The 84-Centimetre Bounce
A group tests which ball bounces highest. They drop a tennis ball, a rubber ball, and a golf ball from 100 cm onto a concrete floor and read the top of the first bounce against a ruler taped to the wall. Tennis: 62, 58, 61 cm. Rubber: 71, 70, 69 cm. Golf: 45, 44, 46 cm. On a fourth tennis drop, a student's hand knocks the ruler and the ball reads 84 cm. The group argues about three things: whether to keep the 84, whether three drops per ball is enough, and whether comparing the golf ball is unfair because "it's not the same kind of ball as the others."
1. What should the group do with the 84 cm reading, and how should they report it? Explain your reasoning.
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Drop it from the averages - but record why, not silently.
- The 84 cm is 22 cm above the tennis ball's next highest reading (62). That gap is far larger than the 3–4 cm spread in all three balls' good trials, which is a signal that something went wrong rather than natural variation.
- The group has an identified cause: the ruler was knocked. That makes it a procedural error, not a surprising result.
Reporting: list all four readings, mark the fourth as invalid with the reason, average the three valid ones (tennis mean ≈ 60.3 cm), and state the range. Silently deleting it would look like hiding an inconvenient number. Because they know the cause, they do not need to throw out the whole set - but they should redo the tennis drops to confirm.
2. The group says comparing the golf ball is unfair because it is "not the same kind of ball." Is that a problem for this investigation? Explain.
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It depends entirely on the question being asked, and the group has not written one down.
- If the question is "Which of these three balls bounces highest?" the comparison is fair. Different materials are exactly what is being compared, and the golf ball really did bounce lowest (about 45 cm).
- If the question is "How does material affect bounce?" the comparison is confounded. The balls differ in material and in size, mass, and surface hardness, so the group cannot credit the 15 cm gap to material alone.
So the fix is not to drop the golf ball; it is to state the question. For a material test, they would need balls of the same size and mass made of different materials - which the group does not have - and they should say so as a limitation.
3. The group has 4 cm spread on the tennis ball and 2 cm on the rubber ball. What is one improvement to measurement technique, and why does the size of the spread matter for the conclusion?
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Improvement: film each drop in slow motion against a grid taped behind the ball, or drop the ball through a short cardboard tube so it always falls from the same spot and lands in the same place. Then read the bounce height from the still frame. Eye-tracking a fast bounce against a wall ruler easily costs a few centimetres.
Why the spread matters: the tennis–rubber gap (about 60 vs 70 cm) is 10 cm, more than double the 4 cm spread, so that difference is probably real. But if a gap were only 3 cm while spreads were 4 cm, the difference would be indistinguishable from measurement noise. The group should compare gaps between means with the spreads before claiming one ball bounces higher.