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 .(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 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 23 August 1923[4] 04:09.2 Jules Ladoumègue France 4 October 1931[4] Paris 04:07.6 Jack Lovelock 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 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 21 June 1954[4] Turku 03:57.2 Derek Ibbotson United Kingdom 19 July 1957[4] 03:54.5 Australia 6 August 1958[4] Santry, Dublin 03:54.4 New Zealand 27 January 1962[4] Wanganui 03:54.0 Peter Snell New Zealand 17 November 1964[4] 03:53.6 Michel Jazy France 9 June 1965[4] Rennes 03:51.3 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 17 May 1975[4] Kingston 03:49.4 John Walker New Zealand 12 August 1975[4] Göteborg 03:49.0 United Kingdom 17 July 1979[4] 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 Algeria 5 September 1993[4] Rieti 03:43.1 7 July 1999[4] Men’sWorld Record Mile

6 Time Name Nationality Date Event/Place 2:55:18 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 , 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 Finland 22•Aug•20 Antwerp, 2:29:02 Albert Michelsen United States 12•Oct•25 Port Chester, United States 2:30:57 United Kingdom 5•Jul•29 London 2:26:14 Son Kitei Empire of [44] 21•Mar•35 , 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 19•Apr•47 Marathon 2:20:42 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 10•Sep•60 Rome, Italy 2:15:16 Japan 17•Feb•63 Beppu•Ōita Marathon 2:14:28 Leonard Edelen United States 15•Jun•63 Polytechnic Marathon 2:14:43 United Kingdom 6•Jul•63 Port Talbot, 2:13:55 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 Australia 3•Dec•67 Marathon 2:08:34 Derek Clayton Australia 30•May•69 Antwerp, Belgium 2:09:28 United Kingdom 23•Jul•70 , Scotland 2:09:12 United Kingdom 31•Jan•74 , New Zealand 2:09:06 Shigeru So Japan 5•Feb•78 Beppu•Ōita Marathon 2:09:01 Netherlands 26•Apr•80 Marathon 2:08:18 Australia 6•Dec•81 2:08:05 United Kingdom 21•Oct•84 Marathon 2:07:12 20•Apr•85 Marathon 2:06:50 Ethiopia 17•Apr•88 2:06:05 20•Sep•98 Marathon 2:05:42 Morocco 24•Oct•99 2:05:38 Khalid Khannouchi United States 14•Apr•02 2:04:55 28•Sep•03 2:04:26 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.

Example 10 Which performance is more unusual:

Wilt Chamberlain scoring 100 points against the N.Y. York Knicks on March 2, 1962 in the NBA or Wayne Gretzky scoring 92 goals in the ’81-’82NHL season?

Example 11 Which music sales record is more impressive (as of June 15, 2016 according to Wikipedia):

7 Michael Jackson, Thriller (48.1 million albums) or Bing Crosby, White Christmas (50 million physical singles) or Wiz Khalifa featuring Charlie Puth, See You Again (20.9 million digital singles)? We will develop sophisticated techniques to measure variation even in seemingly incomparable situations.1

5 Testing Claims

No matter what time of year it is, I see ads on a particular channel claiming that now is the best time ever to buy silver! Is it?

6 Making Sound Data-based Decisions (Predict- ing the Future)

A key skill in statistics is to predict the unknown (or a future event) by analyzing patterns in data sets. It is a safe bet that retail stores in a mall should hire extra help starting around Thanksgiving. It is also a safe bet to not count on that job lasting past the …rst week of January. Predicting the future based on past results works only up to a point. Sales of VHS tapes steadily rose for many, many years. Then they didn’t while DVD sales rose. Now, the format of choice is Blu-ray. Unforeseen events or catastrophes wreak havoc with predictions. Wayne Gretksy led his team in scoring in his …rst 14 seasons as a professional hockey player. It seams natural to predict he would do so again in his 15th season. However a back injury prevented him from playing as many games as he usually did.

1 Everyone who told you you cannot compare apples and oranges was lying!

8 7 Chance

Elvis Presley and David Bowie share the same birthday (January 8). Is this surprising? Is this meaningful? Understanding probability is key to using data to make predictions or estimations. How many people do you need in a room to have a 50% chance that at least two will share a birthday (disregarding year)?

8 Literacy and Homework

Mark Twain once said that "the man who doesn’t read good books has no advantage over the man who can’tread them." Reading and writing are critical skills for this class! Yes, this Statistics class! One must be careful with words and pay attention to their meaning. We rarely "solve for x" in this course. We analyze scenarios in order to determine what is going on and apply the best technique available. That requires reading skills. Vern Law, the 1960 Cy Young winner, one said "experience is a hard teacher because she gives the test …rst, the lesson afterward." This class is much easier since the lessons and homework are provided before the tests. Of course, you must actually do the homework for the lesson to occur before the test!

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