Number Sense, Part II - Computations and Benchmarks
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8/26/2014 1 Number Sense Computations and Benchmarks This video is designed to accompany Module 1 in Beyond the Numbers Student-Centered Activities for Learning Statistical Reasoning a publication of the Van-Griner Publishing Company Check the 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 ft 2 750,000 melons/acre = 750,000 melons/43,560 ft 2 That’s a little over 17 melons per square foot.
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Transcript of Number Sense, Part II - Computations and Benchmarks
8/26/2014
1
Number SenseComputations and Benchmarks
This video is designed to accompany
Module 1
in
Beyond the NumbersStudent-Centered Activities for Learning
Statistical Reasoninga publication of the Van-Griner Publishing Company
Check the 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.
8/26/2014
2
Percentages or Absolutes?
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.
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?
Percentages or Absolutes?Baby cured of HIV: What does this mean for the future of treatment?Published March 04, 2013FoxNews.com
Absolute number cured: That’s one baby cured
Percent cured: That’s a 100% success rate.
Details: Same regardless, but 100% success rate gives very different impression.
*Unfortunately, in mid-summer 2014 the infection reappeared in the child.
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.Both statistics could be useful. But sometimes one creates a more extreme picture than does the other. Be wise, be aware.
8/26/2014
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Former New York City mayor Rudy Giuliani
“My chances of surviving prostate cancer in the United States? Eighty-two percent.”
“My chances of surviving prostate cancer in England? Only 44 percent under socialized medicine.”
On the Campaign Trail
Apparently used data from the year 2000
49 British men in every 100,000 were diagnosed with prostate cancer, of whom 28 died within five years — about 44 percent.
Similar data in U.S. leads to the 82 percent five-year survival rate in the U.S.
Had Correct Data
Relevant Facts
The PSA was widely used in the U.S. prior to 2014.
Rarely ever used in the U.K.
Prostate cancer often develops slowly.
Early detection in U.S. likely inflating importance of the five-year survival rates. How?
8/26/2014
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Politicized Inference?
So in the U.S. detection might 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 using the metric “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 just over 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 Center for Disease Control website …
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Benchmarks to Know6. About 35,000 die in traffic accidents
7. About 17,000 deaths are homicides
8. About 16,000 deaths are from AIDS
9. There are about 40 million black Americans
10.About 16% of Americans identify 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.
Is this possible?
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.
