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."

http://www.nytimes.com/2001/08/25/opinion/25PAUL.html?ex=999742780&ei=1&en=74f9826ef6256b9c

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