The other morning, I was lying in bed and for some reason, found myself wondering what the population of Niskayuna is. While this is easily Google-able, as I said, I was in bed, and didn’t want to get up to get a device with Internet connectivity. So I tried to Fermi-problem my way to an answer using numbers I could come up with without opening my eyes.

The starting point for the estimate was the fact that SteelyKid’s kindergarten class has 20-odd kids in it, and there are three kindergarten classes in her school. The school is one of five elementary schools that Niskayuna operates (Birchwood, Craig, Glen Cliff, Hillside, and Rosendale). Making the assumption that all the classes are roughly the same size, that would add up to around 300 kindergarteners (20 per class, three classes per school, five schools).

Assuming that more or less all of the kids who start kindergarten need to get through high school, that’s a total of 3,900 school-age kids (300 per grade year, 13 grade years), which I’ll round up to 4,000 because I only want to deal with one significant figure.

So, if there are 4,000 school-age kids, how do you get from that to the total population. The simplest thing I came up with was to estimate the fraction of the population those kids represent. If you take the average lifespan to be something in the 70-80 years range, the 13 years of school correspond to something like one-fifth or one-sixth of the total. So you’d multiply the total number of kids by 5-6, and come up with a bit over 20,000.

A more complicated approach (which I actually came up with first, because I was half asleep and that leads to weird things) is to go by way of the number of households. If you said that the average family has something like two kids, then you’d have around 2,000 families with kids in school. If you said the average family was four people, that’d give a total of 8,000 people from families with kids in public school. Then you need some sort of multiplier to account for families without school-age kids (or those with kids in private schools, etc.).

That’s pretty tricky, but going down the mental list of houses in the neighborhood, I’d say maybe one in four has a family with school-age kids (based on the number of bus stops, yards with toys, etc. that I see when I’m out walking Emmy. But, of course, the no-kids households are smaller, more or less by definition, so if you call those two per household, you get 8,000 people in families with kids in school (2,000 families, four people per) and another 12,000 people in families without (6,000 families, two people per) for about 20,000 total residents. The one-in-four estimate might be on the high side, though, because we’re in a kind of kid-heavy neighborhood, so that’s probably a lower bound.

That is, of course, a much dodgier estimate than the previous one (which is why I went looking for a simpler technique in the first place), with several additional dubious assumptions. You get the same ballpark figure either way, though: something on the high side of 20,000.

If you look up the actual answer, the 2010 census figure is just shy of 22,000. So, score another victory for the general Fermi estimation method.

Of course, by the time I came up with all that, I had totally lost track of why I woke up wanting to know the population of Niskayuna. I still have no idea what I was after– I think it started with wanting to know the number of families for some reason, and morphed into wanting the overall population, but whatever the reason was, it’s totally gone. It is, however, a decent topic for a silly blog post…

Silly….? THIS. IS. PHY-SICS!!!!!

For that matter, you also came close on the number of households (Wikipedia says about 7800 vs. your estimate of 8000). And you guessed right about the average household size (your estimate implies 2.5 people per household, actual is 2.56). Score a couple more for the Fermi method.

Seat of the pants estimates for the win. How often is 7862 households actually a more useful answer than ~8000? Probably only if you’re collecting their taxes or votes.

Not sure why you couldn’t have just multiplied 300 people per year of age * 70 years estimated life expectancy = 21,000 population.

Philip