If one estimate is off by 2x and another is off by ½x, those cancel out because the exponents are additive.
Edit: Parent deleted comment…oh well.
Some questions about your result:
How many piano tuners work at any of those piano tuner companies?
How many piano tuner companies are not on yelp?
How many piano tuners are employees of instrument stores instead of working freelance/for a tuner company?
Those are all harder to answer without industry information than the simple deductions the handout makes from common sense/knowledge.
I have the feeling it is important that people understand the limits of technology. Even though we like to say something doesn't exist if it isn't on Google, things very often do irregardless.
While this may be a good estimate, what about businesses not on Yelp?
"Professional Piano tuner" doesn't seem the most technologically advanced profession, so I think it's safe to assume that there are several, if not dozens more in existence in the NY area.
Searching for a seamstress in my town turns up a few results for dry cleaners. A look on craigslist returns a much larger result.
That said, I actually know a piano mover in NYC and he's not on Yelp, or any website. His business is very much conducted via word of mouth and physical exchange of business cards.
discussions of the defects of PowerPoint slides as a communication tool.
The slides shown here cover some interesting ground, and I was glad to see the specific reference to Enrico Fermi, who popularized the kind of estimation question discussed here in certain circles. Certainly, it is beyond dispute that
"Although most engineers remember key numbers related to
their field, no-one has every detail at their fingertips
"Hence we need to estimate not only the values of numbers we need, but which numbers are appropriate, and how to perform
"the emphasis here is on 'order of magnitude' estimates – to the nearest factor of 10
"it is also important to remember that these are rough estimates and to place only appropriate reliance on the results"
The last point is the most crucial. It is vital to remember how much uncertainty there is in your estimates, or overall in your model that includes both exactly measured and estimated values. The model is not reality. It is not easy to get engineers to remember that they have to look into the mechanism of the model to understand how it works. That's why a NASA Mars probe failed when one part of the engineering team used United States customary units while another used metric units to design modules of the probe that were supposed to communicate values to each other.
I love chalk and talk but it puts a lot of load on the speaker. My Electricity and Magnetism professor basically pushed it to the limit I think. He had a carefully cultivated temper that was bad enough to keep 100 students totally silent for 50 minutes and he used about five different colors of chalk, but there are limits to what you can scrawl out on a blackboard.
You can distribute written documents, this gives you maximum opportunity to convey information, but you can't force people to actually read them. Going from a paper memo to email exacerbates this I think. Best case scenario, you can present very clear and well structured information but if you go past two pages you have to wonder if anyone is really paying that much attention. As a "best case example" I'd look at something like this memo that Robert McNamara wrote to LBJ about a month after LBJ took office: https://www.mtholyoke.edu/acad/intrel/pentagon3/doc156.htm . A benefit of written work is that you are committed to your words. But: creating a concise and readable written document that will effectively spread your thoughts is excruciatingly difficult. You can't write a book of background info every time you have a staff meeting.
About remembering that you have a rough model though, I think the key thing is that when you realize that there is something you are interested in measuring and once you have a model then you can start looking for quantities you can actually measure to (in)validate and tighten the model. Always be model checking.
Additionally, having chalk & talk meant that many students showed up to class, instead of just relying on "reading" printouts of slides that the professor made available. I would venture a guess that I would have performed rather poorly in a class that had powerpoint slides, due to my inherent laziness in my early 20s.
Chalk, we spent more time dictating and deciphering the babbling fool who can't communicate it all concisely from memory.
NYC also has lots of concert halls, and any decent concert hall will tune the piano to be used in a performance on the day of. A hall like Carnegie hall would have several pianos tuned every day.
I no do math, so maybe those things aren't enough to have a material effect on the number of piano tuners.
Free PDF edition available there.
(For example gravity is "unexplained" in some way. You have two masses, they deform the space, and with some approximations you can use the formula F=GmM/R^2. But, for example, why do masses deform the space?!?!?!?!?! But luckily you can measure it, just drop a stone or find a gravity lens, so gravity exists.)
Not exactly relevant when all you're concerned with is determining whether or not someone can "estimate the answer without any specialised knowledge". But, then again, why would you only be concerned with something so trivial?
An imbalance of supply can increase/decrease the population by maybe as much as 2x (or .5x). An order of magnitude can be the difference between a market that's worth considering and one that's too small to currently be serviceable.
This is important because in business getting a right(ish) answer quickly is often more important than getting a precisely correct answer slowly. While you're measuring precise supply and demand, FermiCo has already concluded that the market is too small and moved on.
p.s. irregardless is a great word.
Asking someone to talk through a problem like those discussed is often very useful. It gives you an insight into how they think, the background knowledge they can draw on and their understanding of accuracy of data. It's fairly obvious when someone's bullshitting (especially if they talked through the process with you), and any good candidate will be honest about the inaccuracies inherent in their assumption.
This means that when I go and plug the orbit of a satellite into STK, I'm already looking for an answer within a certain level of precision. While this isn't good enough for an answer to "how much stress does the bolt that holds down the payload have to be capable of withstanding" it does give you a sense of what that answer should be.
This is a very useful tool for realizing when your equation is returning complete crap because you are using the wrong unit (as pointed out by tolkenadult and the Mars probe example).
I still think in those terms, asking whether the answer to a problem, whether a SWAG, estimate, or careful calculation, could actually be correct
But you're not actually asking them to know it, you're asking them to reason about it. So perhaps instead of asking "How many gas stations do you think are in this town?" try asking "Could you give me a reasonable estimate of the amount of gas stations in this town?".
I think a lot of people just lock up when they're asked something they don't know in a synthetic situation even when in a real situation they would actually make very good judgements since in any real situation the context is often so much more clear, unless you like to keep your employees in the dark..
I've had that mental block happen, not when asked to estimate something like balloons in a gym, but when asked to estimate something I knew for a fact was a single search query away.
I was asked, "So how many travelers or trips in the US each year?"
Googling "how many travelers in us" gives http://www.ustravel.org/news/press-kit/travel-facts-and-stat... as the top result.
Knowing this is that kind of data, I was unable to put myself in a frame of mind to make believe reasoning through it. The interviewer told me to just pretend we were white boarding a marketing plan for a travel tool. I pointed out that in such white boarding or brainstorming conversations, someone would look that data point up because it's obvious a lookup would be more quickly available and more accurate than running through a Fermi style reasoning chain.
Partly because the best developers are "lazy", morally opposed to reinvention of wheels, your point about performance in a synthetic situation is dead on.
What would your approach be to work out how many gas stations are in your town? Have you done that calculation, and come out with a reasonable answer? What assumptions did you have to make?
The problem I see is that for most of these you at least need SOME information (e.g. the number of inhabitants of NYC) to start from.
To get that initial information you'll most likely use a search engine anyway, so why not just invest a little more effort to find a exact number?
Some people freeze. Some of those people stay frozen even after a bit of discussion. Some people just cannot start the process of answering a question like this.
Luckily, most places have stopped asking questions like this because they'r ejust not very good for whatever those people are recruiting for.
There are 40M persons in Spain, 50% are women, 50% of women have an age suitable for the trade, it is impossible that 3%, or 1 in 30 are prostitutes.
This lecture note is credited to Professor Ben Quine, a popular and favourite eng prof at York University, Canada.