What’s Black and White and Doesn’t Add Up? : Newspapers: Mathematician says journalists can mislead readers with the misuse of statistics. His book shows how figures can be biased.

The Earth’s population laid end to end would stretch to the moon and back eight times, a group worried about overpopulation might accurately assert. But another group could say just as correctly that, if everyone had his own 20-by-20-by-20-foot cube, all would fit in the Grand Canyon.

Beware of such fancy figuring, says a math professor who’s written a book on how to read newspapers.

What does a number-cruncher know about news? Enough, says Prof. John Allen Paulos, to help readers sort through the mathematical muddles that sometimes get into print.

“We’re kind of overwhelmed with numbers in stories,” said Paulos, author of the 1988 book “Innumeracy,” about Americans’ unease with basic math. “We need to read numbers stories with some skepticism.”

For example, although both the above calculations on the world’s population are true, they give conflicting impressions of whether that population is too large.

Paulos, who teaches at Temple University in Philadelphia, offers a crash course in skepticism in his latest book, “A Mathematician Reads the Newspaper.” It’s a quirky, erudite look at the use, misuse and neglect of numbers in the news.

A devoted newspaper reader since childhood, Paulos says reporters and editors aren’t stupid but are “susceptible to the same mathematical foibles as everyone else.” Too often, he says, they omit important numbers.

For example, a story about a disease that paralyzes 260 people nationwide may be frightening, but it’s helpful to look at the big picture: It afflicts only one in a million Americans.

“In addition to who, what, when and where, reporters should ask, how many? How likely? Is this a survey or just an anecdote? Is the rate going down or going up?” Paulos said before a recent lecture to the Smithsonian Associates. “And who came up with these numbers? What method did they use?”

If the reporters don’t ask, readers should. His key advice: Learn to think logically. And bear in mind that coincidences are more common than most people think.

If a woman with breast implants gets a rare, terrible disease or a cellular phone user develops cancer, it’s tempting to blame the implants or the telephone. People tend to jump to such conclusions--without statistical evidence--for the same reason they gravitate toward conspiracy theories to explain AIDS or an assassination, Paulos said.

“It’s a kind of beguiling superstition people have that significant events have to have significant causes,” Paulos said. “And that’s not true.”

Another case of searching for meaning that isn’t there: The business pages are full of analysts purporting to explain why the stock market rose or fell.

Market shifts are almost always the result of random fluctuations, what mathematicians call “chaos theory,” Paulos said. “One never hears of chance, however, in the neat post hoc analyses that follow each market’s close.”

Paulos says the sports pages, sprinkled with batting averages and point spreads, are a great way to learn math. But even there, readers should stay alert.

During the baseball strike, the owners liked to point out that the average annual salary for players is $1.2 million. True, but half the players earn less than $500,000.

Paulos even has a quarrel with the food section. He hates to see recipes calling for vague amounts--a couple of medium-sized potatoes, a dash of salt--that are followed by a precise nutritional summary: 761 calories and 428 milligrams of sodium per serving.

He admits that sometimes he may take the mathematical mind-set too far. Sort of like the three statisticians who took up duck hunting: The first one’s shot sailed six inches over the duck. The second one’s shot flew six inches below the duck. At this, the third statistician excitedly exclaimed: “We got it!”