Using the NHL's website stats, to show a function I will be using the number of goals that Chicago Blackhawks LW Patrick Sharp (my favorite player) has scored since his debut in the windy city in the 2005-2006 season. The goals shown are only regular season goals, not including post-season. Even though the Blackhawks won the cup last season (2012-2013), I will omit the results of that season because the season was only half of the games normally played.
X (season) Y(number of goals scored)
2006 9
2007 20
2008 36
2009 26
2010 25
2011 34
2012 33
These numbers represent a function because each input (x/season) has only one output (y/number of goals scored). Patrick Sharp can only have however number of goals he scored that specific season be listed for his overall total for the year, he cannot go back and say he scored 36 goals and 23 goals for the 2007-2008 season, he, along with all players, only get one number.
As shown by the graph and the data table, the function is non-linear.
This is shown one clearly by the out of shape line on the graph but also by the average rate of change which follows
33-9 24
------- = ------- = 4
2012-2006 6
This is quite different from the interval ROCs, such as
20-10 10
------- = ------ = 10
2007-2006 1
Also, this is not a mathematical model and cannot be explained by a simple y=f(x) model where y is the number of goals scored and x is the year, because many other factors play into performance of a season and cannot be calculated by math, only estimated but with a player like Sharp who has up and down years, predicating is near impossible. Sadly, math cannot tell us how our favorite players will perform in a season.
Part B) http://www.washingtonpost.com/blogs/wonkblog/wp/2014/01/15/40-charts-that-explain-the-world/
Even though the title promises NHL stats, I will be using a different article for the non-function. An interesting article on the Washington Post did a study of "40 Charts that Explain the World"
Number 8 on the list showed how people in affluent countries died and compared 1990 to 2010. The bar chart showed technology has improved and how the major causes of death have changed thanks to those said advances. While the relationship is less death and causes of death over time, this is still not a function. This comparison is not a function because the inputs, 1990 and 2010, have multiple outputs, (cancer, flu, car accidents, etc)
Sport stats are a great place to look for functions. Did you make the graph yourself?
ReplyDeletevery good example for part b.
ReplyDeleteYour stuff was really well organized and put together, great job! Hockey stats are always interesting because they often lead to a variance from year to year. I actually chose a goalie stat because I thought it would be helpful to work with a small variance.
ReplyDeleteI liked your graph! And I especially liked that you wrote out all the x and y data.
ReplyDeleteDope stats on the NHL! I don't even like hockey but its easy to follow
ReplyDeleteI really like your examples
ReplyDeleteExamples were well put together! Interesting data trends from the NHL
ReplyDeleteNice work, great examples !!
ReplyDeletezack,
ReplyDeletei love all of these hockey examples! nice job on your first example. your explanations are very well detailed and i love that you showed the calculations for the rates of change to prove that the relationship is not linear.
your second example is very interesting, but in reality, it is an example of several functions. each country is a function of ventile in one graph and percentile in the other graph. make sure you understand why this is true!
professor little