Class Photo HW: Summary Due Before class Friday Chapter 2 - PDF document

Today  Today: Benford’s Law » HW: Applications of Benford’s Law Benford’s Law  Wednesday » Benford’s Law Conclusion Real World “Digit” Patterns  Friday » Chapter 2 Discussion (Quiz?), » Class Photo  HW: Summary Due Before class Friday » Chapter 2 » Hardcopy due: Friday before class » Softcopy due midnight before the class Friday. 1 2 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Benford’ Law is about Number Distributions Oh No! Coin-toss Again Number of Heads  Specifically about the Distribution of the First Number of Tails 50 Digit in real world data.  Before getting into the trenches of Benford’s Law lets simply talk about (review) different Distributions. » What do they look like?  Uniform Distribution  So lets explore: » Excel’s Random : 0 to .99 » What is a numeric Distribution? =IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds down to 1 and half to zero. 3 4 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA 1000 Roles of a Single Die Example: Human Height  IF we take the population of earth and then sort them according to height  Uniform Distribution =IF(INT(RAND()+0.5)=1,"H","T") INT: Rounds down to the nearest INT Add .5 so half the numbers rounds  Normal Distribution : Gaussian Distribution 5 6 down to 1 and half to zero. Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA

What about Benford’s Law? Bell Curve What is its Distribution?  Heights of people Numeric Data Leading DIgit 2 35 2  Size of things produced by machines 9 75 9  Blood pressure 1 24 1  Test Grades in a LARGE class. 5 36 5 611 6 385 3 196 1  http://www.mathsisfun.com/data/standard- 745 7 normal-distribution.html 385 3 7 8 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Example: Population of all the countries in the world 9 10 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA The Ideal: Benford’s Law 11 12 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA

When does it not work well?  Benford’s Law works Accurately when:  When number’s are assigned! Or there are thresholds (max/min). » Numbers Span several order of magnitudes » Check numbers » Invoice numbers  Example: Populations Goes from 10s to » Number’s with built in max and minimum billions! » Benford’s Law applies YAY! 13 14 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA More Examples Benford’s Law  Read Resource: Wikipedia!  http://en.wikipedia.org/wiki/Benford's_law 15 16 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA http://testingbenfordslaw.com/twitter-users-by-followers-count 17 18 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA

More Examples  Heights of buildings  http://www.youtube.com/watch? v=O8N26edbqLM  Amount of money in your wallet  Rolling of a die  10 minute Videos: » 1 Die, value of ‘dots’ have a uniform distribution » http://www.youtube.com/watch?v=vIsDjbhbADYs » 2 Dice: Question: Are Values of the dots: » http://www.youtube.com/watch?v=XXjlR2OK1kM – Uniform – (country from last video) – Non-Uniform – Benfordian 19 20 Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA Maria Hybinette, UGA