Let’s start with a math problem:
JOURNALISTIC MATH TEST Q1: In which country has COVID-19 spread to the greatest part of the population?
C) San Marino
D) United States
Did you answer D?
If so, it may be because of the reports that the United States leads the world in coronavirus cases and deaths. It’s true that as of mid-June there were around 2 million cases in the U.S., 240,000 cases in Spain, 60,000 in Belgium and 700 in San Marino.
But to know whether COVID-19 has spread more in the U.S. than elsewhere, you need to factor in total population. For every 100,000 inhabitants, there were 618 cases in the United States, 523 in Belgium, 519 in Spain and 2,045 in San Marino. So the correct answer is C.
But in journalism, we put things in context. And with numbers, that means evaluating their significance, which is key in an epidemiological crisis that is largely a numbers game.
Here are some tips on dealing with numbers in stories and making sure your calculations are foolproof, along with some more problems to test your journalistic math skills.
Be clear and consistent
At NPR (which follows AP style with some exceptions), we spell out whole numbers up to and including nine. Numbers from 10 upward, as well as those in headlines, ages, percentages, fractions and decimals, are represented with numerals.
In any story, numbers should be used sparingly. They should be there for a reason. We don’t want to overload people, especially in audio scripts, where one number per sentence is usually enough.
JOURNALISTIC MATH TEST Q2: Which is written better for audio?
A) The organization carried out the survey with 40 people calling 489 clinics around the country in the span of three days.
B) The organization had 40 people working on the survey. They called 489 clinics around the country. And they did it in three days.
If you chose B, you will make great radio.
Help the reader or listener visualize the number with equivalents, especially when giving measurements.
JOURNALISTIC MATH TEST Q3: Which is a better way of representing area?
A) The wildfire consumed 660,000 acres.
B) The wildfire consumed an area the size of Rhode Island.
If you chose A, consider a career change to engineering. (Full disclosure: Many years ago I went from engineering to journalism!)
Check the math
Double check any calculation that appears in your story. And then check it again. Do this, even if it’s attributed.
JOURNALISTIC MATH TEST Q4: Last year this actuality appeared in an NPR story about distracted driving.
“The average time that somebody spends looking at the phone is four seconds. Now if you are driving at highway speeds, four seconds, you’ve just traveled four football fields without looking.”
Was the math correct?
Here’s how to check:
Assume that by “highway speeds” the speaker means around 65 miles per hour.
A mile is 1,760 yards. So multiplying 65 miles per hour x 1,760 yards per mile, we find that car going that speed is traveling at 114,400 yards per hour.
Now we have to convert from hours to seconds. There are 60 minutes in an hour and 60 seconds in a minute, so 60 x 60 gives us 3,600 seconds in an hour.
So we divide 114,400 by 3,600 to figure out that the car is moving 31.77 yards per second, which means that in four seconds the car covers 127.08 yards.
A football field is 100 yards long. Four football fields would be 400 yards, or 480 yards if you include all the end zones. Either way, the speaker’s math was way off. Even if you had assumed a different highway speed, like 55 or 75 mph, you would see that the actuality was wrong.
NPR had to remove the actuality and issue a correction, even though the mistake was the speaker’s. Checking the math (and triple checking by reading this Politifact column) would have prevented the error.
A percentage is a ratio of something relative to the total, expressed in hundredths. If you have three apples and two oranges in a basket, for a total of five pieces of fruit, then you’re carrying 60% apples and 40% oranges.
When you describe a change, then you have to give a percentage relative to the amount you start with. For example, if you initially had only the three apples in your basket and then you added the two oranges, then you would be increasing the fruit content of the basket by 66%. That’s because you divide 2 oranges ÷ 3 pieces of fruit initially, not 2 oranges ÷ 5 pieces of fruit at the end.
An increase in percentage points is a completely different concept. It is the incremental change arrived at by adding or subtracting percentages. So if an interest rate goes up from 2% to 3%, that’s a 50% increase but a jump of only one percentage point.
JOURNALISTIC MATH TEST Q5: In a middle school science class, 75% of students got an A on their first quiz. On the second quiz, 100% got As. What was the percent increase in students getting As?
