Tuesday, March 16, 2010

Math Quiz for Presidential Candidates

Darren writes that the President has become innumerate. This immediately brought to mind Paulos's proposed "Math Quiz for Presidential Candidates."

I agree completely. I think students should know most of these, too, so I gave the quiz to some of my classes when I was sick. I told the sub to try it as well, but she refused!

I think 6 is my favorite. (Below the fold)

Since ABC is constantly fiddling with those links, I reposted it here:

The Quiz
Below are just 10 of the many politically neutral questions that might be asked. The answers follow.

1. A crucial number to know is the population of the country of which you want to be president. What is the approximate population of the United States? of the world? What percentage of the latter is the former?

2. A news article claims that 15 percent of all strokes occur sometime between noon and midnight on either Friday or Saturday, perhaps because of increased celebrating on the weekends. Do you check with the Centers for Disease Control? Do you stop campaigning on weekends? What's your reaction to this statistic?

3. You must understand the electoral process, of course, so given the way the Electoral College is set up, what is the theoretically smallest number of actual votes (not electoral votes) a candidate can receive and still be elected president?

4. Approximately how many Americans died in the attacks on 9/11? There's no moral comparison, of course, but approximately how many die in auto accidents annually? from heart disease annually?

5. You're campaigning in a state in which the percentage of employees who subscribe to a particular drug plan has risen 1 percentage point, from 1.5 percent to 2.5 percent. By what percent has this figure risen? By what percent must it fall to return to its former level?

6. In Disproportia, a small Midwestern town, the average tax cut per household is $2,200, but the median tax cut is $150. What does this say about the distribution of taxable incomes in the town? If the founder of a high-tech company were to move into the community, which is more likely to rise, the mean or the median tax cut?

7. Roughly how big is the federal budget? What fraction of it is discretionary and non-military? By contrast, what is the gross domestic product (to the nearest trillion dollars)?

8. If the government spends $1,000 per second, it will take approximately 17 minutes to spend $1 million. At this rate, about how long will it take to spend $1 billion? How long to spend $1 trillion? One comparison: The $87 billion supplementary budget for Iraq is approximately how many times the annual U.S. contribution to the U.N.?

9. An ace pollster on your staff claims that 63.86 percent of 100 Americans surveyed support your foreign policy. What's your reaction to these numbers?

10. If FAWUA, the federal agency with an unpronounceable acronym, deposits $1 billion in an escrow fund at 7 percent, how long until the deposit is worth $2 billion? $4 billion? Alternatively, if the agency borrows $1 billion at 7 percent and makes no payments on it, how long until it owes $2 billion? $4 billion?
The bottom line: A president should be able to put 2 and 2 together, both numerically (the easy part) and otherwise.

The Answers
1. About 290 million. A bit more than 6 billion. A little less than 5 percent.
2. By itself that's not very impressive evidence. The time period after 12 p.m. on Fridays and Saturdays constitutes 1/7 or 14.3 percent of the week so, as a first approximation, you'd expect roughly that percentage of strokes over any two days after 12 p.m.
3. Candidate X could receive as few as 11 votes and his opponent, candidate Y, tens of millions. Specifically, if California, New York, Texas, Florida, and the 7 other states with the most electoral votes each had a turnout of 1 voter who voted for X, and the other 39 states voted unanimously in the millions for Y, X would win.
4. Approximately 3,000, 40,000, and 700,000, respectively.
5. It's risen by 67 percent, but must be cut by only 40 percent to reach its former level.
6. By the definition of "median," half the households receive less than $150 in tax cuts, half more, so there are some very wealthy people in town. These people, like the new company founder, drag up the average tax cut much more than they do the median cut.
7. About $2 trillion, 20%, and a bit more than $11 trillion, respectively.
8. About 11.5 days for $1 billion, 32 years for $1 trillion, and roughly 250 times as much, respectively.
9. The question at issue is impossibly vague, the number surveyed is relatively small, and the precision of the figure is entirely bogus. Fire the pollster.
10. About 10 years and 20 years, respectively. It's important to know that the length of time it takes money to double at an annual interest rate of r percent is roughly 70/r. In this case 70/7 equals 10 years, and a second doubling requires another 10 years.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and A Mathematician Plays the Stock Market. His Who's Counting? column on ABCNEWS.com appears the first weekend of every month.


  1. I have 2 of Paulos' books. I liked Innumeracy the best.

  2. Innumeracy is very good. Beyond Innumeracy takes the same theme farther, so is equally good but a slightly tougher read because of the topics. "Mathematician reads the Newspaper" and "Mathematician plays the Stockmarket" are likewise worth buying for yourself, especially if you find them in Amazon Used and New for a couple bucks. "Irreligion: Why the Arguments for God Just don't Add up" is more problematic and certainly too controversial to have in a classroom.