The police reporter is given the annual report of violent crimes in the city for last year: 17,030. Two years ago, the total was 22,560. The reporter knows that she has to give a percentage decline:

(Two years ago) 22,560 - (last year) 17,030 = 5,530 (decline)

5,530 / 22,560 = .0245 or a 24.5 percentage decline

The reporter writes:

Violent crimes in Freeport declined 24.5 percent last year from the previous year.

The police department's annual survey reveals that 17,030 violent crimes were committed last year, compared with 22,560 the year before, or 5,530 fewer crimes.

Simple as figuring percentages seems, reporters have trouble with it all the time.

Oops

During the surge in the cost of power in California, one of the bright spots was the Los Angeles Department of Power & Water. It was charging $40.80 for 750 kwh, whereas the privately owned Pacific Gas & Electric was charging $91.29 for the same number of kilowatt hours. This was "56 percent greater," said the west coast reporter for the News Hour on PBS.

The calls cascaded into the station, and the next night, Jim Lehrer apologized to viewers. The difference was considerably greater, 123.75 percent, he said.

One of the most common mistakes in calculating percentages is putting the difference over the wrong denominator. Here, the reporter put the difference, $50.49, over the PG&E rate instead of putting it over the DP&W rate. If you say aloud what the comparison is that you intend, the denominator will be correct:

The Pacific Gas & Electric rate is $50.49 greater than the Los Angeles Power & Water rate. So I put $50.49 over $40.80.

When comparing old and new, former and current, original and present, we are figuring the change or difference from the old, former or original.

Use with Care

Percentages work with large numbers, not well with small numbers. Take a couple of New York Times stories that contained these sentences:

Of the 24 institutions surveyed, 92 percent assessed surcharges.

Of 41 druggists checked, 93 percent were selling the mercury capsules.

Let's do the math:

92 percent of 24 is 22.08.

93 percent of 41 is 38.13.

Just what is .08 of an institution? Has anyone seen .13 of a druggist? The percentage exactitude turns out to be silly. The reporters should have used the round numbers, 22 institutions and 38 druggists.

Numbers and Rates

New York City has more murders than any city in the country. California has more infant deaths than any other state in the U.S. Does that make New York City the murder capital of the country, California the most dangerous for child-bearing?

The answer is, no. Raw numbers do not always tell the full story. For many comparisons we are better off using rates. A rate takes a second factor into consideration. In the case of crime, the rate is figured on the basis of population. In the case of infant mortality, the rate is deaths per 1,000 live births. Using the rate instead of the raw number, we find that 20 cities have a higher rate than New York City's murder rate.

New York City: 564 / 7,420,000 = .000076

We multiply the rate by 100,000, as the murder rate is expressed as murders per 100,000 population. The rate is 7.6.

New Orleans: 103 / 465,500 = .0002212 X 100,000 = 22.1 (rounded off)

Next, let's figure out the infant mortality rate. This is an important figure for journalists as the infant death rate is used as a gauge of a community, state or nation's commitment to the health of its citizens.

In a recent year when California had 3,007 infant deaths—far more than any other state—it ranked 45th in its infant mortality rate. The California rate was 5.8, whereas Alabama, with 633 infant deaths—about a fifth of California's total—had an infant mortality rate of 10.2, almost twice California's rate.

Here is how we do the infant mortality rate for the two states.

Number of deaths of infants under 1 year / Number of live births = Infant Mortality Rate

California: 3,007 / 518,229 = .0058024

We multiply the rate by 1,000, as infant mortality is expressed in the number of deaths per 1,000 live births. The result, rounded off, is 5.8

Alabama: 633 / 62,123 = .0101894 X 1,000 = 10.1894 = 10.2 (rounded off)

Apples and Oranges

The series "AIDS in the Priesthood" had electrifying material. The extensively researched 10-part series in The Kansas City Star said hundreds of priests across the U.S. have died of AIDS-related illnesses and hundreds more are living with HIV. The Star reported that Catholic priests are dying at a rate four times that of the general population.

Hold it. Read that comparison again—priests are dying at a rate four times the rate of AIDS deaths in the general population. Priests (all men) are being compared with the general population (men, women and children).

When the proper comparison is made—priests to men in the general population—the death rates are about the same.