Numbers can make or break your copy - includes related information

Numbers can make or break Soon after leaving the cradle, we learn to count. From that time on, numbers are critical to much that we understand and do. So it's not surprising that many writers use numbers to establish contact with readers. Unfortunately, many writers also use numbers badly.

In a random collection of manuscripts, you're likely to find such errors or infelicities as--

* Fuzzy numbers: Words like "few" and "several" that might have yielded to one more phone call.

* Incomprehensible numbers: Big numbers unrelieved by any effort to make them imaginable.

* False precision: A number that is more precise than is physically or mathematically possible.

* Unnecessary precision: A number that, while defensible, is more precise--and harder to read--than is necessary for its purpose.

* Mishandled percentages: Comparative increases or decreases that are mathematically misstated.

Good style books address some, though not all, of these issues. This article will cover the ground more completely, perhaps more clearly, and probably with more acerbity than most style books.

A matter of disrespect

Many writers simply don't like numbers. They may have taken an early dislike to arithmetic. In any case, they probably avoided--or at best tolerated--such reinforcers as algebra and trigonometry, let alone statistics.

Whatever the cause, the consequences can occasionally be extreme. I know one writer who, when he became a managing editor, refused to allow Arabic numerals in print because, he said, they made the page look terrible. He made an exception for the folio line.

More commonly, it is difficult to persuade a writer to do extra reporting to pin down a number. The effort just doesn't seem worthwhile in comparison to the effort, perhaps, to fine-tune a phrase.

More troublesome, though, is the misunderstanding of, and possibly disrespect for, such numbers as do exist. Too many writers, through ignorance or carelessness, handle numbers inaccurately.

That's too bad because numbers, properly handled, are one of the most powerful tools we have for producing a concrete image. Good writers put a lot of energy into turning the abstract into the concrete. They use numbers to help.

Compare, for example, the force of these three unrelated sentences ...

* There were a few "no" votes.

* Several middle managers were let go.

* The parade route was quite long. to the force of these ...

* There were three "no" votes.

*Six middle managers were let go.

* The parade route was four miles.

Admittedly, there are times when it's difficult to get an exact number. But I have found that most often the number is missing because the writer did not bother to press his source with "how many?" To the five W's and one H we tell journalists to chase, we may need to add: "And get the numbers."

The force of numbers in copy is directly related to the images they produce. It is easy to visualize small numbers because we deal with them all the time. They are the size of a family, the four wheels on a car, the number of pennies we get for a nickel, the number of players on a football team, the number of eggs in a carton, and so forth.

Tougher to visualize

Numbers beyond 12 are usually tougher to visualize. They don't connect as readily to daily experience. Even when a number does connect in one context, it may not in another. I can visualize the 102 keys on my PC keyboard fairly well, but I have trouble "seeing" a group of 102 people.

Sometimes we can exploit the ability to visualize small numbers by reducing large numbers to smaller clusters. For me, a bridge tournament of 16 tables is a sharper image than a tournament of 64 players. And, although I don't recommend this antiquated measure, I can also visualize "a gross" better than I can the number 144 because I see it in terms of 12 bundles.

Sometimes, though, we are stuck with big numbers that just won't go away. And it doesn't always matter.

If your readers regularly deal with those big numbers, you don't want to waste their time by making those numbers more accessible to a general audience. The Wall Street community, for example, has no trouble dealing conceptually with a number like $240 million, although most of the rest of us do.

Even a general reader need not always be able to visualize such a number. The number may be less important than the fact that a year ago it was $200 million or that the largest prior deal of that sort was only "half the size."

Those reservations aside, making a large number meaningful in itself adds to readability and comprehension. In last spring's extensive reporting on the student-led protest in Beijing, journalists estimated the size of the crowd in Tiananmen Square at various times as 100,000, 300,000 and a million. The fact that the crowd grew in size was important in itself. But so were the numbers, and they weren't easy to visualize without help.

