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How a Chart Can Mislead

The same numbers can be drawn to argue opposite things. A vertical axis that does not start at zero, a broken scale, unequal category widths, a 3-D effect, or a picture whose area grows faster than its height all change what a reader sees without changing a single value.

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What a learner can do afterwards

  • Redraw a bar chart with a truncated axis so it starts at zero, and describe what changed in the impression it gives
  • Spot three features of a published chart that make a difference look larger than it is
  • Explain why doubling the height of a pictogram symbol more than doubles the area a reader perceives

1 · Read

Honest bars always start at zero. When the axis starts at zero, a bar twice as tall truly means twice as much, and the picture matches the numbers. The moment the axis is cut, small gaps balloon. Check every chart in three seconds: where the axis starts, whether widths match, and what the labels say.

Try it together

Two stalls sold 48 and 52 fish. Drawn from zero, the bars stand nearly level, as the chart here shows. Drawn from 40, they show 8 against 12 units of ink, looking half again as big for a mere 8 percent gap. Same sales, opposite story: the cut axis lied.

Stall A48Stall B52

Read values first, reason second. Read each bar against the axis, never against its neighbour, subtract for the gap, then judge big or small. A 4-unit gap near 50 is modest: 4 out of 50 sits under a tenth. Charts that hide the zero hide that share, so redraw them from zero in your head.

A pictogram uses one small icon repeated over and over, like a row of fish icons, to stand for a count. Beware pictures that grow in two directions instead of repeating: a doubled-height icon that also doubles in width covers four times the paper, and tall narrow bars plus 3D gloss add fake volume. Honest pictograms repeat one fixed icon, so count the icons and ignore their sizes.

Start axes at zero, read values before judging, and count icons instead of trusting their size.

2 · Watch

Take it off screen

Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.

Where it sits

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.

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How a Chart Can Mislead · Mathematics, ages 11 to 13 · LightMySky