http://www.weather.com/weather/wxclimatology/monthly/USDC0001
These are the yearly average from the temperature in Washington DC. The statistics show that the overall temperature has dropped since 2009.
This is the relationship between the weather and the year has no correlation. The weather is the F and the year is the X. This is a linear function because it has a constant rate of change over each year that
the data was recorded. This function is not a mathematical model because the output is not dependent on the input.
Part B
http://www.baseball-reference.com/players/r/rodrial01.shtml
This article is on one of the greatest baseball players of all time and his stats. They show his stats from when he first started in the MLB to now in his veteran career. The article argues that MLB younger hitters do better than older hitters. This is not a function because age has nothing to do with how good a batter is. The age is not dependent on how well the hitters hit. Young players hit just as well as older players.
hi, jonathan,
ReplyDeleteyour examples are good ones, however, your analysis of them is not entirely correct. for your first example, when i pulled up your url, i only saw monthly averages not yearly. additionally, this relationship is not linear. be careful when explaining the variables. the weather is the input and the average is the output.
in your second example, i really like that you tried to use sports statistics. that's great! your explanation, however, is not relevant to whether the relationship is a function or not. your explanation (age and hitting well not being dependent on each other) supports the criteria for not being a mathematical model.
If you were to discuss this relationship using ONE of the relationships with year, like games played, then you could discuss the relationship between year and games played, for instance. if year is the input value and games played is the output value, you can see that there are different inputs paired with the same output values, which means that the relationship is still a function.
However, if you considered the relationship between two other quantities, like games played relative to runs scored, the you would see that if we say that games played is the input and runs scored is the output, then when the player played 162 games (input value), he scored 124, 125, and 133 runs (output values). at this point, you could say that this relationship is NOT a function.
please review the criteria for what constitutes a function and a mathematical model and how the criteria are different. if a relationship is not a function it can never be a mathematical model.
professor little