One way to help is to draw on a familiar image--familiar if only because it's a press or TV staple. For example, a crowd of nearly 100,000 would fill the Rose Bowl and a crowd of 300,000 would fill that stadium three times over. Sticking with football images, a ship 550 feet long would stretch almost twice the length of a gridiron, which may be easier to visualize than a 10th of a mile.

Another technique is to compare the number to another large number which, while not easily visualized, nonetheless has some meaning to readers. A crowd of a million people is about equal to the entire population of Detroit or Dallas. Even if readers don't know either of those cities, the comparison is likely to start them making comparisons with cities they do know.

Sometimes it helps to translate the number into different units of measure. Last spring, NASA launched its Magellan spacecraft on a 795-million-mile journey to Venus. It's easier for us to appreciate the immensity of that distance when we learn that it will take 15 months. Similarly, "a stack of $100 bills as high as Kareem Abdul-Jabbar" or "enough money to buy a 19-inch color TV every day for a year" may convey the immensity of a lottery prize much better than the actual dollar amount.

Turning numbers into things

The problem of visualization is not limited to big numbers. You can tell a reader that a new portable phone measures five inches long, two inches wide and one inch deep--and he will not have any trouble visualizing each of those dimensions individually. But putting those dimensions together mentally is another step. You might do better by telling him that it's "the size of a TV remote control but a bit thicker." He'll get the picture a lot faster.

That's not to knock common units of measure. Most people react instantly to such length measures as inch, foot and yard; such area measures as square foot and square yard; such volume measures as quart and gallon; and such weight measures as ounce and pound.

The images suggested by metric units are less certain. There has been an on-and-off campaign to convert the American people to metrics, and many products are now made in metric sizes. Wine drinkers know liters and auto mechanics know millimeters. But if communication and not "education" is the aim, you're better off skipping metrics.

Even the common English units of measure are usually less easy to visualize than common objects. The image of the TV remote control is a safe one because of the ubiquitousness of TV remote controls. Thanks in part to TV itself, many other images are almost universally familiar--especially those having to do with people, animals, objects around the home, cars and popular sports.

Some images have been overused. It would be nice to find a substitute for "refrigerator-sized," for "the size of a loaf of bread," and for "the size of a beer can." But they do work.

If you're over 40 years old, you had better be careful not to rely on out-of-date images. Once upon a time, everyone knew how big a "cup" or a "pint" was. With home cooking fast diminishing, those images are fading fast. And you'd better forget about "the size of a bread box."

Conversely, as the remote-control example suggests, there are new images to consider. Despite the inexactitudes, you can often be safe with "the size of a Toyota" or "the heft of a computer monitor.

A visual image helps, but it is seldom an adequate substitute for the number itself. And whatever you do with images, both readability and comprehension depend on how you handle the number on its own.

A common error is to cite a number that is overly precise. The excess may simply slow the reader and impede comprehension. Or it may do all that and, in addition, be dead wrong.

For an example of the more benign case, consider such possible phrases as "a 22.3-foot-long limousine" or "a $15.60-an-hour worker." In both examples, the syntax suggests that we are not making a comparison with another car or with another worker. We are merely positioning the car or the worker in a general way. Rounding off those numbers to 22 and 16, respectively, makes for easier reading and more immediate comprehension.

When we do that, we lose precision but not accuracy. Mathematically, when we say "22 feet" we mean somewhere between 21.5 feet and 22.5 feet--a range that encompasses the precise measurement in this case.

Now let's change the syntax a bit. What about, "The limousine is 22.3 feet long"? Here the number is part of the predicate and so carries a lot more emphasis. We're still not comparing the number to another, and we know that mathematically it's okay to round off the number. But do readers understand that, or will they assume that "22 feet" means 22 feet to the nearest inch?

Many editors will do the rounding but will then play it safe by inserting the hedge word "about" ahead of the number. The question to ask first is, What are the possible consequences if readers do assume a precision not intended? Normally, the answer is nil, and the right move is to strike "about." The more "abouts" you find in a piece, the easier that decision becomes.

I alluded to the case of precision that's wrong. That can happen in a number of ways.

