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Kindly comments on Fermi Estimates - Less Wrong
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Here's one I did with Marcello awhile ago: about how many high schools are there in the US?
My attempt: there are 50 states. Each state has maybe 20 school districts. Each district has maybe 10 high schools. So 50 * 20 * 10 = 10,000 high schools.
Marcello's attempt (IIRC): there are 300 million Americans. Of these, maybe 50 million are in high school. There are maybe 1,000 students in a high school. So 50,000,000 / 1,000 = 50,000 high schools.
Actual answer:
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Numbers vary, I think depending on what is being counted as a high school, but it looks like the actual number is between 18,000 and 24,000. As it turns out, the first approach underestimated the total number of school districts in the US (it's more like 14,000) but overestimated the number of high schools per district. The second approach overestimated the number of high school students (it's more like 14 million) but also overestimated the average number of students per high school. And the geometric mean of the two approaches is 22,000, which is quite close!
I tried the second approach with better success: it helps to break up the "how many Americans are in high school" calculation. If the average American lives for 80 years, and goes to high school for 4, then 1/20 of all Americans are in high school, which is 15 million.