Fermi+Example

HOW MANY PIANO TUNERS ARE IN NEW YORK CITY?
How might one figure out such a thing?? Surely the number of piano tuners in some way depends on the number of pianos. The number of pianos must connect in some way to the number of people in the area. 10,000,000 No Yes. Perhaps there are 2,000,000 families in NYC. No. Perhaps one out of every five does. That would mean there are about 400,000 pianos in NYC. Some people never get around to tuning their piano; some people tune their piano every month. If we assume that "on the average" every piano gets tuned once a year, then there are 400,000 "piano tunings" every year. Let's assume that the average piano tuner can tune four pianos a day. Also assume that there are 200 working days per year. That means that every tuner can tune about 800 pianos per year. The number of tuners is approximately 400,000/800 or 500 piano tuners.
 * Approximately how many people are in New York City?**
 * Does every individual own a piano?**
 * Would it be reasonable to assert that "individuals don't tend to own pianos; families do?**
 * About how many families are there in a city of 10 million people?**
 * Does every family own a piano?**
 * How many piano tuners are needed for 400,000 pianos?**
 * How many piano tunings can one piano tuner do?**
 * How many piano tuners are needed in NYC?**

Use different assumptions for various factors. It is unlikely that you can justify an answer greater than a factor of 10 or smaller than a factor of 10 from the number originally obtained; that is to say, there are probably not more than 5000 tuners and surely no less than 50. Thus the answer obtained is good to within an "order of magnitude".
 * Try it yourself.**