2 from 0 to 24 in an equally tall plotting area.
  • The bars in chart 2 are half the drawn height of the corresponding bars in chart 1. Both still represent A = 8, B = 10, C = 12.
  • The total is 30 tokens, and C − A = 4 tokens on either chart.

Different scales can change an impression. These diagrams do not establish what every viewer notices, or make an unlabelled or cut-off bar axis acceptable.

A different way.

Use the two supplied charts, read the numbers aloud or compare only A and C. No personal data, software or drawing accuracy test is needed.

If you want more.

Keep one zero-based scale and reverse the category order in a third chart. Explain how order changes the reading sequence while the values and total remain 8, 10, 12 and 30.

Something to keep?

Did I read the axis before judging the size of the difference?

You can keep a question, a sketch or a change of mind. A finished product is optional.

This opens an editable starter in your project tools. It asks before replacing open work. Choosing it does not save or share your work automatically.

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