You need to estimate the number of gas stations in the United States. Which approach best exemplifies Fermi estimation?
ARecall the number from memory, or look it up in a reference source
BGuess 'around 100,000' based on a gut feeling that seems reasonable
CDecompose: (US population) × (fraction of households with cars) × (fill-ups per year per car) × (minutes per fill-up) ÷ (minutes of service capacity per station per year)
DMultiply the number of US cities by an average guess of gas stations per city
Fermi estimation requires decomposing into independently estimable factors, not a single educated guess. Option D is a start but stops too early — it relies on a single hard-to-estimate factor (stations per city) rather than breaking into smaller, more tractable quantities. Option C decomposes into quantities you can estimate from things you actually know (car ownership rates, fill-up frequency, service time). Errors in individual factors partially cancel, typically getting you within an order of magnitude of the true value (~150,000 US gas stations).
Question 2 Multiple Choice
Why do Fermi estimates built from many decomposed factors often achieve better accuracy than single direct guesses at the same quantity?
AMore multiplication steps push estimates toward larger numbers, correcting for the human tendency to underestimate
BIndividual factor estimates can err high or low; across many factors, these errors partially cancel, reducing the overall error
CBreaking problems into sub-questions forces at least some factors to be looked up, importing real data into the estimate
DThe geometric mean of many uncertain estimates converges to the true value by the law of large numbers
The key insight is error cancellation: when you have five factors each off by a factor of 2, some will be overestimates and some underestimates, and they partially offset. This is not guaranteed (errors could compound), but it is reliably better than a single guess where all the error is concentrated in one judgment. The structure of decomposition is what produces the accuracy.
Question 3 True / False
A Fermi estimate that lands within a factor of 5 of the true answer should be considered a failure because the goal is to achieve the correct order of magnitude.
TTrue
FFalse
Answer: False
A factor of 5 is well within the target accuracy of Fermi estimation. The goal is to be within an order of magnitude (factor of 10) — sufficient for the decisions and prioritization Fermi estimates inform. Demanding more precision defeats the purpose: Fermi estimation is a tool for structured reasoning under uncertainty, not for replacing precise calculation. Being within a factor of 5 is an excellent result.
Question 4 True / False
After completing a Fermi estimate, identifying which single factor contributes most of the uncertainty in your final answer is a useful diagnostic.
TTrue
FFalse
Answer: True
When you decompose into factors, you can see which ones, if wrong by 2×, would swing your answer by 2×, and which ones, if wrong by 2×, would only change it by 10%. High-sensitivity factors are where to invest further research. Low-sensitivity factors can be estimated loosely without consequence. This triage of uncertainty is one of the key benefits of decomposition that a direct guess cannot provide.
Question 5 Short Answer
Why is it important to decompose a Fermi estimate into multiple independent factors rather than making a single 'educated guess'?
Think about your answer, then reveal below.
Model answer: A single guess has no internal structure — you cannot check it, identify where it might be wrong, or know which part to refine. Decomposition forces you to estimate each component using what you actually know (population sizes, behavioral rates, physical quantities), and the structure becomes visible and criticizable. Critically, errors in different factors can partially cancel: one factor you overestimate and one you underestimate will offset. The discipline of decomposition is what transforms guessing into structured estimation with predictable accuracy.
The practical payoff is not just a better number — it is knowing *why* you believe the number and *where* your uncertainty lives. That diagnostic information is what makes Fermi estimation useful for prioritization and decision-making, not just number-getting.