(Extracted from Wikipedia)
An example problem, of a type generally attributed to Fermi, is “How many piano tuners are there in Chicago?” A typical solution to this problem involves multiplying a series of estimates that yield the correct answer if the estimates are correct. For example, we might make the following assumptions:
- There are approximately 9,000,000 people living in the Chicago metropolitan area.
- On average, there are two people in each household in Chicago.
- Roughly one household in twenty has a piano that is tuned regularly.
- Pianos that are tuned regularly are tuned on average about once per year.
- It takes a piano tuner about two hours to tune a piano, including travel time.
- Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.
From these assumptions, we can compute that the number of piano tunings in a single year in Chicago is
(9,000,000 persons in Chicago) ÷ (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 225,000 piano tunings per year in Chicago.
We can similarly calculate that the average piano tuner performs
(50 weeks/year) × (5 days/week) × (8 hours/day) ÷ (2 hours to tune a piano) = 1000 piano tunings per year.
Dividing gives
(225,000 piano tunings per year in Chicago) ÷ (1000 piano tunings per year per piano tuner) = 225 piano tuners in Chicago.
In 2009, the actual number of piano tuners in Chicago was about 290.