This fileSAT Math scoresshows the SAT Math scores in the 50 states and the District of Columbia; each state and the District of Columbia is classified by region of the country: Midwest, Northeast, South, and West.

Numerical summaries of center and spread exhibit characteristics of the SAT Math scores in the Midwest, Northeast, South, and West regions.

Question 1.Find the values of the following numerical summaries:

a.

meanSAT Math score in theMidwest(use 3 decimal places in your answer)

b.

medianSAT Math score in theNortheast

c.

standard deviationof SAT Math scores in theSouth(use 3 decimal places in your answer)

d.

Interquartile Rangeof SAT Math scores in theWestIn addition to the SAT, each year thousands of students also take the ACT standardized test. Both the SAT and ACT are used in the college admissions process. SAT Math Scores can go as high as 800 while the maximum ACT Math score is 18. Since the two exams use very different scales, comparisons of performance are difficult. A convenient, though not exact, rule of thumb to determine the ACT Math score from the SAT Math score is

or equivalently,

Question 2. Use the above linear transformation to determine the equivalent ACT Math score numerical summaries from the SAT Math score summaries in question 1.

a.

equivalentmeanACT Math score in theMidwest(use 3 decimal places in your answer)

b.

equivalentmedianACT Math score in theNortheast(use 3 decimal places in your answer)

c.

equivalentstandard deviationof ACT Math scores in theSouth(use 3 decimal places in your answer)

d.

equivalentInterquartile Rangeof ACT Math scores in theWest(use 4 decimal places in your answer)

Region SAT (Math) Midwest 528 Midwest 459 Midwest 577 Midwest 548 Midwest 514 Midwest 542 Midwest 522 Midwest 546 Midwest 564 Midwest 499 Midwest 555 Midwest 543 Northeast 471 Northeast 463 Northeast 473 Northeast 486 Northeast 473 Northeast 470 Northeast 463 Northeast 461 Northeast 466 South 514 South 511 South 470 South 441 South 466 South 443 South 521 South 517 South 478 South 519 South 440 South 523 South 437 South 525 South 461 South 470 South 490 West 476 West 481 West 484 West 484 West 486 West 487 West 497 West 502 West 513 West 519 West 523 West 527 West 539