Don t Believe Everything You Hear

Transcription

1 AAA Statsitics Don t Believe Everything You Hear Jay Lehmann College of San Mateo MathnerdJay@aol.com prenhall.com/lehmanninfo True or false? Men are less likely than women to ask for directions when lost. Men: 34% Women: 37% (no statistical difference) 4 hours: 0.5% Never made it: 0.7% Toilet Bowls True or false? Toilet water twirls: Northern hemisphere: clockwise Southern hemisphere: counterclockwise If true, the reason why is the Coriolis effect. False! (for both questions) Outline 1 Dogs: $1.95 in savings! Gaspard Gustave Coriolis Lightning 3 Grades 4 Carbon Intensity

2 Dogs Equivalent Human Years for - Pound Dogs True or false? One dog year is equivalent to about 7 human years. False! Issues: Mature by 1.5 years Weight matters Dog Years Human Years Source: Fred Metzger, State College, PA Equivalent Human Years for - Pound Dogs Dog Years Human Years Source: Fred Metzger, State College, PA H (human years) D (dog years) H (human years) 90 H = 4.49D D (dog years) H (human years) H = 7D 90 H = 4.49D D (dog years)

3 Jeanne Calment Oldest Dog: Bluey February 21, 1875 August 4, years and 164 days Australian cattle dog 19 November 14, years and 5 months Human Equivalent Years for Bluey Online Conversion Programs Bluey 29 years and 5 months h(29.42) = 4.49(29.92) about 148 human years Online Explanation The formula used above is from a canine expert and is a bit more accurate. (as accurate as one can judge these things) The formula is.5 dog years per human year for the first 2 years, then 4 dog years per human year for each year after. (2,21), m = 4: H 21 = 4(D 2) H = 4D + 13 H = 4.49D Calculator Model Metzger s Model Equivalent Human Years Dog Human Years Years Pounds 90 Pounds Difference Source: Fred Metzger, State College, PA

4 Equivalent Human Years Using Age and Weight to Estimate Human Years Dog Human Years Years Pounds 90 Pounds Difference Source: Fred Metzger, State College, PA f (D, W ) = (4.49D ) + W 35 (0.94D 3.4) 35 = 0.027DW D 0.097W $1.95 value! Zorba Zorba 343 pounds 8 years Heaviest Dog Zorba 343 pounds 8 years f (D, W ) = 0.027DW D 0.097W f (8, 363) = about 90 human years Life Expectancy of Australian Cattle Dog Australian cattle dog pounds life expectancy of humans: 77.6 years f (D, W ) = 0.027DW D 0.097W = 0.027D() D 0.097() D 13.5 about 13.5 years reported life expectancy: years

5 Student Assignments Women, Men, and Dogs Find linear model for pound dogs Compare Metzger s model to rule-of-thumb model Meaning of slope and intercepts Model breakdown Estimate human age of Bluey Find inverse of linear model Find multivariate model Percentage of women who... find at least one quality in their dog they d like to see in their man: 88% agree that if my dog was a man, he d be my boyfriend. : 34% Student Quote Number Guy Song Explorations are helpful and introduce new ideas in an easy manner. I like them easy to follow and they re short. The class is not hard if you do the homework, projects, and pass all the tests. prenhall.com/lehmanninfo Two Beliefs About LIghtning LIghtning Bolt True or false? Lightning never strikes the same place twice. False! 1 sec: 1 mile away False!

6 Double LIghtning Bolt Speed of Sound Versus Temperature v: speed of sound (m/s) T c : temperature (Celsius) In mi/s: In s/mi: v = 0.6T c v = 0.66T c Standard model 0% humidity 1mi v = (0.66T c ) m v = T c v = T c Speed of Sound Versus Temperature In s/mi: 1 v = T c Lightning Lab on the Web 1 T c v Celsius Seconds Per Mile speed of sound 4.7 seconds per mile A Lesson to Learn By Locating the Lightning Lab on the Web 1 Google: Meteorology: Understanding the Atmosphere Ackerman and Knox 2 Then select Thunder and Lightning (Chapter 11).

