Math for Journalists

Math for Journalists• “Two and two the mathematician continues

to make four, in spite of the whine of the amateur for three, or the cry of the critic for five.” -- James Whistler, 1878

• “A single death is a tragedy. A million deaths is a statistic.” -- Joseph Stalin

• “There are three kinds of lies: lies, damn lies and statistics.” -- Benjamin Disraeli

Math for Journalists• Is math your friend? Many people enter

journalism because they hear that there isn’t too much math.

• Consider however stories on job growth, population change, cost of living, unemployment, the stock market, trends, and budgets; they all require numbers.

Math for Journalists• It doesn’t stop there.• The fire had 10 victims, five men and four

women. What was the other one?• The game started at 9 p.m., one hour after

the scheduled 7 p.m. kickoff. How?• The $66 million budget is 33 percent higher

than the 2003 budget of $33 million. Really?

Handling Numbers• First, always check every number in a story.• Just as a good reporter would call a phone

number to make sure it is correct, that same reporter would check any number in a story.

Handling Numbers• Problems often start with percentages.• Avoiding those problems start with an

understanding of what percentages are.• The word “percentage” comes from the

Latin Per Centrum, which means per hundred.

• So 50 percent really means 50 per hundred or 50/100, which is 50 divided by 100, or 0.50.

Handling Numbers• Remember that any time you run across a

percentage, just move the decimal two places to the left.– 50 percent = 0.50– 75 percent = 0.75– 100 percent = 1.00– 150 percent = 1.50

Handling Numbers• There’s a secret to understanding

percentages and it’s one word: Of.• In math lingo, “of” means “multiply.”• A bonus word is “is,” which means

“equals” in equations.

Handling Numbers• Here’s an example.• If you invest $10 with a securities company

and your year-end statement shows your account is 50 percent “of” your original investment, what “is” your current wealth.

• If you triple your money, did you increase your wealth 300 percent?

Handling Numbers• NOPE!• If you triple your $10 investment, you’ve

increased your wealth 200 percent.• You now have $30, but the increase is $20.

That’s 200 percent.• This leads to the weird concept of

percentage increase.

Percentage Increase• A percentage increase means “how much

more” you have of something.• If your boss shakes your hand and tells you

that you will now be making 150 percent of your old $10 hourly salary, you get $15 an hour.

• Instead, ask your boss for a 150 percent raise. That means you would make $25 an hour.

Percentage Increase• Here’s the formula for percentage increase:

(New number - Old number) x 100Old number

= Percentage Increase

Percentage Increase• So if your $10 salary increased to $25, this

is the size of your raise:($25-$10) x 100 = $15 x 100 = $1,500 $10 $10 $10

= 150 percent• That’s all you need to know about

calculating percentage increases, except for one little item.

Percentage Increase• Don’t use rounded numbers with percentage

increases. • Here’s an example.• Say the city’s budget is $4.7 million, up

from $3.7 million the past year.• Using the formula we would arrive at a

27.03 percent increase.

Percentage Increase• Sadly, I fudged the budget numbers. The

problem is that I used rounded numbers.• The old budget was really $3,651,001. The

new one is $4,748,988.($,748,988 - $3,651,001) x 100 =

$3,651,001$1,097,987 x 100 = $109,798,700 = $3,651,001 $3,651,001

• percentage increase = 30.10 percent

Percentage Increase• As you can see, 30.10 percent is different

from 27.03 percent.• That’s why you don’t use rounded numbers

when you figure the percentage increase.• Remember: Whenever you see a chart or

graphic that uses rounded numbers, be sure that the footnote makes this clear.

Rounding Numbers• To round any number, just select how many

digits you want it to have.• If the NEXT digit is 5 or more, round UP.• If it is less than 5, make no change.• For instance, round 50.970 to the nearest

hundredth. You get 50.97. Round 50.975 and you get 50.98.

• Round either of those to the nearest tenth and you get 51.0.

Percentage Increase• There is one more common trap. • Let’s pretend that 55 percent of Americans

voted in the 2000 election. Now let’s say that 60 percent vote in the 2004 election.

• So that’s 5 percent increase, right?• Wrong. You cannot directly compare the

two because the underlying numbers are different: some voters died, some moved overseas, etc.

