Number Sense
Part II – Computations and
Benchmarks
This video is designed to accompany
pages 1-12
in
Making Sense of Uncertainty
Activities for Teaching Statistical Reasoning
Van-Griner Publishing Company
Implausible Numbers
An article in the journal Science on insects
attacking plants, mentioned a California field
that produces 750,000 melons per acre
1 acre = 43,560 ft2
750,000 melons/acre = 750,000
melons/43,560 ft2
That’s a little over 17 melons per square foot.
Percentages or
Absolutes?
Have a look at this flight
table regarding the airport
in Lexington, Kentucky. Is it
fair to say Comair, with 158
on time flights is much
superior to Atlantic
Southeast with only 65?
Lexington’s Bluegrass Field – July, 2007
Airline
Total flights
On time
Pinnacle Airlines Inc.
141
122
Skywest Airlines Inc.
123
88
Atlantic Southeast Airlines
91
65
Expressjet Airlines Inc.
84
55
American Eagle Airlines Inc.
155
97
Comair Inc.
255
158
Delta Air Lines Inc.
28
13
Probably not. Comair is only on-time 62% of the time compared to
71% for Atlantic Southeast. Makes obvious sense to look at rates
in this case.
.
Percentages or
Absolutes?
Baby cured of HIV: What does this
mean for the future of treatment?
Published March 04, 2013
FoxNews.com
Absolute: That’s one baby cured out of one baby treated.
Percent:
That’s a 100% success rate.
Details:
Would be the same regardless but we have to be ready to uncover them.
Percentages or
Absolutes?
Maternal Health in the U.S.
It's more dangerous to give birth in the United States than in 49 other countries. African-American
women are at almost four times greater risk than Caucasian women. A safe pregnancy is a
human right for every woman regardless of race or income.
Maternal mortality ratios have increased from 6.6 deaths per 100,000 live births in 1987 to 13.3
deaths per 100,000 live births in 2006.
Absolute: That’s an increase of 6.7 deaths per 100,000 live births.
Percent: An increase of (13.3/6.6)= 2.02, so just over a 100% increase
since 1987.
Could both be useful. But sometimes one creates a more extreme picture
than does the other. Be wise, be aware.
Endless Possibilities!
United States - 82
United Kingdom - 44
In a 2007 campaign advertisement, former New York City mayor Rudy Giuliani
said, “I had prostate cancer, five, six years ago. My chances of surviving
prostate cancer—and thank God, I was cured of it—in the United States?
Eighty-two percent. My chances of surviving prostate cancer in England? Only
44 percent under socialized medicine.”
He apparently used data from the year 2000, when 49 British men in every
100,000 were diagnosed with prostate cancer, of whom 28 died within five
years — about 44 percent. Using a similar approach, he cited a corresponding
82 percent five-year survival rate in the U.S ….
Five-year Survival Rates
The PSA is widely used in the U.S. but not in the U.K. Prostate
cancer is a cancer that often develops slowly and is not the
cause of death in an elderly male. So in the U.S. we have
detection coming at 50 and the patient living to 70; in the U.K.
detection might come at 67 and the patient lives to 70. Both
have same time of death, but U.S. looks better with a stronger
“five-year” survival rate.
What Can You Do?
Be alert, and be aware.
Be ready and willing to question what you read
and hear.
Be comfortable with fractions and percentages.
Be well-versed in some basic “benchmarks.”
Benchmarks to
Know
1. U.S. population is about 300 million
2. Each year about 4 million babies are born in the
U.S.
3. About 2.4 million Americans die each year
4. Roughly 1 in 4 who die, do so of heart disease
5. Roughly 1 in 4 who die, die from cancer, more or
less.
*From Joel Best’s book Stat-Spotting …
Benchmarks to
Know
6.
7.
8.
9.
10.
About 43,000 die in traffic accidents
About 17,000 deaths are homicides
About 16,000 deaths are from AIDS
There are about 40 million black Americans
About 14% of Americans identify themselves as
Latino
Useful? How?
Claim has been made that over 4 million women
in the U.S. are battered to death each year by a
spouse or boyfriend.
Hmmm, only about 2.4
million people die in the
U.S. per year … all
together!
One-Sentence Reflection
Competence with fractions,
percentages, and a knowledge of
common benchmarks go a long
way toward the goal of correctly
forming human inferences from
statistical constructs.