1 Welcome Welcome to MATH 1107: Elementary Statistics. Elementary Statistics is an outstanding course as part of a liberal arts education. Everyone can bene…t from a better understanding of statistics and data. Everyone. Algebra, Trig and Calculus are very important to many …elds of study; but not all …elds of study. Statistics is important in every day life and decision making. Daily news presents statistics about issues both important and mundane. What does the margin of error in a political poll mean? Which of those side e¤ects from a new medication should I worry about? What past performance data should I consider when drafting my fantasy sports team? What past performance data should I consider when making any decision about the future? Why are canned soups and ice cream frequently buy one get one free at the grocery store but gasoline never is? 2 What is Statistics? Statistics is the science of data! Collecting, classifying, organizing, analyzing, interpreting, making decisions from, etc. Statistics is a part of your everyday life even if you haven’talways noticed. Example 1 The average score on Test 1 in MATH 8000 at the University of Nowhere is 75. Example 2 The tallest ice cream cone was over 9 feet tall and scooped in Italy.(http://www.icecream.com/icecreaminfo). Example 3 California produces the most ice cream in America (http://www.icecream.com/icecreaminfo). 1 Example 4 How has the price of gold ‡uctuated in 2016? http://www.kitco.com/charts/popup/au0365nyb.html Example 5 Top 5 interstates for most fatal accidents per mile in 2013 (http://commuting.blog.ajc.com/2015/11/06/americas- deadliest-interstate-is-in-georgia-study-says/) I-285 in Georgia I-710 in California I-240 in Oklahoma I-495 in Delaware I-240 in Tennessee Example 6 Georgia is the seventh-worst state in the country for fatal car acci- dents in total (1,085 incidents in 2013). Texas ranked no. 1, with 3,044 deaths from car accidents in 2013. The …rst example provided here is a work of …ction. I made up the data and it looks nice. I refer to such examples as toy data. Such data sets are good to play with and can make a point. The other examples are real. As a science, Statistics is very important because of its applications in the real world. I grab lots of example data from Wikipedia. It is a nice source for pop culture stu¤. Most all sports data comes from http://www.sports-reference.com/. It con- tains lots of data about baseball, basketball, football, hockey and the Olympics. Using real data can help answer the timeless question in every mathematics course. What is this good for? 2 3 Raw Data is Ugly Graphical representations of data always look pretty in newspapers, maga- zines and books. What you haven’t seen is the blood, sweat and tears that it sometimes takes to get those results. 3 http://www.hockeywidgets.com/newblog/uploaded_images/graph2- 775937.jpg 4 Data from the National Highway Tra¢ c Safety Administration, illustrated by Vox, show all 2,867 fatal accidents on major American interstates in 2013 4 Understanding Variation Knowing an average value (or a predicted average) is a good start to un- derstanding data. But it is not enough. We must also understand how data varies. The same unit of measurement may not always have the same value or meaning. Example 7 The average score on Test 1 in MATH 8000 at the University of Nowhere is 75. Of the 100 students in the class, half scored a 50 and the other half scored 100. Example 8 The average score on Test 1 in MATH 8000 at the University of Nowhere is 75. Each of the 100 students in the class scored a 75. Example 9 Consider the progression of world record marathon times verses the progression of world record mile times (from Wikipedia.org). Decreases in the record mile time are by less than 3 seconds. Decreases in the record marathon time are by minutes. A 3 second decrease in a mile time is more signi…cant than a 3 second decrease in a marathon time. 5 Time Athlete Nationality Date Venue 04:14.4 John Paul Jones United States 31 May 1913[4] Allston, Mass. 04:12.6 Norman Taber United States 16 July 1915[4] Allston, Mass. 04:10.4 Paavo Nurmi Finland 23 August 1923[4] Stockholm 04:09.2 Jules Ladoumègue France 4 October 1931[4] Paris 04:07.6 Jack Lovelock New Zealand 15 July 1933[4] Princeton, N.J. 04:06.7 Glenn Cunningham United States 16 June 1934[4] Princeton, N.J. 04:06.4 Sydney Wooderson United Kingdom 28 August 