Consider the case of a crowd estimate. If you know the size of an area in hundreds of square feet, you can estimate the percentage of the area that's filled by a crowd, calculate that area in hundreds of square feet, and multiply by the average number of people you believe is occupying a 10-foot square. That will give you a crowd estimate. If you did that in Tiananmen Square one day last spring, you might have gotten a figure of 963,478.

No one would put that number in a story. But you might be tempted to write "estimated at 960,000." Even the rounded number, though, implies--because of that first zero--a measurement that's accurate within 5,000 people, or half of a percentage point. Given the approximations used to produce the figure, that's patently ridiculous. It is more reasonable to round off the figure to one million, which implies a figure that's accurate to within 50,000 people, or 5 percent--a not-impossible level of precision. It's better still to acknowledge explicitly the roughness of the measurement by using language such as "estimated to number between 900,000 and a million." Admittedly, that makes it tough for a headline writer.

It's not hard for an editor to be properly skeptical about the precision of a crowd estimate. It's harder when a number comes from a source that purports to be scientific. Too often, in fact, the more precise such a number appears to be, the more credence is placed in it.

Consider this case: The lead of a 1988 story in The New York Times attributed to an epidemiological study the statement that injuries caused by firearms in the United States "cost an estimated $429 million a year in hospital expenses alone and 85.6 percent of that is borne by taxpayers." Two paragraphs later we learned that the statement was based on a study of 131 patients admitted to one San Francisco hospital with firearm injuries in 1984.

Clearly, the numbers are the result of projecting to the United States as a whole the experience of one hospital. The 429 figure implies a figure between 428.5 and 429.5. The 85.6 figure implies a figure between 85.55 and 85.65. Can we believe that such a cost projection can be made with an accuracy of a 10th of a percentage point? Or that the percentage of cost borne by taxpayers can be legitimately estimated within six-hundredths of a percentage point?

At the very least, those numbers should have been rounded to 430 and 86, implying accuracy in the neighborhood of 1 percent. However, a more defensible statement would have been: "... were estimated to cost more than $400 million a year in hospital expenses alone and roughly five-sixths of that is borne by taxpayers." That would put the implied accuracy of the projections within a more believable range of 8 percent to 13 percent.

Another way to produce false precision is to tack zeros onto a decimal figure. This happens most often when a writer is trying to achieve visual consistency in a series of numbers, especially in a table. If you know that one piece of metal is 0.03 inches thick and another is 0.035 inches thick, it's wrong to make the first figure 0.030. The first figure, 0.03, means more than 0.025 and less than 0.035. The second figure, 0.030, means more than 0.0295 and less than 0.0305. In the world of sheet metal, that's a big difference.

You will find examples of false precision in the press every day. The ultimate responsibility lies with editors. The problem starts, however, with researchers of all sorts who, lost in the wonderful world of numbers, forget where those numbers came from.

The most common manifestation is survey results. Suppose you select 1,000 people at random across the United States and ask each one how many hours a day, on average, he or she watches TV. Let's assume you get 714 answers, and 551 of those answers are two hours or more. That's a percentage that's likely to show up in a report as 77.2 or even 77.17. More often than not, even a publicity news release based on the survey will tell you that "77.2 percent of Americans watch TV two or more hours a day." Worse yet, it may tell you that last year the number was only 75.4 percent. And a writer may easily conclude that "TV-watching is increasing."

The truth is that such a survey result has a range of error large enough so that the decimal point in any result is meaningless. It would help if those who promulgate survey results were careful to put a numerical range around each result. That range should be large enough so that it is 99 percent certain to include the true percentage for the total population of interest. That range will often stretch three percentage points, and sometimes twice that much, on either side of the reported result.

In our hypothetical TV case, then, the correct statement might be, "The survey shows that somewhere between 73 percent and 81 percent of Americans watch TV an average of at least two hours a day." Or you may be content to say "three-quarters."

To most of us, it doesn't really matter whether the number is 70 percent or 80 percent. But it may matter if we think the percentage is increasing when it's not. Even if the range of 99 percent certainty in the TV case is only plus or minus two percentage points, the previous year's result falls within the range of error. That means we don't know whether TV-watching is increasing or not.

