“All the math you need to know to tell your stories you learned by the 4th grade.”
— Malcolm Gibson

Don't be numbed by numbers
(or the quest for accurate numbers

“Remember, 'number' can refer to numerals, but it also can mean that it 'numbs' people. Numbers can be a real 'number'* in stories.”
— Also from Malcolm

*Prounounced NUM-uhr, as in “My face is number after the second injection of Novocain.”

   “Aha, this probably contains an error! I must check it carefully.” 
    That's the reaction any good writer, reporter or copy editor should have when encountering a number in a story, caption, headline or graphic. 
    Many of us who are attracted to writing and editing profess a regrettable lack of interest in and understanding of numbers. The following material is designed to help you realize that most such numbers are not baffling. You already know enough or soon can learn enough to equip you to "do the math" when numbers appear in a story you are editing. And never — repeat, “never”— make the reader “do the math.” 
    Remember, credibility is a newspaper's most prized possession. Errors erode credibility. Quantitative information breeds errors. So develop this reflex action: When you spot a number in a story, assume it is incorrect until you do the math and have assured yourself the information is reliable enough to warrant risking your newspaper's credibility. 

The Easy Numbers
    Checking the accuracy of some quantitative information requires no more than fourth-grade arithmetic and the determination to be careful. Such is true for these types of errors: 

    Inconsistency: The numbers need to be consistent with the other information given. 
    For example, one reporter wrote: The governor said his highest four priorities for the coming year would be education, crime and economic development. 
    An effective copy editor should deliberately count the priorities noted. Doing so reveals the inconsistency: Three priorities are noted, not four. Either the reporter omitted one of the four or the governor identified only three priorities. The copy editor should consult the reporter and make the appropriate change in the story. What do you do if the reporter or source is not available for confirmation? Change the four to three or, better yet: The governor said among his highest priorities for the coming year were education, crime and economic development. 

    Six of one, half dozen of another? Similar problems often arise when these types of topics are noted in stories. Always make sure, even if you have to use your fingers and toes to do the counting. 
    1. A story says six people were arrested in a drug raid, but seven names are listed. 
    2. A story reports that a $723,000 expenditure included $500,000 for payroll expenses, $180,000 for travel and $121,000 for materials and supplies. (Note that those items total $801,000, which is more than the reported total of $723,000.) 
    3. A story states that the school's enrollment dropped by 242 students since last year, and later the reporter writes that this year's enrollment is 16,456 compared with last year's 16,688. (Note that when you compare the two enrollment numbers you find a difference of 232, not 242.) 
    4. An obituary about a woman dying in January 1998 says she was 75 years old at the time of death. Later in the obituary her date of birth is given as December 20, 1923. (Note that if the date of birth is correct, the age should be 74. She would not have been 75 until December 1998.) 

    Nonsense: Insist that numbers and the terms accompanying them make sense to you. 
    For example, a story arrived at one newspaper's copy desk stating that the Civil War was fought in the 1960s. That newspaper and its readers were fortunate that an alert copy editor knew that the war dated back to the previous century. 
    Similar problems can arise when these types of topics are noted in news and feature stories: 

      Time is of the essence. A story states, “The average wait for a new driver's license in Lawrence is 90 minutes, compared to the state average of an hour and a half.” (Because these compared intervals are the same, there likely is an error here. Otherwise, the sentence should be recast to note that the wait in Lawrence is the same as the state average.) 

    Hmmm, a new twist on crime. Another story states, of Topeka's 965 victims of serious crime last year, 321 were arrested. (An alert copy editor should quickly detect the absurdity here; crime victims should not be subject to arrest.) 

    Now that's a bargain! Too frequently a reporter will write something like this: “The new hospital is expected to cost between $26 and $31 million.” (A good copy editor immediately notes that no hospital can be built for $26 and thus edits the story to say between $26 million and $31 million.) Note: This is a common error because of the way we speak. But what’s OK in conversation is not always OK in writing, and this is one of those cases. 

    Bright kid? An obituary says Mrs. Jane Doe, who died in 1997 at age 81, was graduated from the University of Kansas in 1926. The alert copy editor does the math, realizes that Mrs. Doe likely did not graduate from the university at age 10. 

Some More Challenging Numbers
   Some efforts to correct the numbers in news and feature stories require a bit of specific knowledge. Especially notable are these: 

    Percentages: Sometimes raw numbers fail to reflect significance. Is an increase of 500 a large increase? The answer, of course, is that it depends on the context. 
    For example, if there had been 650 cases of AIDS reported in Kansas last year, and this year's total had grown to 1,150, that increase of 500 would have been dramatically large. But if there had been 42,250 AIDS cases reported nationally in the same period, and the national total had grown to 42,750, that increase of 500 would have been relatively insignificant. 
    The concept of percentages is a powerful tool with which we can tell readers the context of many raw numbers. The two most common uses of percentages in news and feature stories are: 
    1.  To show how a part relates to the whole (i.e., how much of the total national budget goes for defense). 
    2. To show in relative terms how much something has increased or decreased (i.e., relatively how much the price of gasoline has increased in a month). 

