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Statistics · Cumulative frequency & box plots

Chapter 1 · 3

The idea

Box plots

What each of the five marks on a box plot means, why the box holds the middle 50% of the data, and why a longer section means the data there is more spread out — never that there is more of it.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

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Statistics · Cumulative frequency & box plots

Box plots

What each of the five marks on a box plot means, why the box holds the middle 50% of the data, and why a longer section means the data there is more spread out — never that there is more of it.

Why it works

Not a picture of how many

A box plot is not a picture of how many. It is a picture of *where the values sit*. Almost every mark lost on box plots comes from forgetting that one sentence, so it is worth seeing exactly where the five marks on the plot come from.

Start with data, in order. Here are the marks of 2020 students in a test out of 6060, with a bar dropped after every fifth value:

12, 18, 21, 23, 25 ∣ 25, 27, 28, 29, 30 ∣ 30, 32, 33, 34, 35 ∣ 35, 42, 48, 53, 5812,\ 18,\ 21,\ 23,\ 25\ \mid\ 25,\ 27,\ 28,\ 29,\ 30\ \mid\ 30,\ 32,\ 33,\ 34,\ 35\ \mid\ 35,\ 42,\ 48,\ 53,\ 58

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The rest of the explanation, plus 3 worked examples you step through move by move.

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