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IB Math Studies Internal Assessment:
What is the Relationship between SAT Scores and Family Income of the Test Takers around the World?

Exam Session: May 2011
School name: International School Bangkok
Teacher: Mr. Demille
Date: December 8th, 2010
Course: IB Math Studies
Word Count: 1,832
Name: Billy Egnehall

What is the Relationship between SAT Scores and Family Income of the Test Takers around the World? Introduction
The SAT examination is mostly in today’s world of academics, a requirement of getting accepted into collage. Not only is it enough to take the examination but the student has to pass with an average score or above to even have his/her application be considered. Many students around the world recognize this and therefore apply to prep schools for the SAT or their parents send them to a higher educational institution for that purpose. The prep schools such as Princeton are not cheap however as it helps give advice on how to best tackle the SAT examination, neither are higher educational institutions. Also it can be considered a luxury service by some middle class and low class societies in the world to be able to attend either one. This being said, the SAT prep course and higher educational institutions are, as a result, aimed at the high class societies in the world or those who can afford it. If this is true, it would put families with a higher income at an advantage for their children to get accepted into collage compared to families who cannot afford for their children to take the course or school fee and learn the advice of how to pass the SAT examination with a high score. Are the collages which students aim to be accepted into for a better education really based on which families can afford for their children to take the SAT prep course or learn at a higher educational institution? The data collected from Collage Board in year 2007 was analyzed to determine whether there is a relationship between SAT scores and family income of the test takers around the world (Rampell). Statement of Task

The main purpose of this investigation is to determine whether there is a relationship between SAT scores and family income of the test takers around the world. The type of data that will be collected is the SAT scores and family income of the two-thirds of test takers who voluntarily reported it to collage board when signing up for the SAT examination worldwide. The SAT scores are used to determine how high of a score the test taker got and family income to determine the possibility to send their children to SAT prep schools or better educational institutions. The data used to generate the data breaks down the average score for ten different income groups of $20,000 range.

Plan of investigation

I am investigating the relationship of SAT scores and family income of the test takers around the world. I have collected data on SAT scores and family income of the test takers around the world. With the collection of data that I have acquired, a number of mathematical processes were used to analyze the data: a scatter plot of the data, calculation of the least squares regression line and correlation coefficient. I am going to do a χ2 test on the data to show the dependence of SAT scores and family income of the test takers around the world.

Mathematical Investigation
Collected Data

Family income of test takers| Percentage of test takers
within each family income group| Critical
reading| Math| Writing| ∑|
Less than $10,000| 4%| 427| 451| 423| 1301|
$10,000–$20,000| 8%| 453| 472| 446| 1371|
$20,000–$30,000| 6%| 454| 465| 444| 1363|
$30,000–$40,000| 9%| 476| 485| 466| 1427|
$40,000–$50,000| 8%| 489| 496| 477| 1462|
$50,000–$60,000| 8%| 497| 504| 486| 1487|
$60,000–$70,000| 8%| 504| 511| 493| 1508|
$70,000–$80,000| 9%| 508| 516| 498| 1522|
$80,000–$100,000| 14%| 520| 529| 510| 1559|
Table 1: Mean SAT scores per...
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