Math for Journalists

The Journalism School’s budget for computer programs jumped from $5,500 to $7,300. By what percent did it increase?

Percent difference = N/O – 1 (New number/ Old number -1) (7,300/5,500) = 1.327

Subtract 1, and you get .327

To convert .327 to a percent, Move the decimal two places to the right: .327 = 32.7%

Comparing apples and oranges • Rates (percent) • Index numbers (CPI) • Percentile rankings (SAT v. ACT) • Standardized scores (standard deviation units)

Percent is a rate per hundred

• First, convert the fraction to a decimal by division.

• ¾ = .75

• To get a rate per hundred, multiply by 100 • .75 * 100 = 75 • Another word for “rate per hundred” is “percent.”

Other rates

• To get a rate per thousand, multiply by 1,000.

• .75 * 1000 = 750 • To get a rate per hundred thousand, multiply by 100,000 • .75 * 100,000 = 75,000

Example

• A military unit of 41,000 persons had 49 suicides over a 10-year period. Its 10-year suicide rate was: • .1195 percent • 1.195 per thousand • 119.5 per hundred thousand • Choose a rate that yields whole numbers

A gallon of paint covers 400 square feet. How many gallons to coat one side of a fence that is 7 feet high and 300 feet long?

First figure the area: 7 * 300 = 2,100 square feet

A gallon does 400 square feet.

How many 400s in 2,100?

2,100/400 = 5.25

The police force has 693 officers, 5 percent more than it had before. How many did it have before?

What number when multiplied by 1.05 yields 693?

Answer: 693/1.05

660

Valuation is $127,500 and tax is $1,466.25. What is the rate per $100 valuation?

How many hundreds in $127,500?

1,275 What number multiplied by 1,275 yields 1,466.25?

Answer: 1,466.25/1,275 = $1.15

If algebra makes it easier …

1,275 * X = 1,466.25

X = 1.466.25/1.275

X = 1.15

The pizza problem

¾ of a pizza To divide 4 ways

3/4 = 6/8 = 12/16 Each roommate gets 3/16 of the pizza.

Do order-of-magnitude checks The coach expressed concern because .05% of his team members failed a preliminary drug screening.

Drug-using athletes

5 percent = 5 out of 100 or 1 in 20 .5 percent = 5 out of 1,000 or 1 in 200 .05 percent = 5 out of 10,000 or 1 in 2,000

RALEIGH, N.C. (AP) - American history is being preserved at the North Carolina birthplaces of two of the nation's early presidents, James K. Polk (1845-49) and Andrew Johnson (1865-69). Polk pushed an expansionist vision during his term, adding about 500 million square miles to the Western United States.

Think!

The distance from New York to Los Angeles is about 3,000 miles.

A square with 3,000 miles on each side would contain 3,000 * 3,000 or 9 million square miles.

Therefore, the entire continental USA could easily fit inside 9 million square miles.

RALEIGH, N.C. (AP) - In an Aug. 17 story about presidential birthplaces, The Associated Press erroneously reported the amount of territory added to the United States during the presidency of James K. Polk. The correct figure is 1.2 million square miles, not 500 million square miles.

Anything wrong?

Average gas price likely to top $2 Fuel could hit record as soon as this weekend

The record is …

In nominal dollars: $2.05 In constant 2004 dollars: $2.95

Broiled Filet Mignon, French Fried Potatoes, Bread, Butter, and Beverage $2.75

What’s that in constant 2005 dollars?

Consumer Price Index

• June 1948 = 24.2

• January 2005 = 190.7

24.2 = 190.7

2.75

X X = (190.7 * 2.75) / 24.2

http://www.bls.gov/cpi/home.htm

$2.75 in 1948 had the same buying power as $21.67 in 2005.

How to write with numbers

• First rule: no more than two numbers in a paragraph

Example

Revenue at the largest generator of electricity in the USA soared to $61.3 billion in 2001 from $13.7 billion in 2000. Yet to get that much more revenue, the company added 5% more workers to 27,726 and assets declined 13% to to $47.3 billion from $54.5 billion.

--USA Today

How to write with numbers

• Second rule: if you use two numbers in a paragraph, it’s better if they can be compared with each other.

Example

• Boston had a season total of 78.1 inches of snow by Tuesday. Its average annual total is about 42 inches.

--USA TODAY, March 2, 2005

How to write with numbers

• Third rule: don’t use more significant digits than you need.

• If 62.34% of the public supports Bush, report it as 62%. • Remember: polls are never accurate to fractions of a percentage point.

On the other hand …

• Felony theft is defined as taking goods worth $50 or more. A shoplifter steals a sweater priced at $49.99.

• Should the prosecutor round to $50 and file a felony charge?

Writing with numbers

• Express the concept in words first.

• Then back it up with the numbers.

• Show the numbers as part of a system.

Example

A new study finds what may seem obvious to even casual observers: Many National Football League players are obese.

--USA TODAY, March 2, 2005

Five paragraphs later …

• 56% or players qualify as obese, roughly 30 or more pounds over a healthy weight.

• About 26% of football players qualify as severely obese, and 3% are morbidly obese.

Writing with numbers

• Choose your typical value carefully • Mean = the value each case would have if each case were the same (and the total was constant).

• Median = value of the middle case.

• Mode = the most frequent value.

Where money is involved, the mean can be misleading

The tax relief is for everyone who pays income taxes – and it will help our economy immediately: 92 million Americans will keep, this year,

an average

of almost $1,000 more of their own money.

-- George W. Bush, State of the Union Address, 2003

Income < 10K 10-20 20-30 30-40 Percent of returns 19.2

17.5

13.9

10.1

Tax saving in dollars 5 63 204 351 More than 80% receive less than $1,000

Graduates of what UNC department have the highest mean salary?

• School of medicine • School of journalism • School of law • Department of geography • School of business administration

(Michael Jordan majored in geography!)