Andrew Hacker writes:
I have the class prepare a report on how many households in the United States have telephones, land and cell. After studying census data, they focus on two: Connecticut and Arkansas, with respective ownerships of 98.9 percent and 94.6 percent. They are told they have to choose one of the following charts to represent the numbers, and defend their choice.
The first chart suggests a much bigger difference, but is misleading because the bars are arbitrarily scaled to exaggerate that difference.
I hate to see this sort of thing in the New York Times. Millions of people read the Times, it’s an authoritative news source, and this is not the graphics advice they should be given.
Let me break this down. The first thing is that it’s a bit ridiculous to make this big graph for just 2 data points. Why not map all 50 states, why just graph two of them?
The second thing is . . . hey, be numerate here! 98.9% and 94.6% look really close. Let’s ask what percentage of households in each state don’t have phone ownership. When X is close to 1, look at 1 – X. Then you get 2.1% and 5.4%, which indeed are very different.
P.S. Hacker also writes this:
In the real world, we constantly settle for estimates, whereas mathematics — see the SAT — demands that you get the answer precisely right.
Ummm, no. The SAT is a multiple-choice test so of course you have to get the answer precisely right. That’s true of the reading questions on the SAT too, but nobody would say that reading demands that you get the answer precisely right. He’s confusing the underlying subject with the measuring instrument!
Speaking more generally of mathematics: of course there are lots of mathematical results on estimation and approximation. I mean, sure, yeah, I think I see what Hacker’s getting at, but I’d prefer if he were to say that there is a mathematics of estimation and approximation, and that this is an important part of studying the real world.