Piano tuners

So how many piano tuners are there in Chicago?

I approached the problem this way: I know the city of Chicago has more than 1 million people, and I think it has less than 10 million. I was going to say that I think it has closer to 10 million--something like 6 or 8--but I decided to go with the rule of thumb and use the geometric mean, or 3.15 million (I'm glad I did--we'll see why in a minute). I figure that the proportion of piano tuners is somewhere less than 1 in a 1,000 people--I've only ever met one, and that was when I was a kid and we had our piano tuned--but that they're probably more frequent than 1 in 100,000 people. The geometric mean would then be that 1 in 10,000 people are piano tuners (come to think of it, my home town had about 10,000, and he might have been the only piano tuner in town--pretty good estimate). OK, so 1 in 10,000 people out of 3.15 million Chicagoans is 315 piano tuners, Q.E.D. Time to hit Google...

So, it turns out the population of Chicago is 3 million--thank you geometric mean! And estimates of tuners? Here's one example:

From the almanac, we know that Chicago has a population of about 3 million people.
Now, assume that an average family contains four members so that the number of families in Chicago must be about 750,000.
If one in five families owns a piano, there will be 150,000 pianos in Chicago.
If the average piano tuner
serviced four pianos every day of the week for five days
rested on weekends, and
had a two week vacation during the summer,
then in one year (52 weeks) he would service 1,000 pianos. 150,000/(4 x 5 x 50) = 150, so that there must be about 150 piano tuners in Chicago.

An interesting solution (Wikipedia gives essentially the same)--I would never have tried to estimate the time it takes to tune a piano, about which I know nothing (although in hindsight I suppose I know that it doesn't take more than a day--it certainly didn't for that guy when I was a kid--and it probably takes more than an hour, so the geometric mean of 1 and 8 hours is about 2-3 hours!). Still, I like my solution better--I made fewer estimates. ;)

Interestingly, I didn't find anywhere how many piano tuners there actually are in Chicago.