More math mistakes

According to a picture that is making the rounds on Facebook, Halliburton will make enough money to pay off a $200,000 fine in "just 23 seconds".

$200,000 per 23 seconds is $274 billion per year. The "23 seconds" number appears to come from an article in the Huffington Post:

http://www.huffingtonpost.com/2013/07/26/halliburton-fine_n_3659293.html

This article claimed it uses the 2012 revenue numbers. However, Halliburton's revenues are actually only about $28.5 billion per year:

http://www.halliburton.com/public/news/pubsdata/press_release/2013/Q412_Earnings_Release.pdf

More bad math in the news

Ann Coulter on immigration:

Nearly three times as many Americans support reducing immigration as want it to stay the same, according to Gallup polls. A grand total of 5 percent of the population want to increase legal immigration -- 10 times less than want to decrease it.

 In other words, 50 percent of Americans want to decrease immigration, 17 percent of people want immigration to say the same, and 5 percent of people want to increase immigration. What about the other 28 percent?

In an email from Maryland PIRG

Maryland PIRG (Public Interest Research Group) is a student advocacy organization that I somehow got on the mailing list of at Maryland and they still send me stuff. Their most recent email included the following:

"Some proposals in Congress would significantly cut student aid - the U.S. House voted to slash Pell Grant funding by $5.7 billion – cutting, on average, $785 in financial aid for over 9 million students."

"over 9 million" * $785 is over $7 billion, not $5.7 billion. (On the other hand, this may make sense if the $785 number is the median, and not the mean.)

From USA Today

A recent article in USA Today discussed standardized testing in D.C. public schools. It mentioned that some high-performing schools have very high numbers of answers erased on tests (when you erase an answer on the Scantron sheet and put in a new one, the machine can detect the residue). The article claimed that this could be possible evidence that teachers tampered with the tests prior to submitting them for grading.

The following quote appeared:

"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That's more than half of D.C. schools."

This statement is not too surprising. If the distribution of erasure rates were symmetrical, then in any given year half of them will be above average. Since the schools above average will change from year to year (if only due to random variation), then over a 3-year period more than half of the schools will be above average in at least one of those years. (For instance, if the erasure rates are random and independent, then each year each school will have a 1/2 probability of being above average, so each school will have a 7/8 probability of being above average in at least one year.)

Aside from this sentence, the rest of the article was actually fairly good statistically. It mentioned that this particular school hasd erasure rates so far higher that it wasn't due to chance, and included a lengthy discussion of possible alternative explanations for the data.

More from the Daily Illini

In reference to a FOIA request from a student environmental group for information about coal disposal at the University power plant:
"The letter also said the University has seven days to submit the unredacted documents. Hardy said the University received the request Jan. 30 and plans to respond by the Feb. 9 deadline."
[Again, this actually makes more sense than it sounds. The "seven days" is seven business days.]

This was in the paper yesterday

"Even with a 2 percent a year spending cap written into the bill, Rep. Roger Eddy, R-Hutsonville, said state spending would be able to grow 17.5 percent over four years."

Saving Green by Going Green

A recent article in the Daily Illini reported on a proposed increase in the "student sustainability fee," a fund which will provide funding for energy-saving initiatives. As an example:

He pointed out that their recent project of replacing Krannert Center’s fluorescent lights with LED’S will pay for itself in three years and save the University roughly $70,000 per year. The committee funded half of the project with a $225,000 grant.

First of all, observe that this statement is mathematically incorrect. If half of the project cost $225,000, then the total cost of the project was $450,000, so it will take about 6.5 years to pay it back at $70,000 per year.

Second of all, observe the economic puzzle. Effectively, the project is an investment with a guaranteed annual rate of return of $70k/$450k = 15.5 percent. So as long as the market rate of interest is less than 15.5 percent, which I assume it is, the optimal strategy of the university is to borrow money to finance this project, and even after paying back the interest they will actually have more money - so they should do that even in the absence of any additional funding from a "sustainability fee."

(Here is an economics article discussing similar anomalies, mostly in the context of individual purchasing decisions like whether to buy a new refrigerator.)