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Guesstimate #2: How many high schools are there in Canada?




How many high schools are there in Canada? Your first reaction might be to throw up your hands and say "who knows?!" (well, actually your first reaction might be to say "who cares?!" , but we'll ignore that...). The number of high schools in Canada isn't the kind of information that most people carry around in their heads (well, at least not the kind of people that you'd usually want to talk to). Yet with just a few moments of thought you can make a surprisingly good guesstimate.
How many high schools are there in Canada? It depends on a number of different factors:

How many people are there in Canada? The more people there are, the more high schools are needed.


Of course not everybody in Canada is in high school. So what fraction of the Canadian population is high school age?


How many students are there per high school? The more students we cram into each school the fewer of them we need to build.

We can write this mathematically in a much more succinct way:


Nhigh schools = NCanadians x fhigh school age / Nstudents per school

where Nhigh schools is the number of high schools in Canada, NCanadians is the number of people who live in Canada, fhigh school age is the fraction of people who are high school age, and Nstudents per school is our best guess as to the average number of students in a typical Canadian high school.



Now that we've considered all of the different factors that go into our estimate of the number of Canadian high schools, let's put in some numbers:




NCanadians = ?
The current population of Canada is approximately 30 million people. So NCanadians = 30,000,000.




fhigh school age = ?
Well, let's see... If we assume that the average life expectancy in Canada is 75 years, and a person spends 4 years of their life in high school, then at any given time, the fraction of all people currently in high school is 4/75 = 0.053. So fhigh school age = 0.053.




Nstudents per school = ?
Hmmm... that's a bit trickier. Of course not all schools will have the same number of students. Fredericton High School in New Brunswich has nearly 3000 students. There are 1200 students at Leaside High School in Toronto. Gull Lake High School in Saskatchewan has only 220 students. Since the number of students varies from school to school, we'll have to guess at an average number. 200 students per school? 500? 1000? 3000? It's hard to decide. Since most high schools are located in small towns rather than big cities like Toronto or Fredericton, let's assume Nstudents per school = 500.



So based on the above numbers we guesstimate that the number of high schools in Canada is


Nhigh schools = 30,000,000 x 0.053 / 500 = 3180 high schools.

Now for the moment of truth: how many high schools are there actually in Canada? According to the Ontario Ministry of Education, the latest count puts the number at 3500 Canadian secondary schools. If you're curious, you can find a listing of home pages for 491 secondary schools in Canada by clicking here.


So our guesstimate was actually pretty good! Not bad, considering that we had to make a number of guesses and approximations! We've ignored complications like the fact that not everyone goes to high school, that some people die before they reach high school age, that some people take more than four years to complete high school, etc. A guesstimate focuses on the most important factors in order to come up with a number that is easily calculated, and close to the expected "true" number, without worrying about all the details.

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