1) To An Order Of Magnitude, How Many Piano Tuners Are There In New York City?

In a class, we were asked to estimate the number of piano tuners in New York City. Can any of you tell me how many there are?

The SDMB membership usually takes a pretty dim view of helping students do their homework.

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I’ll help you find out how to get your own answer, though. Go to Yahoo! Yellow Pages and search in New York City for “Pianos – Tuning.” You’ll probably find some entries.

Good luck.

This is an example of a problem called a “Fermi Question.” Its an approach for when you don’t have enough information to solve the problem. The idea to is to set parameters (or assumptions if you like), and figure the problem from there. If any of your assumptions turn out to be wrong, you can simply adjust the numbers later.

You are not expected to find the true number of piano tuners in NYC, but rather to formulate a solution to the problem.

It’s a classic “Fermi” question – see the link


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.

etc etcFermi Questions

Fermi questions receive their name from Enrico Fermi, an Italian physicist known for his participation in the Los Alamos atomic bomb project and the development of quantum theory.Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that “word problems” have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than “the answer”, and promote non-traditional problem solving strategies.

Oh, sorry. I didn’t realize I had wandered into some sick teacher’s idea of torturing a reference librarian.

We now return you to your regularly scheduled broadcast.

BTW does this project have anything to do with the controversy surrounding teaching kids “fuzzy” collaborative, process vs rote, results oriented problem solving behaviors?

Actually, KtK its the oposite of a problem intended to harass reference librarians! You are not supposed to search and search for the “correct” response. No data is needed outside of the question and your own experience.

Astro the goal of the problem is not “collaboration” but its intended to teach students how to approach “impossible” problems: problems for which sufficient data is not available. Its an approach Fermi was known for. At the Trinity atomic test, using some bits of paper that he dropped when he felt the shockwave of the atomic blast hit, on the spot he estimated the force of the blast to be 10,000 tons of TNT. (The actual value, which tooks several weeks to compute, was 18,600 tons of TNT.)

Your reply should go something like this. This is just an EXAMPLE that I just threw together:

How many people live in New York City?

Guess: Abou 8.5 million

Out of 8.5 million people, what is the size of the average household?

Guess: 2.58.5/3.5 = 3.4 million households in NYC

Out of 3.4 million households, what percentage own pianos?Guess: 10%

Out of the 340,000 households in NYC that own pianos, how often do they get their pianos tuned?

Guess: Once every 3 years on average

How many pianos can a piano tuner tune in a day?

Guess: 3

How many days does the average piano tuner work each year?Guess: 300

Give 5) and 6) each piano tuner can tune 900 pianos a year.

Given 4) 113,333 pianos are tuned each year in NYC.

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Given 7) and 8), there must be about 126 piano tuners in NYC (113,333 / 900 = 126).

KneadToKnow September 4, 2002, 8:17pm #9

Real scientists actually calculate things this way?

No wonder we keep losing satellites.

Chronos September 4, 2002, 8:54pm #10

Actually, KneadToKnow, there are probably a lot of satellites which could have been saved if someone had bothered to do the “Fermi problem”. You don’t actually get your Official Number for the satellite thrusters this way (for that, you do look up all the information you need), but it’s very useful for a preliminary estimate, or to check your answer. Often, the ultimate question that’s being answered is something like “Is this practical?”, for which a precise answer isn’t needed. For instance, suppose I want to build a new particle accelerator to test a theory of mine. How much would such an accelerator cost? I’d first go through the rough estimation. If my estimate was that the accelerator would cost fifty trillion dollars, then I’ve saved myself the trouble of a detailed estimate, since I know that there’s no way I’ll get a grant that big. If my estimate is that the accelerator will cost fifty bucks, then I’ll probably skip the detailed calculation again and just buy the components as I need them, since fifty bucks is in the range that I can pay for out of my own pocket or lump in with “miscellaneous expenses”. If my estimate is a hundred thousand dollars, then I’ll need to write up a proposal, and I’ll need a more detailed figure, so I’ll do more calculations.

It can also help to find mistakes in a problem. When you’re doing a problem mathematically by the formulae, a mistake will often end up being a big mistake. If I do the rough estimate and find that it’s off by twenty orders of magnitude, you can bet I’m going to go back to my calculations to see where I went wrong.

In the Manhattan Yellow Pages I have in my office (1998-99 Bell Atlantic) there are 34 entries under “Pianos – Tuning, Repairing & Refinishing.”

Richard_Pearse September 5, 2002, 12:21am #12

Yes, but how many tuners work for each company?

Corrvin September 5, 2002, 3:43am #13

I’d beg to differ with guess #4… while people who own and play pianos may have them tuned every three years (and I’d bet this guess was made by someone who played piano) people who own but don’t play may never have their piano tuned; or they may own and tune it for 3 years, keep it for 15 untuned, and then tune it again when their children start piano lessons. Given that piano players tune their pianos every 3 years, and piano non-players may never tune theirs, and an arbitrary guess of 50% of pianos belonging to non-players…that gets us to an “every 6 years” figure on average, and thus 63 piano tuners.

Yeesh. Ask something harder, like how many cowboy boots are sold in Konawa, Oklahoma.


Cripes. I had this exact question in an interview. Every time I came up with an assumption, the dickweed interviewer told me I couldn’t use it. FU, PAL! Squirrelly little bastard really pissed me off. And to top it off, he wanted me to do it without paper and pencil. After I got lost with a few multiplications, I asked for a calculator. He said no, and wanted me to keep going. I declined, and said I was tired of his mathematical gymnastics. (I didn’t get the job. Thank God.)

A classic question to be asked during a “case interview” – typically by a management consulting firm (e.g., McKinsey, Boston Consulting Group, etc.).

As a consultant, I have been on the giving and receiving end of this type of case question, and Shagnasty has pretty much got it. There are alternatives (e.g., add to households some assumptions about churches, music schools or other locations that are likely to have a piano or two), but the basic approach is spot on.

The point is to see how the person thinks in a problem-solving way, not in arriving at an answer…

I’ve been asked questions like these numerous times in job interviews. Two of them that I remember are:

“How many refrigerators are there in the United States?”


“How many pennies are currently inside the Galleria Mall in Houston?”

I would just like to mention that any hostility anyone may perceive in my attitude toward this question is a completely accurate reflection of my feelings about it. Not because I think the underlying point is bad, but because I believe this particular example is crappier than a bedpan in a Tijuana emergency room. Either of the questions Jackknifed Juggernaut provides above would be vastly superior, IMHO.

Canned Answer:

The yellow pages say 72 entries:



Best 30 Pianos in New York, NY with Reviews –

Pianos in New York on See reviews, photos, directions, phone numbers and more for the best Pianos & Organs in New York, NY.

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Google+ pages x 3 entries per page = 165 total tuners

PTG – Piano Technicians Guild matches within 100 miles of 10001 (manhatten zip).

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