1937[4] Motspur Park 04:06.1 Gunder Hägg Sweden 1 July 1942[4] Göteborg 04:06.2 Arne Andersson Sweden 10 July 1942[4] Stockholm 04:04.6 Gunder Hägg Sweden 4 September 1942[4] Stockholm 04:02.6 Arne Andersson Sweden 1 July 1943[4] Göteborg 04:01.6 Arne Andersson Sweden 18 July 1944[4] Malmö 04:01.3 Gunder Hägg Sweden 17 July 1945[4] Malmö 03:59.4 Roger Bannister United Kingdom 6 May 1954[4] Oxford 03:57.9 John Landy Australia 21 June 1954[4] Turku 03:57.2 Derek Ibbotson United Kingdom 19 July 1957[4] London 03:54.5 Herb Elliott Australia 6 August 1958[4] Santry, Dublin 03:54.4 Peter Snell New Zealand 27 January 1962[4] Wanganui 03:54.0 Peter Snell New Zealand 17 November 1964[4] Auckland 03:53.6 Michel Jazy France 9 June 1965[4] Rennes 03:51.3 Jim Ryun United States 17 July 1966[4] Berkeley, Cal. 03:51.1 Jim Ryun United States 23 June 1967[4] Bakersfield, Cal. 03:51.0 Filbert Bayi Tanzania 17 May 1975[4] Kingston 03:49.4 John Walker New Zealand 12 August 1975[4] Göteborg 03:49.0 Sebastian Coe United Kingdom 17 July 1979[4] Oslo 03:48.8 Steve Ovett United Kingdom 1 July 1980[4] Oslo 03:48.5 Sebastian Coe United Kingdom 19 August 1981[4] Zürich 03:48.4 Steve Ovett United Kingdom 26 August 1981[4] Koblenz 03:47.3 Sebastian Coe United Kingdom 28 August 1981[4] Bruxelles 03:46.3 Steve Cram United Kingdom 27 July 1985[4] Oslo 03:44.4 Noureddine Morceli Algeria 5 September 1993[4] Rieti 03:43.1 Hicham El Guerrouj Morocco 7 July 1999[4] Rome Men’sWorld Record Mile 6 Time Name Nationality Date Event/Place 2:55:18 Johnny Hayes United States 24•Jul•08 London 2:52:45 Robert Fowler United States 1•Jan•09 Yonkers[nb 5], United States 2:46:53 James Clark United States 12•Feb•09 New York City, United States 2:46:05 Albert Raines United States 8•May•09 New York City, United States 2:42:31 Henry Barrett United Kingdom May 26, 1909[nb 6] Polytechnic Marathon 2:40:34 Thure Johansson Sweden 31•Aug•09 Stockholm, Sweden 2:38:16 Harry Green United Kingdom 12•May•13 Polytechnic Marathon 2:36:07 Alexis Ahlgren Sweden 31•May•13 Polytechnic Marathon 2:32:36 Hannes Kolehmainen Finland 22•Aug•20 Antwerp, Belgium 2:29:02 Albert Michelsen United States 12•Oct•25 Port Chester, United States 2:30:57 Harry Payne United Kingdom 5•Jul•29 London 2:26:14 Son Kitei Empire of Japan[44] 21•Mar•35 Tokyo, Japan 2:27:49 Fusashige Suzuki Empire of Japan 31•Mar•35 Tokyo, Japan 2:26:44 Yasuo Ikenaka Empire of Japan 3•Apr•35 Tokyo, Japan 2:26:42 Son Kitei Empire of Japan[44] 3•Nov•35 Tokyo, Japan 2:25:39 Suh Yun•bok South Korea 19•Apr•47 Boston Marathon 2:20:42 Jim Peters United Kingdom 14•Jun•52 Polytechnic Marathon 2:18:40 Jim Peters United Kingdom 13•Jun•53 Polytechnic Marathon 2:18:35 Jim Peters United Kingdom 4•Oct•53 Turku Marathon 2:17:39 Jim Peters United Kingdom 26•Jun•54 Polytechnic Marathon 2:18:05 Paavo Kotila Finland 12•Aug•56 Pieksämäki, Finland 2:15:17 Sergei Popov Soviet Union 24•Aug•58 Stockholm, Sweden 2:15:16 Abebe Bikila Ethiopia 10•Sep•60 Rome, Italy 2:15:16 Toru Terasawa Japan 17•Feb•63 Beppu•Ōita Marathon 2:14:28 Leonard Edelen United States 15•Jun•63 Polytechnic Marathon 2:14:43 Brian Kilby United Kingdom 6•Jul•63 Port Talbot, Wales 2:13:55 Basil Heatley United Kingdom 13•Jun•64 Polytechnic Marathon 2:12:12 Abebe Bikila Ethiopia 21•Oct•64 Tokyo, Japan 2:12:00 Morio Shigematsu Japan 12•Jun•65 Polytechnic Marathon 2:09:36 Derek Clayton Australia 3•Dec•67 Fukuoka Marathon 2:08:34 Derek Clayton Australia 30•May•69 Antwerp, Belgium 2:09:28 Ron Hill United Kingdom 23•Jul•70 Edinburgh, Scotland 2:09:12 Ian Thompson United Kingdom 31•Jan•74 Christchurch, New Zealand 2:09:06 Shigeru So Japan 5•Feb•78 Beppu•Ōita Marathon 2:09:01 Gerard Nijboer Netherlands 26•Apr•80 Amsterdam Marathon 2:08:18 Robert De Castella Australia 6•Dec•81 Fukuoka Marathon 2:08:05 Steve Jones United Kingdom 21•Oct•84 Chicago Marathon 2:07:12 Carlos Lopes Portugal 20•Apr•85 Rotterdam Marathon 2:06:50 Belayneh Dinsamo Ethiopia 17•Apr•88 Rotterdam Marathon 2:06:05 Ronaldo da Costa Brazil 20•Sep•98 Berlin Marathon 2:05:42 Khalid Khannouchi Morocco 24•Oct•99 Chicago Marathon 2:05:38 Khalid Khannouchi United States 14•Apr•02 London Marathon 2:04:55 Paul Tergat Kenya 28•Sep•03 Berlin Marathon 2:04:26 Haile Gebrselassie Ethiopia 30•Sep•07 Berlin Marathon 2:03:59 Haile Gebrselassie Ethiopia 28•Sep•08 Berlin Marathon Men’sWorld Record Marathon This comparison is even more di¢ cult when the contexts are dramatically di¤erent.