Percentage Increase• What you can say, however, is that the

number increased by 5 percentage points.• You cannot calculate the percentage

increase in this example, unless you have access to the original numbers.

• Be careful.

More Math Stuff• Average. To get the average, just add the

numbers in a series and divide by the total numbers you added.

• For instance, the average of five numbers -- 4, 6, 8, 9 and 13 -- is 40/5=8.

• The average is also sometimes referred to as the mean.

More Math Stuff• Sometimes averages or the mean can be

misleading.• Say a company president makes $200,000

and the four employees each make $20,000.• This leads to an average salary of $56,000

($280,000/5=$56,000).• While the average is lucrative, the median

tells another story.

More Math Stuff• Median. The median is the middle number. • In the case of the office it’s $20,000. (The

series contains $200,000, $20,000, $20,000, $20,000 and $20,000.)

• Remember: If you see the word median in a story, be sure that the story explains what this number is. A median house price indicates that half the homes cost more and half cost less.

More Math Stuff• Rates. Sometimes numbers are so large that

the best way to communicate them to the reader is to show their relationship to another, smaller number. There are all kinds of rates.

• Property tax rates. These are usually expressed as taxes per $100 of assessed property value.

More Math Stuff• So, if your tax rate is $1.25 on a house

valued at $100,000 with no exemption, the tax bill would be:

• Tax rate x assessed property value =• ($1.25/$100) x $100,000 =• $0.0125 x $100,000 = $1,250

More Math Stuff• Murder Rates. If Sin City had 5,000

murders in a year and Angel Heights had 500 murders that same year, it is possible to compare the two rates.

• To do it, you have to have the population for each.

• Fortunately, places like the Oklahoma Department of Commerce and U.S. Census Bureau track the population.

More Math Stuff• If Sin City has 8.3 million people and Angel

Heights has 400,000 here’s the math:• Sin City = 5,000/8.3 million = 0.0006024• Angel Heights = 500/400,000 = 0.00125• As you see, it’s tough to compare these two

decimals. That’s why murder rates are normally per 100,000 people.

• To get that number, simply multiply by 100,000.

More Math Stuff• Sin City = 0.0006024 x 100,000 = 60.24 deaths• Angel Heights = 0.00125 x 100,000 = 125 deaths• Now, as we can easily see, Sin City is much safer

than Angel Heights, recording 60.24 deaths per 100,000 population compared with 125 deaths per 100,000 in Angel Heights.

• These same formulas work with other calculations, such as infant mortality, which is usually expressed in deaths per 1,000 births.

Scientific Polls• Editors, and therefore reporters, have a long-

standing fascination with polls. Here are some basic rules for handling polls.

• 1. There must be a scientific basis for the selection of those interviewed.

• 2. The methodology must be listed in detail.• 3. A margin of error must be listed.• 4. The above basics must be in the story and in

any accompanying graphic.

Numbers in Print• As you have noticed, the AP Stylebook has a

number of rules for numbers. Keep these in mind.

• Never spell out ages. He is 5.• Never spell out votes. The council voted 5-4.• Never spell out percentages. About 14 percent of the

class is paying attention.• Never spell out money. I found 5 cents.• Never spell out numbers with millions or billions.• Never spell out height or depth. She is 6-foot-2. The

closet is 4 feet by 12 feet. A 3-by-5-foot rug will fit.

Almost Done• Since you are now brain-dead, here’s a few

more things to pile on while you’re helpless.• Very Kiloton: a thousand tons, 1,000• Very Megaton: a million tons, 1,000,000• Very Gigaton: a billion tons, 1,000,000,000• Big Teratons: a trillion tons, 1,000,000,000,000

• Itty Millisecond: thousandth, 0.001• Itty Microsecond: millionth, 0.000001• Itty Nanosecond: billionth, 0.000000001• Bitty Picosecond: trillionth, 0.000000000001

The Final Stop• A few metric conversions as a send off:• 1 pint = 0.4732 liters• 1 quart = 0.9464 liters• 1 gallon = 3.7854 liters• 1 inch = 2.54 centimeters• 1 foot = 0.3048 meters• 1 yard = 0.9144 meters• 1 mile = 1.6093 kilometers• 1 meter = 100 centimeters• 1 kilometer = 1,000 meters