The perils of percentages

While 100 is a fairly large number to visualize, readers seem to understand percentages pretty well. Sometimes, though, we make it difficult for them.

There is the problem, for example, of the percentage increase. All too often we'll see a sentence like this: "This year, 95 percent of the class passed the reading test, compared with only 82 percent a year ago--a 13 percent improvement." The 13 percent, of course, is wrong. The improvement was 16 percent, found by dividing the difference between the percentages by the first, or lower, percentage.

That doesn't mean that 16 percent is necessarily the best number to use. In many cases, it's simpler and clearer to stick with the numeric difference. But the statement then should be: "...--an improvement of 13 percentage points." That distinction between "percent" and "percentage points" is one that every editor should insist on.

The distinction also applies to decreases. The only difference is that percent in this case is calculated by dividing the difference by the higher, rather than the lower, percentage.

Percentage also cause problems when they grow beyond 100. Take the case of a police statistic indicating that reported burglaries grew from 47 to 106. With no easy ratio to fall back on, a writer might resort to percentages. Too often we may then read that "burglaries increased by 225 percent." It's true that burglaries during the second period were 2.25 times as many as, or 225 percent of, those during the first period. But the growth in burglaries was just 125 percent. In cases like this, the difference between the wrong percentage and the right percentage is always 100.

When applied to a decrease, percentages beyond 100 are a no-no. Since 100 percent represents totality, it is incorrect to reduce anything by more than 100 percent. Such errors usually occur when a writer uses as his divisor the smaller number rather than the larger. But a writer may occasionally apply a percentage greater than 100 to a case where, say, net income of $45 million has turned to a net loss of $15 million. Calling that an income reduction of 133 percent makes a certain kind of sense, but it's not strictly correct, andon a fast read it's mind-boggling.

The problems with comparative increases and decreases are not confined to percentages. They occur as well with such expressions as "three times greater than" and "three times lower than."

To go back to the crowd in Tiananmen Square: When the crowd grew from 100,000 to 300,000 people, it would be correct to say that it "tripled in size," or that it became "three times" its original size, or that it became three times as great as, or 300 percent of, its original size. But it would be, at best, ambiguous to say that the crowd became "three times greater than" its original size. Although most readers will assume you mean the crowd tripled, some careful reader will assume that the crowd grew by three times its original size, and thus quadrupled. The simplest expression, "tripled in size," is much the preferable one.

Now let's assume the crowd shrank from 300,000 to 100,000. Needless to say, it did not shrink by 300 percent or 200 percent, nor was the smaller crowd "three (or two) times smaller than" the larger crowd. It would be correct to say the crowd was "two-thirds smaller." It would be simplest to say the crowd was "one-third its previous size."

In fact, it is often helpful to use a simple fraction, or ratio, instead of a percentage. In the earlier TV example, I suggested that a hypothetical survey statistic might be changed from 77.2 percent, which implies far greater accuracy than warranted, to "three-quarters." However, "three-quarters of Americans" is a pretty abstract concept. A better way to put it is, "... three out of four Americans watch TV an average of at least two hours a day."

Numbers are powerful, but too many numbers in close proximity are a drag. Compare the readability of the following two sentence:

* The five children are 14, 13, 10, 8 and five years of age.

* The five children range in age from five to 14.

Admittedly, there are contexts in which the individual ages might be important to know. More often, the range will suffice.

With care, though, you can convey a bit more information, where it's relevant, and still avoid speckling the page with numerals. For example:

* Although the five children range in age from five to 14, the two eldest are only a year apart.

Numberic overload occurs often when a writer deals with changes over a period of time. Consider the following:

* In 1986, Standard Inc. earned a profit of $870,000 on revenues of $5.7 million. In 1987, profits were up to $3.4 million, on revenues of $12.1 million. And last year Standard earned $11.2 million on revenues of $29.7 million.

