No Trend - New York Times August 25, 2001, NEW YORK TIMES. How to Find a Trend When None Exists, by John Allen Paulos
PHILADELPHIA -- The news reports wash in with frightening regularity. Average citizens might be forgiven if they thought that shark attacks were one of the major menaces facing mankind during the month of August. These attacks are a watery nightmare for those involved, but nevertheless they are very rare 40 worldwide so far this year, 29 of them in the United States, most of these in Florida.

Lowly arithmetic tells us the story. The rate that such incidents occur is obtained by dividing the number of incidents by the millions of people in the water. The rate is as tiny as it has been in past years, and one can only conclude that the actual chances of a shark attack are tiny.

August being a perennially slow news month, news reports like this proliferate without any substantive competitors, and they make the world seem much scarier than it is. Consider the hazards posed by the dreaded West Nile virus or deep-vein thrombosis from sitting on long flights. Contemplate the risk of abduction by a stranger. These perils can, of course, result in tragedies, but they are not even a minuscule fraction as deadly as alcohol, to cite just one banal example.

Another ongoing story that looms much too large is air rage passengers losing their composure and punching flight attendants, berating gate agents or abusing other airline employees. The annual number of incidents involving abusive passengers is approximately 3,500, but only 10 percent of these are serious enough to warrant any action by the airlines against a passenger, according to the Air Transport Association.

This may still sound like a dreadful problem. But close to 2 million Americans fly every day. That's about 700 million passengers annually. Dividing 700 million by 3,500 incidents, or by 350 serious outbursts, we find that about one in 200,000 passengers is involved in any air rage incident annually, and only one in 2 million is involved in a serious one. Compare those figures to the behavior and arrest rates at sporting events, and you'll appreciate what a docile bunch air travelers are.

Even more significant events become distorted when filtered through the news media. Consider the wildfires raging in the West. They're an important story, especially when lives are lost and homes destroyed. But the severity may be exaggerated by the way statistics are given in the news. I doubt that one American in 20 knows how many acres are in a square mile, for example, yet the extent of the fires is always given in acres.

If we're describing the amount of forest consumed in the fires, which sounds worse: 3,100 square miles or 2 million acres? Since one square mile contains 640 acres, the figures are equivalent. But in an era when few Americans share their rural forbears' clear sense of what an acre is, 2 million acres may sound like more.

Often a little arithmetic is enough to counter a lot of anxiety, but let me stop here. I think some sharks are approaching the beach.

John Allen Paulos, a math professor at Temple University, is the author of "Innumeracy" and "A Mathematician Reads the Newspaper."

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