Transcript Getting the Math Right (PowerPoint)

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
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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
Percent of
returns
Tax saving
in dollars
< 10K
19.2
5
10-20
17.5
63
20-30
13.9
204
30-40
10.1
351
More than 80% receive less than $1,000
Graduates of what UNC department
have the highest mean salary?
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School of medicine
School of journalism
School of law
Department of geography
School of business administration
(Michael Jordan majored in geography!)