What’s Your Function?

Analia Brache

Blog submission number 2 - What's your function? 

Due Date: January 17, 2014

Point value: (20 points)

Part A:

According to an article written in NY Times by Catherine Rampell in 2009, there exists a functional relationship between SAT scores in each section and the test-takers’ family income because there is exactly one output per input: the wealthier the family, the higher the score in each of the sections. Voluntarily, test-takers report their family incomes right before taking the exam. College Board, the non-for-profit organization used for administration of tests of aptitude and achievements, gathered the income information and correlated it to the SATs scores within the years previous to 2009. Graph 1 represents the average scores of 10 income groups in $20,000 range each in relation to the scores per section.

Graph 1

So if we use W to represent the wealth of the families, and S to represent the scores in each of the sections, S= f(W) would be our function notation, so yes it is mathematical model since the scores of each section (output) depend on the families’ wealth (input). To be more specific, the scores in each individually tested section are a function of the wealth of the families. So, Scr= f(W), Sw= f(W) and Sm= f(W). (cr= critical reading (purple), w= writing (blue) and m=math (green)). However, they are not functions of each other.

None of them are linear functions because the rate of change between each interval is not constant, due to the fact that the scores grow irregularly in each of the different family incomes. For example, calculating the rate of change in random intervals of the Math section,

ROC1= 528  -    512/                             = 16/20   = 0.8

       80,000 – 60,000    

ROC2= 550    -   542/                            = 8/20      = 0.4
       140,000 – 120,000

In addition, Graph 1 shows that the three lines connecting the results are not linear.

Part B

A research article by Mathew Keller published in 2013 in PLOS Genetics based on The Genetic Correlation between Height and IQ between various relative pair types is a non-function relationship because there is more than one output per input. The following table shows the results:

The relationship shows that although some people may have the same IQ, such as DZM and DZOS, their height is different, which means that the height is not a function of the IQ. Similarly, some people may have the same height, such as DZM and FA-DAU, but not the same IQ, so the IQ is not a function of the height.