Educators are constantly evaluating the efficacy of public schools in the education and training of American 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. Originally, the SAT provided scores in reading and mathematics. Now, three scores are provided: reading, mathematics, and critical writing. SAT scores for each of the 50 states and District of Columbia for the years 2011, 2010, and 2001 are saved in the accompanying file. Data for the first five and last two states are shown in the table below.

a. Use graphs to display the SAT mathematics score distributions in 2011 and 2010. How did the distributions of state scores change over the year?
b. Repeat part a, but compare the distribution in 2011 with the one in 2001. How did the distributions of state scores change over the past 10 years?
c. As another method of comparing the 2011 and 2001 SAT mathematics scores, compute the paired difference by subtracting the 2001 score from the 2011 score for each state. Summarize these differences with a graph. Compare the results to those of part b.
d. Based on the graph, part c, what is the largest improvement in SAT mathematics score? Identify the state associated with this improvement.

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2 2010 State Read 2001 Math Read Alabama Alaska Arizona Arkansas California Wisconsin Wyoming 546 Math 536 487 499 515 568 590 543 489 498 511 523 559 514 523 554 518 564 513 524 515 602 569 575 551 498 584 547 517 593 568 572 603 545