C) It’s impossible to know without interviewing the teacher.
D) It’s hard to believe that everyone got As, so you need to talk to all the students to make sure the question is correct.
If you answered C, your suspicion game is strong. And if you answered D, your journalistic instincts are sharp. But the correct mathematical answer is B. The 25% of kids who additionally got As is one third of the initial 75%, so that’s a 33% increase. If the question had asked “what was the increase in percentage points,” the correct answer would have been A.
Speaking of percentages, a news-friendly way of expressing a percentage is as a ratio. It’s easier to grasp that 1 in 12 people in a city rely on food banks, than to try to visualize 8% of the population.
On the other hand, you may want to use percentages when dealing with fractions that don’t lend themselves to simplicity. While 1 in 5 may be a better way of representing 20% of a group, 12 in 50 is better rendered as 24%.
Or you could say, about one in four. Which brings us to approximation.
Approximations and rounding
Approximation is a splendid thing. It makes things easier for the reader or listener. But avoid approximating an exact number.
Let’s say you’re not sure whether there are 292 or 293 passengers and crew on an aircraft. You can say there are “around 290,” or “nearly 300,” or even “at least 292.” But “approximately 292 passengers and crew” is an oxymoron because 292 is an exact number.
Just because you know the exact number of something doesn’t mean your audience needs to know it. If you’re reporting that a state has 83,845 coronavirus cases, consider rounding it off to say 84,000 cases.
If you have several figures, be consistent with the ones you round off.
JOURNALISTIC MATH TEST Q6: Which of the following are consistent?
A) In mid-May, Tennessee had 18,301 coronavirus cases and 301 deaths while Minnesota had 17,038 cases and 757 deaths.
B) In mid-May, Tennessee had around 18,000 coronavirus cases and 300 deaths while Minnesota had 17,038 cases and 757 deaths.
C) In mid-May, Tennessee had 18,301 coronavirus cases and around 300 deaths while Minnesota had around 17,000 cases and 757 deaths.
D) In mid-May, Tennessee had around 18,000 coronavirus cases and 300 deaths while Minnesota had around 17,000 cases and 760 deaths.
The correct answers are A and D.
Robert Benincasa, of NPR’s Investigations Unit, crunches a lot of numbers when he analyzes data for his reporting.
“You always have to ask, ‘Compared to what?’” he says. “To me, that means that most of the time, raw numbers aren’t enough.”
That’s why, as we saw above, the United States isn’t the country with the most pervasive spread of coronavirus. It’s the same for many other data-based stories.
Benincasa says that typically with such tallies, “there needs to be a denominator, and it needs to be the right one.”
So, while U.S. public debt is at the highest level in history, it was higher around World War II when compared to the size of the national economy. And when you talk about how many people die on the roads each year, the fatality rate per population size and miles traveled is what really matters.
We all know that we are now in the 21st century because our count of centuries begins in the year zero.
The same principle applies to other time periods. A 14-day lockdown that began on May 4 didn’t end on May 18. It ended on May 17, because May 4 counted as the first day.
Use your fingers to count the days if you have to. Or make tick marks.
Billions and billions
We live in an age of billions and trillions, so get the number of zeros right. Sometimes, they get lost in translation.
Until the 1970s, the British said “one thousand million” for the number Americans refer to as one billion, while for them one billion was our trillion. And a trillion to them was actually a billion of our billions. But just because the British followed the lead of their former colony doesn’t mean non-English speaking countries have done so.
In Spanish-speaking countries — though not among hispanophones in the U.S., according to the Royal Spanish Academy — a one with nine zeros after it (1,000,000,000) is mil millones (a thousand millions) and un billon is a one with twelve zeros (1,000,000,000,000).
Other languages including Arabic, French and Portuguese have similar conventions, though it varies by country. In Chinese, one billion is 十亿 (shíyì), which is “ten one hundred millions.” So if you’re interviewing a non-native English speaker keep in mind that their billion may be many multiples of yours. It’s worth asking, “how many zeros does your billion have?”
If you read all the way to here, you clearly care about getting your numbers right. May your journalism be mathematically sound — to the thousand-millionth degree!