Doing the Math

Often the people who give us information are counting on us not to think too hard about it.  They especially count on us not to do the math.  It’s a reasonable expectation on their part because many people are intimidated by anything mathematical and avoid it whenever they can.  But it doesn’t have to be that way and we will make better decisions when aided by some simple calculations.

What brought this to mind was an ad for a railroad saying that they move a ton of freight 450 miles on a single gallon of fuel.  True, railroads are very efficient, but most people hearing this would automatically compare it to auto gas mileage.  You can’t move a ton of freight in your car that gets 25 or 30 miles per gallon.  If you have a truck that can carry a ton of freight it might get only 18 mpg or less.  That’s less than 1/20 of the railroad efficiency.  But that is the comparison they want you to make.  Their real competition, an over-the-road tractor-trailer can carry a 40,000-pound load.  That’s 20 tons.  According to Popular Mechanics:  “New fuel-economy standards that take effect beginning in 2014 will require semi trucks with a sleeper cab to get 7.2 mpg on level roads.”  Using simple math, 7.2 times 20 = 144 or just about 1/3 of the railroad number.  Our new conclusion is that railroads are indeed more efficient, but not by the huge amount we were led to believe (and trucks are often easier to unload).

Another tricky area is percent calculations.  If the stock market goes down by 20%, then goes back up by 20% is does not end up where it started.  Think about it using 100 as the starting point.  If it goes down by 20%, it’s at 80.  Now 20% of 80 is only 16, so a 20% rise leaves it at 96 (not 100).  Likewise when a store runs a discount of an additional 20% off, here’s how it works.  If the original price was $100 and it was reduced by 30%, it now sells at $70.  An additional 20% off is $70 minus $14 (20% of 70 = 14).  The new sale price is now $56.  You can’t take the 20% plus 30% and expect to get it at half price, or $50.  It seems tricky and a little deceptive, but it’s fairly easy when you think it through.

Look closely at news stories reporting percent changes in defects.  One might feature scary headlines saying that the percentage of school buses failing inspection jumped by 50%.  Buried in the article are the numbers.  Did it jump from 4 to 6, or from 50 to 75?  Both are a 50% increase.  What you may never see in the article is the total population.  Are they talking about 10 or 100 or 10,000 buses?  This makes a big difference, but the headline is designed to catch your eye and elicit concern.

Finally, consider how the government, advertisers and advocacy groups describe savings, spending and crises by manipulating time frames.  Instead of $200 billion per year, we hear $2 trillion over the next 10 years.  Auto loan companies lower payments by increasing the term of the loan (but you will ultimately pay more interest).  We hear about certain diseases killing or affecting one person every 6 minutes instead of a total of 87,600 people (less than .03 percent of the population).  The time frame is manipulated to manipulate your reaction to it.

Sometimes doing the math and paying attention to details can make a big difference in your reactions to numbers.  It may even tell you how realistic the numbers are in the first place.  It pays to be careful.