EXAMPLE 9 Oh, those percents

Here are a couple of examples involving percents. During the December 4, 2009, episode of the TV show Fox & Friends, a graphic was displayed with the question heading: “Did scientists falsify research to support their own theories on global warming?” The results, attributed to a Rasmussen Reports Poll on global warming, indicated that 59% of people believed this was “somewhat likely,” 35% thought it was “very likely,” and 26% considered it “not very likely.” That adds up to a whopping 120% of those polled! Turns out that Fox & Friends misquoted the actual Rasmussen Reports Poll results but didn’t notice the error.

Even smart people have problems with percentages. A newsletter for female university teachers asked, “Does it matter that women are 550% (five and a half times) less likely than men to be appointed to a professional grade?” Now 100% of something is all there is. If you take away 100%, there is nothing left. We have no idea what “550% less likely” might mean. Although we can’t be sure, it is possible that the newsletter meant that the likelihood for women is the likelihood for men divided by 5.5. In this case, the percentage decrease would be

EXAMPLE 10 Summertime is burglary time

An advertisement for a home security system says, “When you go on vacation, burglars go to work. According to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.”

This is supposed to convince us that burglars are more active in the summer vacation period. Look at your calendar. There are 14 weeks between Memorial Day and Labor Day. As a percentage of the 52 weeks in the year, this is

193

So the ad claims that 26% of burglaries occur in 27% of the year. This seems to make sense, so there is no cause for concern.

Just a little arithmetic mistake In 1994, an investment club of grandmotherly women wrote a best-seller, The Beardstown Ladies’ Common-Sense Investment Guide: How We Beat the Stock Market—and How You Can, Too. On the book cover and in their many TV appearances, the down-home authors claimed a 23.4% annual return, beating the market and most professionals. Four years later, a skeptic discovered that the club treasurer had entered data incorrectly. The Beardstown ladies’ true return was only 9.1%, far short of the overall stock market return of 14.9% in the same period. We all make mistakes, but most of them don’t earn as much money as this one did.

EXAMPLE 11 The old folks are coming

A writer in Science claimed in 1976 that “people over 65, now numbering 10 million, will number 30 million by the year 2000, and will constitute an unprecedented 25 percent of the population.” Sound the alarm: the elderly were going to triple in a quarter century to become a fourth of the population.

Let’s check the arithmetic. Thirty million is 25% of 120 million, because

So the writer’s numbers make sense only if the population in 2000 is 120 million. The U.S. population in 1975 was already 216 million. Something is wrong.

Thus alerted, we can check the Statistical Abstract of the United States to learn the truth. In 1975, there were 22.4 million people over age 65, not 10 million. That’s more than 10% of the total population. The estimate of 30 million by the year 2000 was only about 11% of the population of 281 million for that year. Looking back, we now know that people at least 65 years old were 12% of the total U.S. population. As people live longer, the numbers of the elderly are growing. But growth from 10% to 12% over 25 years is far slower than the Science writer claimed.

EXAMPLE 12 Stocks go up, stocks go down

On September 10, 2001, the NASDAQ composite index of stock prices closed at 1695.38. The next day the September 11 terrorist attacks occurred. A year later, on September 9, 2002, the NASDAQ index closed at 1304.60. What percentage decrease was this?

194

That’s a sizable drop. Of course, stock prices go up as well as down. From September 10, 2002, to September 9, 2003, the NASDAQ index rose from 1320.09 to 1873.43. That’s a percentage increase of

Remember to always use the starting value, not the smaller value, in the denominator of your fraction. Also remember that you are interested in the percentage change, not the actual change (here, the 41.9% is the correct value to report instead of the 553.34 difference).

NOW IT’S YOUR TURN

Question 9.2