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 2014 and 2010 are saved in the accompanying file. Data for the first five and last two states are shown in the table on the next page.

a. Use graphs to display the SAT mathematics score distributions in 2014 and 2010. How did the distributions of state scores change over the 5-year period?

b. As another method of comparing the 2014 and 2010 SAT mathematics scores, compute the paired difference by subtracting the 2010 score from the 2014 score for each state. Summarize these differences with a graph.

Compare the results with those of part a.

c. Based on the graph, part b, what is the largest improvement in SAT mathematics score? Identify the state associated with this improvement.

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State Alabama Alaska Arizona Arkansas California Wisconsin Wyoming Read 547 507 522 573 498 596 590 2014 Math 538 503 525 571 510 608 599 Write 532 475 500 554 496 578 573 Read 556 516 518 564 501 593 568 2010 Math 550 513 524 564 516 603 565 Write 543 489 498 550 500 578 543