Two estimation questions

It\’s apparently customary, when being interviewed for a job in the consulting industry, to be asked to estimate various numerical quantities:  how many cars are rented each week in the United States?  What proportion of the total mass of American citizens is made up of males?  I think that in asking these questions the interviewer is testing your ability to carry out rapid approximate quantitative reasoning, or, alternatively, to make confident assertions about whose truth you\’re almost completely ignorant — both important skills in that line of work.

Anyway, here are two questions.  I know the answer to the first one, and will reveal it tomorrow.  Put your unreasonably confident answers in comments!

  1. What is the total number of living alumni (all degrees) of UW-Madison?
  2. What is the population of the largest U.S. city without a Chinese restaurant?

Update: (24 Mar)  Commenter QXW is in the lead on question 2, observing that the city of Rye, NY (pop. 14,955) has no Chinese restaurants per Google Maps.  Can it really be true?

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12 thoughts on “Two estimation questions

  1. Michael Lugo says:

    1. My guess was 250,000. (I guessed 25 thousand students, one-fifth of whom graduate in any given year; thus five thousand graduates per year. Figure that the average post-graduation lifespan is fifty years.)

    As it turns out, I’m wrong (I looked it up); the big error is that UW is a bigger school than I realized. But its number of alumni is roughly ten times its number of current students, and I wouldn’t be surprised if this ratio is fairly common.

    2. Fifty thousand? But I’m really not sure. There are two major difficulties here:
    – I could try to guess, say, the number of people per Chinese restaurant in the US (which is surely lower than 50K), cities with large populations probably have more Chinese restaurants per capita.
    – if I could estimate the average number of Chinese restaurants in a city of population x (which I suspect grows faster than linearly in x), and I had the distribution of city sizes, then it would be easy to provide an estimate. But that estimate would have huge error bars — maxima are like that.

  2. anonymous says:

    There are about 29k undergrads at UW-Maddison. Assuming the average graduate is 23 years old and has the life expectancy of 66 years, we compute there should be about 29k/4*43=311.75k living graduates with undergraduate degrees. Additionally, there are about 9k graduate and 2.5k professional students (enrolled at one time). Of course we are surely double counting, since there is overlap with graduates with undergraduate degrees. So (without too much reason) lets throw out the professional students. Now say the average graduate student takes 5 years and graduates at 30. This puts us at an additional 9k/5*36=64.8k graduates, for a total of 376,550.

  3. 1) I’ll go with 350,000 living alums, by a similar calculation to those above. Looking at the numbers for Illinois, I may be a little low, though perhaps UW was not always slightly larger than U of I.

    2) I was going to guess 40,000 based on nothing whatsoever, but playing around on I couldn’t find a city remotely that large without one. The best I’ve come up with is Beulah, Montana…

  4. 1. 250K and 2. 40K. Probably underestimating the first and overestimating the second.

  5. Steve says:

    You may not believe me but I was going to go with 350,000 even before I read the comments above– about 40K grad + undergrad students; many undergrads don’t finish in four years, but most of the grad students are lkely not PhD students but people in two- to three-year degree programs, law school, nursing school and so on– so– of 40K students, something like 10K graduate every year, and the average age for graduates is probably mid- or late-20s; how long do they live after they graduate? mean = something like 45 more years (to their early 70s), if they graduate today. So if nothing had changed over the last several decades I’d guess 10K times 45. But life expectancy used to be shorter, and UW almost certainly used to be smaller– so– without Googling or otherwise fishing for data, I’m going to go with 350K. I may be overestimating (based on my sense of the size of the U of Minnesota), or overestimating (because I underestimate dropout rates), or underestimating (because UW has been the same size for a surprisingly long time, rather than growing during the 1980s and 1990s as higher ed did in general).

    Chinese restaurant: how would you measure such a thing? Is there a trade association (to which literally all Chinese restaurants belong)?

  6. Tomorrow’s been and gone. Where are the answers?

  7. JSE says:

    374,838 UW alumni. I’m kind of shaken by how good a job you guys did. You should all be consultants.

    As for the Chinese restaurant question, I hope I didn’t give the false impression that I had any idea of the answer. Jamestown, ND has a population of around 15,000 and has two Chinese restaurants. But it seems possible that the largest city with no Chinese restaurant is probably not going to be a small, remote city which is the largest city in some large geographic radius (like Jamestown), because such cities are probably going to contain any Chinese restaurants in that radius. If there is a city of 40,000 with no Chinese restaurant (and I’m seriously doubtful) it might be a vaguely defined bedroom municipality which is within a reasonable drive of places that obviously have Chinese restaurants. The best I was able to do was Hawthorne, Florida, in exurban Gainesville, estimated population 1442.

  8. You are right, the Chinese restaurant question probably has a much smaller answer. Playing around with Google search and maps, I found Fritch, TX pop. 2235 and Memphis, TX pop. 2479. The towns in West Texas with more than 10K inhabitants that I checked have Chinese restaurants.

  9. JmSR says:

    #2: The smallest media market in existence is Glendive, Montana. It has a Chinese restaurant that I’ve eaten at.

    Bonus fact:
    My fortune from my visit: “Digital circuits have analog parts”

  10. Norbert Weiner says:

    Also there are some nasty satellite cities like Camden NJ which don’t have much in the way of shopping due to crime and poverty issues.. Camden is too large to not have one, but a smaller place like that might not. I forget which one, but there was one city of this nature of reasonable size which didn’t even have any grocery stores.

  11. QXW says:

    Using Wikipedia and Google Maps, I’ve managed to find a few relatively large number of incorporated places (cities and towns) that don’t seem to have Chinese restaurants:
    Rye (city, not to be confused with the town of Rye), NY pop. 14,955
    Weston, CT pop. 10,276
    Harvard, MA pop. 5,981

    The Northeast has a definite “advantage” here because communities there are more likely to be incorporated than in other parts of the country.

  12. QXW says:

    It turns out that a search finds one Chinese restaurant in Rye. However, Weston, CT still holds up to a SuperPages search.

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