Each state has its own approach to which high school students should take the SAT. Not surprisingly, the participation rate has a strong bearing on a state’s average score. In states where a very small percentage of students take the exam – usually only those who are college bound – the average score is much higher. In states where it is routine for almost all students to take the test, regardless of their plans for post-secondary education, average scores are lower.

This scatter plot shows participation rate vs average combined SAT score. The r^2 value (coefficient of determination) is 0.81; the linear regression is statistically significant (p-value <<0.01). In most states, math is the subject in which students have the highest average score. There were no states in which writing alone was the best subject for students; it tied for the highest with math in two states.

Data source: http://research.collegeboard.org/programs/sat/data/cb-seniors-2013