"We do not expect reporters to be mathematical geniuses. But we do expect them to sidestep their mind-numbing fear of mathematics long enough to ask, 'Does this make sense?' 'What would I conclude from these numbers?'"
- A.K. Dewdney, in 200% of Nothing: From Percentage Pumping to Irrational Ratios, an Eye-Opening Tour through the Twists and Turns of Math Abuse and Innumeracy
At a recent seminar, an editor recalled a tax issue in which the funds raised would amount to a two-thirds jump in spending on a project. She dutifully reported every relevant number her sources gave her, acknowledging much later that she had no clue what any of them meant.
She mentioned that numbers meant nothing to her, other than a quite effective way to mess up a perfectly good story.
It wasn't until years later that she knew enough about numbers, about perspective, and about selectively using statistics in stories, to make sense of the budget issue.
So when it comes time to write about the math that every reporter should know, it's also time to step back and attack the journalist's fear of numbers.
This month, I'll give you a mercifully short list of techniques you must know, and your editors expect you to know.
Next month, I'll give you a couple of tricks you can play on yourself to help overcome the panic, or glazed eyes, that come when you have to deal with numbers or statistics.
Fractions and percents
A percent is just a fraction, expressed as 100ths. You know one-quarter is 25 percent. You may not remember why.
It's because 1 divided by 4 is 0.25. So think of the words, "out of" when you have to figure a percent of total.
Formula: (Portion/Total) X 100 = Percent Example: If 250 people voted for Councilman Jones, and 270 voted for Councilwoman Smith, then the percentage of people voting for Smith is 270 out of (270+250), and the formula is: 270 / (270+250) X 100, or 52 percent.
Percents
This is just the change over time, divided by the starting level. Remember, it's NOT the little number divided by the big number. Changes can be greater than 100 percent. Formula: (Difference / Old value) X 100 = Percent difference, or ((New - Old) / Old) X 100 Example: A budget item rose from $1,500,000 to $1,600,000. Rounding off, the percent change is: (16-15)/15, or 1/15th, or 0.06667 or 6.7 percent. Notice that you can reverse the process: 1/ 0.06667 = 15, so the fraction is 1/15th.
Per capita, and other rates
You often need to level the playing field. It's not fair to say that New York has more crime than other areas, or that drivers of Fords die more frequently than Hyundai owners.
You need to figure a fraction, and often raise it to a bigger base than a percentage, to make a fair comparison.
This is no different than percentages, only the "out of" word gets changed while you change the base to 1,000, 100,000 or something else.
There's nothing magic about 100 as a base. It's convenient, and lots of people think that way. But sometimes, that turns into too small of a number, like in the number of infant deaths each year.
The hard part is figuring out the base. Often, it's the corresponding population of a county, a state or the nation.
For instance, crime rates are computed by dividing the number of crimes by the number of people living in the area, and multiplying by 100,000.
Other times, it's something else that levels the playing field: Infant deaths divided by live births, driver deaths divided by the number of cars on the road.
Formula: (Number / Some base) X whatever will give you a round number, usually 1,000 or 100,000.
Example: There were 80,000 crimes in Pittsburgh out of a population of 2.5 million. There were 60,000 crimes in Tucson out of a population of 700,000. How can you compare the two numbers?
Pittsburgh = 80,000/2,500,000 X 1,000 = 32 crimes per thousand residents Tucson = 60,000 / 700,000 X 1,000 = 85 crimes per thousand residents.
Different kinds of averages
You almost never hear anyone talk about average incomes or average home values. There's a reason they focus instead on the median value. It's because medians ignore the effects of very high and very low values. Average: (Sum / Number of items) Median: The middle item, in a sorted list Mode: The most common value. So in a list of home values [$60,000; $65,000; $70,000; $80,000; $85,000; $130,000; $250,000; $250,000] here are the three possible answers: Average = $148,125, or $1,185,000 / 8 Median = $82,250 (average of the 2 middle values) Mode = $250,000 Most people would agree that the median is the more "typical" value. That's often how you can express it in a story, too.
Adjusting for inflation
It may not be necessary for you to ever know how to adjust for inflation, only that you know you should adjust for inflation. There are plenty of tools available on the Internet for you to use. Many newsrooms keep on hand an inflation calculator. But should you want to try it yourself, make one decision first - what year's dollars do you want to use? I usually choose the most recent, since our audiences understand what a dollar buys today. To do this:
Formula: CPI New / CPI Old X Value Old
Example: Teachers made $28,000 in 1985. How much would that be in today's dollars? The Consumer Price Index was 107.6 then and stands at 157.3 (for year-end 1996): (157.3 / 107.6) X 28,000 = About $41,000.
Compound changes over time
Again, you may never have to do this, but you should know about it. If politicians promise that spending will rise only 3 percent a year, after inflation, it doesn't rise 3 X 10 or 30 percent over 10 years. It rises much more. It's the same principle that makes your own nest egg grow. To compound, convert the percentage back to a multiplier. For 3 percent, it's 1.03, or (3/100) + 1. Then take it to the 10th power: 1.03^10 = about 1.35. Now reverse the process, subtracting 1 and multiplying by 100 to get about 35 percent. Going backwards just reverses the process and use 1 divided by the number of years as your exponent. To get an annual rate for a 35 percent jump in spending over 10 years, use this formula: 1.35^(1/10) = about 1.03, or 3 percent a year.
A look ahead
A far bigger problem that I see on the road, though, is the phobia many reporters have of numbers.
Those who aren't afraid learn the formulas above quite easily, if they don't already know them.
Those who are can get all the cheat sheets in the world, but they simply can't focus their attention on the process.
So getting over the fear is the first step toward actually understanding numbers, rather than memorizing formulas. We will discuss ways to overcome that fear by rounding off, developing a sense of scale, watching television and asking your best sources for help.
These tips will help reporters get over their math phobia and will help readers better understand their news and their world. Sarah Cohen can be reached at (301) 942-2199, or send e-mail to sarah@nicar.org