Fermi Estimate: Sizing the Total Count of U.S. Police Stations
Company: Google
Role: Product Manager
Category: Product / Decision Making
Difficulty: medium
Interview Round: Other
Estimate the number of police stations operating across the United States. Walk through your assumptions and your calculation, and explain how you would check that the result is reasonable.
```hint Follow the jurisdictions
Policing in the United States is organized by city, county and state agencies rather than by land area. Build the count layer by layer, then account for large agencies that run more than one station.
```
### Clarifying Questions
- What counts as a police station: any building from which officers are based and dispatched (headquarters, precinct houses, substations, state patrol posts), or only full-service stations open to the public?
- Should county sheriff's offices, state police and special agencies such as campus, transit and airport police be included? Are federal law enforcement offices out of scope?
- Are we counting buildings or agencies? A city department with 20 precinct houses is one agency but 20 stations.
- Is a point estimate with a range enough, or is a specific level of precision expected?
### What a Strong Answer Covers
- A clear definition of a station and of which agency types are in scope.
- A structure that mirrors how US policing is organized (municipal, county, state and special agencies) instead of a single blanket ratio.
- Round-number assumptions labeled as assumptions, with clean arithmetic leading to a point estimate and a range.
- A sanity check from an independent angle, such as residents per station or officers per station.
- Awareness of which assumption moves the answer most.
### Follow-up Questions
- If you could query the place listings in a map product, how would you validate this estimate, and which listing errors would push the count up or down?
- Which single assumption has the most influence on your total, and how much would the answer change if it were off by half?
- How would your approach change for a country with one national police force?
Overview: A product manager estimation question that asks for the number of police stations in the United States. It tests defining what counts as a station, structuring the count around city, county, state and special agencies, labeling round-number assumptions, and sanity-checking the total from a second angle.