How the media figure percentages

This quote from the Associated Press appeared in the Colorado Springs Gazette on December 13, 2009.

In 1973, there were around 600,000 officers and about 156 gunfire deaths. Currently there are about 900,000 law enforcement officers in the U.S. and only 47 gunfire deaths this year - a per-capita decrease of nearly 21 percent.

Any grade school graduate would calculate a decrease percentage by dividing the change in the measurement by the initial value and multiplying by 100. But that would be:

100×(156 - 47)⧸156 = 69.9%

Checking the concept with a simple rule of thumb, a reduction to no deaths, change the -47 to zero, comes out as a 100% decrease as one would expect.

So just where did the published 21% number come from? The AP does use the term per-capita which once meant per head which was a way to describe a population count in an easier way than by counting feet and dividing by two. Nowadays the term is deprecated because a per-capita tax is a political no-no. Let's assume that the AP employs the term to mean per-policeman.

Dividing the death numbers by those counts of policemen (600,000 and 900,000) yields two other numbers which could be called deaths per policeman: 2.60×10⁻⁴ [2.60E-04] for 1973 and 5.22×10⁻⁵ [5.22E-05] for 2009. Redoing the above calculation using the per-policeman numbers yields 79.9% as the percentage decrease. No. That can't be what the AP means.

Perhaps the AP just took the ratio of the two death counts and mistakenly reported that as a decrease. That arithmetic generates the answer:

100×(47⧸156) = 30.1%

But it's still not the answer that AP shows.

OK. Let's see if they did that with their per-capita method. Bingo!

100×(5.22×10⁻⁵ ⧸ 2.60×10⁻⁴) = 20.1%

which AP reports as "nearly 21%". Or were they using some other computation scheme? In any case that number is a ratio of new to old, fails the rule of thumb test, and cannot be called a decrease in any perversion of English grammar.

In my opinion the authors at AP are not ignorant of simple grade school arithmetic. Rather they are seeking a number to publish which has the desired effect on a reader who is assumed to absorb the text without thinking. It's the same procedure that advertisers use to push discounts and savings while deliberately suppressing the price. Such nonsense does not belong in the news section of a newspaper even when it comes blessed by AP. The Gazette's editors could at least have added a sic after the 21% value.

As it was shown in the Gazette:

Did you notice that the headline talks about a pernicious increase in 2009 but the body goes on to describe a decrease? Do you think they had a reason for selecting the lowest number they could come up with to describe the decrease? Do you think the gratuitous comments on gun-control that AP slipped in had anything do do with the overall decrease?

Every article on page A3 came from the Associated Press. Which ones should I believe? Did they round up 217 mustangs or 217 mustang hooves? Was it 19 or 998 people arrested in Copenhagen? 2600 pounds or 2600 kilograms of uranium to Iran? The numbers are the most important things in the articles and they just have to be reliable. Local editors need to take some responsibility for what they print even when it comes from the Associated Press.

Your comments are welcome and might appear here depending on how I feel. Send them to Doug McNutt. Include "AssPress" in the subject line to get by my spam filters.