If the precise numbers are important, they ought to be put in a table. If year-to-year trends are important, the data ought to be charted. In either case, the text should not contain all of those particular numbers. Here's one of many alternatives:

* Between 1986 and 1988, Standard Inc. quadrupled revenues, from $5.7 million to $29.7 million. During the same period, net income grew by a factor of 12, from $870,000 to $11.2 million.

Watch those averages

An average, or mean, is a convenient way to substitute one number for a whole bunch of numbers. But it's not always appropriate, as we are warned by the familiar story about the man who drowned crossing a stream that averaged only one foot in depth.

Sometimes it's better to use the median rather than the mean. That's especially so when the data are skewed toward the high end--that is, the data stretch out to very large numbers. If you analyze the salaries paid by a small, entrepreneurial company, you may find that the average is $40,000, yet 70 percent of the employees make less. It may be more useful to report the median salary--the salary above which and below which there are an equal number of salaries. In this case, the median might be as low as $20,000.

For many groups of numbers, neither the average nor the median is useful. The average age of the children in the earlier example is 10, and so is the mean age, but both measures are meaningless. The age range is what matters. It would be equally meaningless to say that the profits of Standard Inc., in the earlier example, "averaged $5.9 million over the past three years." The most recent figure and the growth rare are clearly most significant.

More insidious than the meaningless average is the invalid comparison. To resort to a non-numeric cliche, it's important to compare apples to apples.

A familiar example has to do with living standards. Most journalists routinely adjust figures on paychecks and prices in comparing the lot, say, of a Soviet citizen and a U.S. citizen. Many journalists are less careful in using such numbers within the United States itself. A bank president in Knoxville may make 30 percent less in salary than a bank president in Brooklyn. But the comparison isn't useful--not until you factor in the lower cost of housing, commuting and taxes in Knoxville.

It's often possible to use percentages to make valid comparisons. But it's easy to get carried away by percentages. Sometimes they're not appropriate.

If your numbers indicate that in a year's time company A's annual revenues grew from $34 million to $45 million and company B's annual revenues grew from $25 million to $41 million, it may be helpful to point out that company B's revenue growth was 64 percent, that company A's was 32 percent, and that therefore company B's revenues grew twice as fast as company A's revenues.

But suppose instead that company B is small relative to company A, and that its annual revenues grew from $3 million to $5 million. That's still a growth rate that's twice company A's. But the comparison is not meaningful. During that period, for example, company A may have been able to plow $7 million back into the business and company B just $1 million.

Comparisons of survey data can be particularly misleading. Harking back again to TV watching, if you compare a result of 77.2 percent to the previous year's result of 75.4 percent, you get a difference, or growth, of 2.4 percent (or 1.8 percentage points). But if we assume that the range of 99 percent confidence is three percentage points in either direction, the real growth could be anywhere from 10.8 percent to -5.7 percent.

It's easy to make mistakes when comparing sizes. A one-foot tile, for example, is not just 33 percent bigger than a nine-inch tile. When you consider the two areas, you realize that the correct ratio is 144/81, and that the difference in size is 78 percent ("80 percent bigger"). Similarly, a comparison of three-dimensional objects must take into account all three dimensions. A three-foot cube is not 50 percent bigger or 125 percent bigger than a two-foot cube. The correct ratio is 27/8, so the difference in size is 238 percent ("two-and-a-half times as big").

Some objects that come in many sizes tend to grow proportionately in all three dimensions. A boat is a good example. If someone moves up from a 30-foot sailboart to a 40-foot sailboat, that's not an increase of one-third in size, weight or cost. To make the best rough comparison, you need to consider the ratio of the cubes of the length dimensions. Here that ratio is 64,000/27,000, which reduces to 2.4. You can safely say that "the new boat is more than twice the size (and weight and cost) of the old one."

This is just one more illustration of a key precept: You have to think about numbers just as carefully as you do about words. It's worthwhile because, properly handled, numbers are often the most powerful "words" you can use.

John B. Campbell is a magazine editorial consultant. He has been editorial director, Hearst Business Publishing Group, and is a former senior editor of Business Week.

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