This file https://www.webassign.net/userimages/SAT%20Scores%20by%20Region.xls?db=v4net&id=56099 SAT 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)