The Contradictory Survey Responses
A community group surveys 200 residents about a proposed bike lane. Results: 120 support the lane, 60 oppose it, and 20 are undecided. Of the supporters, 45 say they cycle daily; of the opponents, 30 say they cycle daily; of the undecided group, 5 cycle daily. A councillor reads the summary and declares: 'Most daily cyclists in this survey support the bike lane, so cyclists clearly back the plan.' A second councillor counters: 'Only 45 of the 80 daily cyclists support it - that is barely over half, so the claim is weak.' A third notes that the survey did not record how often non-cyclists travel by car.
1. Evaluate the first councillor's claim using the numbers.
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Daily cyclists total 45 + 30 + 5 = 80. Supporters among them are 45, which is 45/80 = 56.25%. So 'most' is technically true but only narrowly - a bare majority, not a strong mandate. The claim overstates the strength of cyclist backing, and it also ignores the 30 daily cyclists who oppose the lane. The reasoning tests whether a reader converts raw counts into a proportion before accepting a verbal summary.
2. What is the significance of the third councillor's observation?
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It identifies a missing variable. The survey measured cycling frequency but not car use, so any inference about how non-cyclists would be affected by a bike lane is unsupported by the data. The observation does not refute either claim; it flags that the dataset cannot answer a question the debate implicitly raises. Recognising an absent variable, rather than only checking the arithmetic present, is the skill being tested.