Educators are constantly evaluating the efficacy of public schools in the education and training of U.S. students. One quantitative assessment of change over time is the difference in scores on the SAT, which has been used for decades by colleges and universities as one criterion for admission. The SATSCORES file contains the average SAT scores for each of the 50 states and the District of Columbia for 2009 and 2005. Selected observations are shown in the following table:

a. Use graphs to display the two SAT score distributions. How have the distributions of state scores changed from 1990 to 2005?
b. As another method of comparing the 1990 and 2005 average SAT scores, compute the paired difference by subtracting the 1990 score from the 2005 score for each state. Summarize these differences with a graph.
c. Interpret the graph you made in part b. How do your conclusions compare with those of part a?
d. Identify the state with the largest improvement in the SAT score between 2005 and 2009.

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State 2009 2005 Alabama Alaska Arizona Arkansas California 1,109 1,036 1,037 1,144 1,013 1,126 1,042 1,056 1,115 1,026 1,202 1,135 1,191 1,087 Wisconsin Wyoming