    Percent calculation: The calculation of a percentage simply involves dividing the part by the whole. For instance, if a country's national budget was $1,322 billion, and the defense department portion of that budget was $268 billion. To determine what percent the defense budget was of the total budget, we calculate as follows: 

% = “part” divided by the “whole”
(“percent” equals the “part” divided by the “whole”)

defense budget as %
of total budget
$268 billion divided by $1,322 billion
.2027231 or
20 percent
     Note that we convert the mathematical answer .2027231 to a percentage by moving the decimal point two places to the right. Usually it also aids reader understanding to round the percentage off to a whole number, if doing so does not mislead or erode credibility. 

    Percent change calculation: The formula for calculating a percent increase or decrease involves one additional element. Remember that here you are calculating the percentage of change from the original number. Thus, you first must calculate the amount of the change. Then you divide that amount of change by the original number. To determine how much the price of milk has increased in a month from $1.09 to $1.19, we calculate as follows:

new price minus old price
divided by old  price
so price increase as
% of old price
$1. 19 minus $1.09
divided by $1.09
(or .10 ÷ 1.09 =
That's a
9% increase
    What if the price of milk went down, not up, and you needed to calculate the percent of change? The same applies — except this time the “part” number is the larger of the two. (When we talk of “part” and “whole” number in dealing with percentages, we really are talking about the new number or the number that changed (“part”) against the original or old number (“whole”) before a change.) So, if milk went from $1.19 to $1.09, you would do the following: 
new price minus old price
divided by old price
so price decrease as
% of old price
$1. 09 minus $1.19
divided by $1.19
(or .19 ÷ 1.19 = .080403)


That's an
8% decrease

    When you see a percentage in a story, recalculate it. If the story does not contain adequate data for such a calculation, ask the reporter for the needed specifics. In most instances, those specifics also belong in the story, so you should insert them. And, again, don't make the reader do percentages if percentages are important to the story. You do them for the reader. 

    Warning! Beware when comparing percentages. Be careful not to confuse yourself or the reader when a story compares two or more percentages. 
    For example, if 68 percent of American taxpayers had filed their tax returns on or before April 15 in 2006, and 72 percent of them had done so in 2007, it clearly would be accurate to say that there had been an increase in the percentage of taxpayers filing by the deadline. But a naive or careless person might note that the difference between 68 percent and 72 percent is 4 percent and thus be tempted to say that the increase was 4 percent. But that would be incorrect. (And, you should know, this is one of the most common mistakes made when dealing with numbers. So, don't say you haven't been warned.) 
    It is true that there would have been an increase of four percentage points, but that is not the same as 4 percent. Except as they relate to interest rates, changes in percentage points tend to be useless information, because they fail to show the needed context. But if you were to do it, what would be the percentage increase between 68 percent and 72 percent? Use our handy-dandy formula: 

new % minus old %
divided by old %
so increase as
% of old price
72 minus 68
divided by 68
(or 72 ÷ 68 =
That's a
6% increase

    Opinion Polls:
Stories about opinion polls often are misleading because the reporter and the copy editor did not exercise adequate care. Some of that care should be focused on checking the numbers using techniques mentioned earlier, and some care should be aimed at ensuring that certain key questions about the poll are answered, including these: 
    1. When and how was the survey done? 
    2. How many were interviewed? 
    3. Who paid for it? 
    4. What is the margin for error? 

    Margin for Error: Any opinion survey worthy of a news story has been analyzed by the pollsters in ways that yield what is called a margin for error. This simply refers to the difference between the results obtained from the survey sample and the results that would have been obtained if the entire group (i.e., every student at the University of Kansas or all the females between 25 and 35 in Oklahoma) had been questioned. 
    Most experts in statistics agree that if a survey is administered to several hundred people who have been carefully and randomly selected, the results can accurately reflect the opinion of the entire U.S. population within a 3 percent margin of error. This means that the results of such a poll would be within three percentage points (plus or minus) of matching the results if everyone in the country had been polled. This means the results could swing by as much as 6 percent. 
    So if you edit a story about a pre-election poll involving two presidential contenders and it shows the Democrat with 53 percent and the Republican with 47 percent, a 3 percent margin of error means that the election is too close to call. Your story should say that. 
    Remember that telephone polls omit from the sample everyone who does not have a phone. In certain rural areas, this can omit a notable percentage of the population.  And with student and urban populations, it eliminates many who rely only on cell phones.

Simplify, Simplify, Simplify
    In addition to being accurate, numbers should be presented clearly and simply. 
    Sometimes this means changing  “66.32 percent of those polled said” to read more simply “two-thirds of those polled said.” 
    Sometimes it means organizing component numbers so they are clear. For example, if the lead of a story says $3.9 million was spent last year to refurbish three local elementary schools, a reader should be able to find quickly and easily in the story that $1.2 million was spent on Washington School, $1.8 million was spent on Lincoln and $.9 million was spent on Jefferson. These data should not be scattered. A discerning reader who wants to add these numbers to see that they total $3.9 million (as I hope you did) should be able to do so quickly and easily.

Keep Your Calculator Handy  
   It should be clear from these observations that an effective copy editor must have easy access to a calculator at all times. Many newsroom computer systems include calculator capabilities. Where computer calculations are not available, use a hand calculator. 


Updated Aug. 13, 2009