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Chapter 2: Q128e (page 131)

Question: State SAT scores.Refer to Exercise 2.27 (p. 84) and the data on state SAT scores. Construct a scatterplot for the data, with the 2010 Math SAT score on the horizontal axis and the 2014 Math SAT score on the vertical axis. What type of trend do you detect?

State

2010 Math SAT

2014 Math SAT

Alabama

538

550

Alaska

503

513

Arizona

527

524

Arkansa

571

564

California

510

516

Wisconsin

608

603

Wyoming

599

565

Short Answer

Expert verified

Answer:

The image is given below:

There is an upward sloping positive trend.

Step by step solution

01

Constructing the scatterplot

We will plot the 2010 SAT Scores on the X-axis and 2014 SAT scores on the Y-axis.

The graph is given below:

02

Detecting the trend 

There is a positive trend in the Math SAT scores. States who have performed well in 2010 have also performed well in 2014 and are towards the top right corner of the graph.

States that have performed poorly in 2010 have also performed poorly in 2014 and lie on the bottom left of the graph.

This has created an upward slope.Therefore, there is an upward trend in the data.

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Most popular questions from this chapter

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Time in bankruptcy.Refer to the Financial Management(Spring 1995) study of 49 firms filing for prepackagedbankruptcies, Exercise 2.32 (p. 86). Recall that three typesof “prepack” firms exist: (1) those who hold no prefilingvote, (2) those who vote their preference for a joint solution;and (3) those who vote their preference for a prepack.

a.Construct a box plot for the time in bankruptcy (months) for each type of firm.

b.Find the median bankruptcy times for the three types.

c.How do the variabilities of the bankruptcy times compare for the three types?

d.The standard deviations of the bankruptcy times are 2.47 for “none,” 1.72 for “joint,” and 0.96 for “prepack.” Do the standard deviations agree with the interquartile ranges concerning the comparison of the variabilities of the bankruptcy times?

e.Is there evidence of outliers in any of the three distributions?

Ranking driving performance of professional golfers.A group of researchers developed a new method forranking the total driving performance of golfers on theProfessional Golf Association (PGA) tour (The Sport Journal,Winter 2007). The method requires knowinga golfer’s average driving distance (yards) and drivingaccuracy (percent of drives that land in the fairway).The values of these two variables are used to compute adriving performance index. Data for 40 PGA golfers (asranked by the new method for a recent tour year) aresaved in the accompanying file. The first five and last fiveobservations are listed in the table below.

a.Find the mean, median, and mode for the 40 driving performance index values.

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Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

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c.What is the interquartile range of the data set (approximately)?

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Ecolabel

Mean

Std. Dev.

Energy Star

4.44

0.82

TripAdvisor

3.57

1.38

Green Leaders Audubon

2.41

1.44

International U.S Green

2.28

1.39

Building Council Green Business

2.25

1.39

Green Key

2.01

1.30
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