Fermi’s problem and its tremendous application
Table of Contents
If you receive a question "How many kitchen faucets sold in a year in Chicago?", how would you answer? Will you go Google to search if there is answer for that question? If you have no clue what to do, let’s read about Fermi’s Problem – a famous question about estimation using logical steps and rough information.
Fermi’s Problem
Define the question:
How many piano tuners are in Chicago?
Break it down into manageable parts
* Estimate the population of Chicago.
* Estimate the number of households.
* Estimate the percentage of households that have a piano.
* Estimate how often a piano is tuned each year.
* Estimate how many pianos a single tuner can service in a year.
Make assumptions and calculations
* Population of Chicago: ~3 million.
* Average household size: 3 people.
* Number of households: 3 million / 3 = 1 million.
* Percentage of households with a piano: 10% (100,000 pianos).
* Frequency of tuning: once per year.
* Pianos serviced by one tuner: 2 pianos per day × 250 working days = 500 pianos/year.
Final estimation
Number of piano tuners = 100,000 pianos / 500 pianos per tuner = 200 piano tuners.
Applying Fermi’s Problem to Market Research
This is a real question I receive when I was doing marketing campaign for a water device company. That is: Estimating number of kitchen faucets sold in a year in Chicago.
Define the question
What is the number of kitchen faucets sold in a year in Chicago?
Break it down into manageable parts
* Estimate number of new houses built in a year
* Estimate number of available houses in the city
* Estimate how long should a faucet be changed
Make assumptions and calculations
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Population: 2,510,000
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Household size: 2.51
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Number of available household = number of houses = 1,000,000
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A faucet will be changed every 15 years
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Total new faucets changed = 66,667 each year
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Number of new houses built each year = 15,000
Final estimation
- Total number of faucets sold each year = 66,667 + 15,000 = 81,667
Conclusion
I would say that Fermi’s problem-solving approach is useful in market research. It is essential when you need to decide if the targeted market is suitable; what would be the cost for Marketing; what will be your ROI. The result number would not be entirely correct, but a rough estimation is truly valuable before you start. Recently some companies have used this approach in interviewing process, in order to assess ability of logic and creative thinking.