How far off are we?

I think the difference between perception and reality is very interesting, and that by studying that difference we can learn an enormous amount about ourselves and our surroundings. I have observed that by hypothesizing first and measuring second the measurement is much more meaningful. For example, imagine standing in the fairway on a golf course, looking across a small pond to the flag in the middle of a large green protected by bunkers front and left. If you are not a golfer, who cares, just play along. A good golfer, or caddy, can look at that flag and say, “its about 125 yards.” But a beginner can’t. You could just tell the beginner, “that flag is 124 yards,” and he could then try and remember what 124 yards looks like, and use it as a reference in the future. Or you could ask the beginner, “how far to that flag?” His response will tell you and him a great deal about how well he’s been doing with distance recognition. If he says, “160 yards” then he is clearly over estimating, and will know immediately upon learning the true yardage that he has a lot to work on. If you just tell him, “124 yards” he won’t every really know how far off his judgment is.
I bring this up because I recently calculated the amount of money my wife and I spend on automobile ownership, and it came out to about $800 a month. We lease one car and own one outright. I drive much less than the average person (maybe 300 miles a month), so our fuel and insurance are less than they would be if I commuted in my car. And the fact that we own one of our cars probably makes our monthly total somewhat less than normal. Beany had a great post about cost of car ownership a couple of days ago with links to AAA and other sites that spell the numbers out nicely.
Now to bring this all together. . . I asked my wife one day, after I’d come up with my $800 figure, how much she figured we spent on car ownership each month, just her gut reaction guess. She started adding up all the various numbers and I asked her to stop adding, and just guess. She doesn’t like to guess at things, so this was asking a lot of her, but she graciously played along and guessed $500. My reason for making her guess, as I’ve already tried to point out, is that the fact that her guess-timate was much lower means something. It means that she wasn’t realizing the true financial impact that owning two cars has on our lives. She knew the cars weren’t cheap, but she didn’t, at her gut level, know how much they really cost. Neither did I, by the way, when I first tried to figure it out. $800 is a large part of our monthly budget!
Tom Vanderbilt discusses the differences between reality and perception frequently in his book Traffic: Why We Drive the Way We Do (and What It Says About Us). For example, people are very bad at perceiving distances, especially greater than 100 yards, and men and women err in different ways. We are pretty bad at estimating speeds, and at timing merges. Most of us understand that we don’t have built in radar guns, and that our estimates of vehicular speed are not amazingly accurate. What we don’t necessarily understand is by how far off our estimates really are. It’s that discrepancy that is really the important thing to know. I feel safer knowing that I really don’t know how fast a car is approaching, rather than feeling like I’ve got a pretty good guess.
I use this technique - forcing a hypothesis before allowing a calculation - often with my students because I think the resulting calculation has a lot more meaning, and is much more memorable compared to the students' preconceived notions. Try it next time you are wondering about something quantifiable. You may learn more than you set out to.

This has been quite the long winded post. Thanks for reading it.