L4 · Same Data, Different Graphs: What Scale Does to the Story

Learning goal

“I can compare two graphs of the SAME data and explain how the scale changes the story: a fair axis starts at 0 with equal steps, an axis that starts above 0 makes differences look bigger than they are, and different keys change how many symbols the same data needs.”

Axis — the line along a bar graph that carries the scale labels (0, 5, 10, 15...).

Exaggerate — to make something look bigger or more important than it really is. A sneaky scale exaggerates differences.

Fair graph — a bar graph whose axis starts at 0 and climbs in equal steps, so bar heights tell the truth about the amounts.

Effect — what a choice DOES to the reader. The effect of starting an axis at 30 is that small differences look huge.

Worked example

Four friends read books this month: Ana 12, Ben 15, Cleo 11, Dan 14. GRAPH X (fair): the axis starts at 0 and climbs by 2s (0, 2, 4, ..., 16). The bars reach 12, 15, 11 and 14 - all four bars are tall, and Ben's bar is only a little taller than Ana's. GRAPH Y (sneaky): the axis starts at 10 and climbs by 1s (10, 11, 12, ..., 16). Now only the parts of the bars above 10 are visible: Ana's bar rises 2 units (12 - 10), Ben's rises 5 units (15 - 10), Cleo's 1 unit, Dan's 4 units. Ben's bar LOOKS more than twice as tall as Ana's - but Ben only read 15 books to Ana's 12, a difference of 3 books. Say it plainly: the data did not change - the STORY changed. Chopping the bottom off the axis exaggerates every difference. A fair graph starts at 0.

Check yourself — explain it

In Graph Y, why does Ben look like a reading superstar?

Paired problem — example still visible

In Graph Y, how many units does Dan's bar rise above the start, and how many books did Dan really read? -> 4 units visible (14 - 10); Dan really read 14 books

Faded completion — last step is yours

"Cleo's bar in Graph Y rises ___ unit above the start, but Cleo really read ___ books. The missing bottom hides ___ books of every bar." -> 1; 11; 10

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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