A Sunday Numeracy Quiz

My Sunday reading turned up three examples of glaring numeracy errors. I make plenty of my own errors, so I have sympathy for the perpetrators. But I did want to highlight them as examples of what can happen when quantitative thinking runs off the rails. And the need to remain mathematically vigilant in your daily life.

So please take this short numeracy quiz. My answers after the fold.

1. How much has teen drinking declined?

In today’s New York Times Magazine, Tara Parker-Pope makes the case that teenagers are more conservative than their parents were. For example, the fraction of high-school seniors who reported that they had recently consumed alcohol fell from 72% in 1980 to 40% in 2011.

I have no beef with those statistics (or that trend), but I do wonder about the chart used to illustrate it. Do you see anything wrong in this visual?

2. What’s a fair way for students to hedge their bets on today’s Super Bowl?

A few pages later (in the ink-and-paper edition), the NYT’s Ethicist, Ariel Kaminer receives a letter from a parent whose child was offered a bet on the Super Bowl … by their school. Leaving aside the propriety of book-making in the class room, what do you think of this wager?

My school charged a dollar for students to bet, or “predict,” which team would win the Super Bowl. It was \$1 for one team, and if you won, you would get a candy bar. If you bet \$3, you could choose both teams and guarantee your candy bar. Is this legal or even morally right?

3. How much does federal compensation exceed private compensation?

In Friday’s Wall Street Journal, finally, Steve Moore makes the case that federal workers are overpaid. What’s wrong in the following excerpt? (ht: Brad DeLong)

Federal workers on balance still receive much better benefits and pay packages than comparable private sector workers, the Congressional Budget Office reports. The report says that on average the compensation paid to federal workers is nearly 50% higher than in the private sector, though even that figure understates the premium paid to federal bureaucrats.

CBO found that federal salaries were slightly higher (2%) on average, while benefits — including health insurance, retirement and paid vacation — are much more generous (48% higher) than what same-skilled private sector workers get.

My Thoughts

1. This chart combines two common charting techniques that overstate comparisons. First, the vertical axis goes down to only 30% or so, not zero. As a result, the height of the 2010 data point appears to be only one-quarter that of the 1970 data point. Second, the chart uses a three-dimensional image to depict a single-dimensional variable. Leaving aside the change in images (cup vs. bottle), that overstates the difference by a factor of 8. Put it all together, and the cup looks to be about 1/32 the size of the bottle, suggesting that teen drinking is about 3% of its 1980 level. In fact, it’s about 56% of that level. (For a similar discussion, see my earlier piece on Honest Tea’s caffeine measurements.

P.S. The text references 2011, but the chart uses 2010.

2. The Ethicist rightly lambastes this offer not just on ethical grounds, but mathematical. If kids want to hedge their bets on the Super Bowl, the could save a dollar by betting on each team.

3. To figure out how much compensation grew, you need to calculate a weighted average, not add the two growth rates. In fact, CBO reports that the overall compensation difference is 16%. And don’t forget some caveats.

2 thoughts on “A Sunday Numeracy Quiz”

1. Great analysis, Don! I sure appreciate your gifts and talents on this kind of data. Best regards.

2. Katie says:

There is another big problem with the math in #2 (the betting case.) I can easily buy a candy bar for a dollar at a vending machine, probably for less at a grocery store. For three dollars I could buy three candy bars. It makes no sense to bet when the prize is worth less than your wager.