7 Just About to Strike... Student Assignments Internet demo Internet calculators of speed and sound Meaning of slope and v-intercept of model Empirical experiment: speed of sound speed of light Student Quote Percentage of Freshmen in Four-Year Colleges and Universities Whose Average Grade in High School Was an A This is without a doubt the best math course I ve taken. I ve taken this very course three times and have either dropped or failed. This is the only class that I ve seen all the information so clearly. Year Percent Source: Higher Education Research Institute Percentage of Freshmen in Four-Year Colleges and Universities Whose Average Grade in High School Was an A P (percent) t (years since 1990) Using Two Points to Find a Linear Model Two good points: (5, 36.1) and (, 42.9) m = f (t) = 1.36t + b = = 1.36(5) + b 36.1 = b b = 29.3 f (t) = 1.36t

8 Percentage of Freshmen in Four-Year Colleges and Universities Whose Average Grade in High School Was an A P (percent) f (t) = 1.36t t (years since 1990) Making an Estimate When did half of all freshman in four-year institutions earn an average grade of A in high school? 05 = 1.36t t =.7 t Model Breakdown Percentage of Grades at Princeton That Are A s When will all freshman in four-year institutions have earned an average grade of A in high school? 0 = 1.36t t = 70.7 t Model breakdown has occurred. (Or has it?) Year Used to Group to Represent of Years Group of Years Percent Source: Princeton University Percentage of Grades at Princeton That Are A s Percentage of Grades at Princeton That Are A s P (percent) t (years since 1970) P (percent) p(t) = 0.61t t (years since 1970)

9 Model Breakdown p(t) = 0.61t Percentage of A s in 05? t = 0: 1970 p(35) = 0.61(35) = % New guidelines: percentage of grades that are A s: undergrads: 35% senior theses and junior projects: 55% In reality, undergrads:.9% Two Conflicting Reports Has grade inflation occurred at four-year institutions? American Academy: yes National Center for Education Statistics: may not be as widespread as people believe Student Assignments Student Quote Find model of freshman data (A s) Estimate when % A s, when 0% A s Find model of Princeton data (A s) Estimate A s for 05 (model breakdown) Student papers: pros and cons on existence of grade inflation Like any other art form, math takes practice and a lot of attention. I guess more like a girlfriend. Carbon Intensity Carbon intensity: the ratio of annual carbon emissions to annual economic output Carbon Emissions E (thousand metric tons of carbon per capita) Bush Administration s goal: lower carbon intensity in 12 to 18% below its level in t (years since 19)

10 Carbon Emissions GDP (1987 thousand dollars per capita) E (thousand metric tons of carbon per capita) E(t) = 0.19t t (years since 19) G (thousands of dollars) G(t) =.41(1.024) t t (years since 19) Carbon Intensity Model t = 0: 19 Model of emissions per capita (thousand metric tons): E(t) = 0.019t Model of GDP per capita ($00): G(t) =.41(1.024) t Carbon intensity: I(t) = 0.019t (1.024) t Carbon Intensities Carbon intensity: I(t) = 0.019t (1.024) t t I(t) Values of Carbon Intensity Model Actual Model s Percent Percent Decade Decline Decline Model s prediction for 02 12: Student Quote It s a way that I haven t seen before. It makes me see math as a part of my life. It makes it easier to me because I m more interested. It s very easy to understand because it s real data. You can t fake real data.

11 Student Assignments Student Quote Describe meaning of carbon intensity. Model carbon intensity (quotient function) Predict decline in carbon intensity from 02 to 12. There is actually no doubt that using actual data not only broadens our understanding of the real world, but it also helps us turn mathematical concepts into tangible and concrete ideas. Number Guy Song and More Info: Handouts From Other Talks, etc. Fill out For more information handout. prenhall.com/lehmanninfo Don t Believe Everything You Hear Jay Lehmann College of San Mateo MathnerdJay@aol.com prenhall.com/lehmanninfo