STAT 302 Course Notes set 1 Introduction to Statistics Statistics The Art and Science of Learning from Data 1 What is Statistics Statistics as a subject matter is a set of scientific principles and techniques that are useful in reaching conclusions about populations and processes when the available information is both limited and variable that is statistics is the science of learning from data According to Google s Chief Economist Hal Varian I keep saying the sexy job in the next ten years will be statisticians The ability to take data to be able to understand it to process it to extract value from it to visualize it to communicate it that s going to be a hugely important skill in the next decades McKinsey Quarterly January 2009 Questions Statistics Can Answer Do people who eat a high fiber cereal for breakfast on average weigh less than people who skip breakfast Statistics can NOT be used to determine whether you personally would weigh less if you ate a high fiber cereal but it can tell us if there is evidence the average weight of high fiber cereal eaters is less than the average weight of all people who skip breakfast Do females live longer than males http www dailymail co uk sciencetech article 1323571 Why women live longer menMale bodies genetically disposable html Statistics only can tell on average whether female live longer than male An interesting case study example Outliers 2008 by Malcolm Gladwell One warm spring day in May of 2007 the Medicine Hat Tigers and the Vancouver Giants met for the Memorial Cup Hockey Championships in Vancouver British Columbia The Tigers and the Giants were the two finest teams in the Canadian Hockey League which in turn is the finest junior hockey league in the world These were the future stars of the sport seventeen eighteen and nineteen year olds who had been skating and shooting pucks since they were barely more than toddlers Outliers page 15 You can t buy your way into Major Junior A hockey Nor does it matter if you live in the most remote corner of the most northerly province in Canada If you have ability the vast network of hockey scouts and talent spotters will find you and if you are willing to work to develop that ability the system will reward you The system is based on individual merit and both of these words are important Players are judged on their own performance not anyone else s and on the basis of their ability not on some other arbitrary fact Or are they Outliers page 17 1 STAT 302 Course Notes set 1 Here is the player roster of the 2007 Medicine Hat Tigers Take a close look and see if you can spot anything strange about it Outliers pages 20 21 Number Name 9 Brennan Bosch 11 Scott Wasden 12 Colton Grant 14 Darren Helm 15 Derek Dorsett 16 Daine Todd 17 Tyler Swynstun 19 Matt Lowry 20 Kevin Undershute 21 Jerrid Sauer 22 Tyler Ennis 23 Jordan Hickmott 25 Jakub Rumpel 28 Bretton Cameron 36 Chris Stevens 3 Gord Baldwin 4 David Schlemko 5 Trever Glass 10 Kris Russell 18 Michael Sauer 24 Mark Isherwood 27 Shayne Brown 29 Jordan Benfield 31 Ryan Holfeld 33 Matt Keetley Position L R C R C R LW L LW L RW L C R RW R C R LW L RW R C L C R RW R C R LW L D L D L D L D L D R D R D L D R G L G R Height Weight Birth Date 5 8 173 February 14 1988 6 1 188 January 4 1988 5 9 177 March 20 1989 6 182 January 21 1987 5 11 178 December 20 1986 5 10 173 January 10 1987 5 11 185 January 15 1988 6 186 March 2 1988 6 178 April 12 1987 5 10 196 September 12 1987 5 9 160 October 6 1989 6 183 April 11 1990 5 8 166 January 27 1987 5 11 168 January 26 1989 5 10 197 August 20 1986 6 5 205 March 1 1987 6 1 195 May 7 1987 6 190 January 22 1988 5 10 177 May 2 1987 6 3 205 August 7 1987 6 183 January 31 1989 6 1 198 February 20 1989 6 3 230 February 9 1988 5 11 166 June 29 1989 6 2 189 April 27 1986 Hometown Martensville SK Westbank BC Standard AB St Andrews MB Kindersley SK Red Deer AB Cochrane AB Neepawa MB Medicine Hat AB Medicine Hat AB Edmonton AB Mission BC Hrnciarovce SLO Didsbury AB Dawson Creek BC Winnipeg MB Edmonton AB Cochrane AB Caroline AB Sartell MN Abbotsford BC Stony Plain AB Leduc AB LeRoy SK Medicine Hat AB Quarter Months O Observed Births 1 January February March 14 2 April May June 6 3 July August September 3 4 October November December 2 Total 25 There is very strong evidence that births are not evenly distributed across the 4 quarters with births in the 1st quarter more likely Why is there an uneven birth distribution 2 STAT 302 Course Notes set 1 an iron law of Canadian hockey in any elite group of hockey players the very best of the best 40 percent of the players will have been born between January and March 30 percent between April and June 20 percent between July and September and 10 percent between October and December The explanation is quite simple It has nothing to do with astrology nor is there anything magical about the first three months of the year It s simply that in Canada the eligibility cutoff for age class hockey is January 1 A boy who turns ten on January 2 then could be playing alongside someone who doesn t turn ten until the end of the year and at that age in pre adolescence a twelve month gap in age represents an enormous difference in physical maturity This being Canada the most hockey crazed country on earth coaches start to select players for the traveling rep squad the all star teams at the age of nine or ten and of course they are more likely to view as talented the bigger and more coordinated players who have the benefit of critical extra months of maturity And what happens when a player gets chosen for a rep squad He gets better coaching and his teammates are better and he plays fifty or seventy five games a season instead of twenty games a season like those left behind in the house league and he practices twice as much as or even three times more than he would have otherwise In the beginning his advantage isn t so much that he is inherently better but only that he is a little older But by the age of thirteen or fourteen with the benefit of better coaching and all that extra practice under his belt he really is better so he s the one more likely to make it to the Major Junior A league and from there into the big leagues …