Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 On this plot, what does each dot represent?
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Each dot is one tree, positioned by two of its measurements at once.
2 Look at this plot of trunk diameter against smooth bark. Write roughly the smooth-bark percentage for a 10 cm trunk, and for a 40 cm trunk.
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At 10 cm the dots sit near 80%, and at 40 cm they are down near 10%.
3 A claim says "every tree in the plot has some smooth bark". How many dots at 0% smooth bark are needed to disprove it?
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1 — a single counter-example destroys any claim containing "every".
Level 2 · Core
4 Which statement is safest to make about a downward-sloping scatterplot?
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The two measurements tend to move in opposite directions — it describes the slope without claiming a cause or ruling out exceptions.
5 Two plots share one quantity: holes against smooth bark, and smooth bark against diameter. For a tree with 40 holes, write the approximate smooth-bark percentage, and then the approximate trunk diameter in cm.
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40 holes corresponds to about 45% smooth bark, and 45% smooth bark corresponds to a trunk of about 25 cm.
6 A scatterplot shows ice cream sales and swimming accidents both rising in summer. How many of these does the plot prove: that they are associated, and that one causes the other?
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Only 1 — the association. Hot weather explains both, so no cause is shown.
Level 3 · Challenge
7 A scatterplot shows trees with more smooth bark having fewer beetle holes.1 The plot shows an association between bark type and holes.
2 The plot proves smooth bark repels beetles.
3 A claim that "every smooth tree has no holes" is disproved by one dot.
Which statements are correct?
2 The plot proves smooth bark repels beetles.
3 A claim that "every smooth tree has no holes" is disproved by one dot.
Which statements are correct?
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The plot shows the two move together (1 ✓) and one counter-example kills an "every" claim (3 ✓), but a graph can never prove a cause (2 ✗). 1 and 3.
8 On the trunk plot, write roughly the smooth-bark percentage at a 20 cm trunk, and at a 30 cm trunk.
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At 20 cm the dots sit near 55%, and at 30 cm near 30%.
9 Of four options, three use the words "all", "every" and "causes", and one says "tend to". Which numbered option is most likely correct if the option using "tend to" is option 4?
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Option 4 — a scatterplot supports "tend to" but cannot support "all", "every" or "causes".