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Chapter 2: Q97. (page 116)

Salaries of bachelor’s degree graduates. PayScale, Inc., an online provider of global compensation data, conducts an annual salary survey of bachelor’s degree graduates. Three of the many variables measured by PayScale are the graduate’s current salary, mid-career salary, and the college or university where they obtained their degree. Descriptive statistics are provided for each of the over 400 colleges and universities that graduates attended. For example, graduates of the University of South Florida (USF) had a mean current salary of \(57,000, a median mid-career salary of \)48,000, and a mid-career 90th percentile salary of $131,000. Describe the salary distribution of USF bachelor’s degree graduates by interpreting each of these summary statistics.

Short Answer

Expert verified

The average current salary is $57,000; half of the graduates get less than $48,000, and another half get more than $48,000. Also, 10 percent of graduates get above $131,000.

Step by step solution

01

Elucidating descriptive statistics

Whenever a researcher generates descriptive statistics, the researcher mainly finds different measurements that summarize a long dataset.The measurements mainly include mean, variance, standard deviation, median, and others.

02

Interpreting the summary statistics

The word, “mean” signifies average, and so $57,000 is the average salary of the graduates passed out from the University of South Florida. As the median is $48,000, it means that half of the total number of graduates are earning less than $48,000, and the other half are earning more than $48,000. Also, 90 percent of the graduates earn below $131,000, which means10 percent earn more than $131,000.

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Most popular questions from this chapter

Question: Hotels’ use of ecolabels.Refer to the Journal of Vacation Marketing(January 2016) study of travelers’ familiaritywith ecolabels used by hotels, Exercise 2.42 (p. 94). Recallthat a sample of 392 adult travelers were shown a list of6 different ecolabels, and asked, “How familiar are youwith this ecolabel, on a scale of 1 (not familiar at all) to5 (very familiar).” The mean and standard deviation ofthe responses for each ecolabel are provided in the table.Which of the ecolabels had the most variation in numericalresponses? Explain.

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

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

Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.

a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph.

Tally for Discrete Variables: DRIVSTAR

DRIVSTAR

Count

Percent

2

3

4

5

N =

4

17

59

18

98

4.08

17.35

60.20

18.37


b. One quantitative variable recorded by the NHTSA is the driver’s severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean.
Descriptive Statistics: DRIVHEAD

Variable

N

Mean

StDev

Minimum

Q1

Median

Q3

Maximum

DRIVHEAD

98

603.7

185.4

216.0

475.0

605.0

724.3

1240.0

C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.

d..Find the z-score for a driver head-injury rating of 408. Interpret the result.

The Apprenticecontestants’ performance ratings.Refer to the Significance(April 2015) study of contestants’ performance on the popular TV show The Apprentice, Exercise 2.9 (p. 73). Recall that each of 159 contestants was rated (on a 20-point scale) based on their performance. The accompanying Minitab printout gives the mean and standard deviation of the contestant ratings, categorized by highest degree obtained (no degree, first degree, or postgraduate degree) and prize (job or partnership with Lord Sugar).

Descriptive Statistics: Ratings

Results for Prize = Job

Variable

Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

54

7.796

4.231

1.000

17

None

35

7.457

4.388

1.000

20

Post

10

9.80

4.54

2.000

17

Results for Prize = Partnership

Variable

Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

33

8.212

4.775

1.000

20.00

None

21

10.62

4.83

3.000

20.00

Post

6

6.50

3.33

2.000

12.00

a.Give a practical interpretation of the mean rating for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar.

b.Find an interval that captures about 95% of the ratings for contestants with a first (bachelor’s) degree who competed for a job with Lord Sugar.

c.An analysis of the data led the researchers to conclude that “when the reward for winning . . . was a job, more academically qualified contestants tended to perform less well; however, this pattern is reversed when the prize changed to a business partnership.” Do you agree? Explain.

Jamming attacks on wireless networks. Refer to the International Journal of Production Economics (Vol. 172, 2016) study of U.S. military jamming attacks on wireless networks used by terrorists, Exercise 1.16 (p. 50). Recall that 80 recent jamming attacks were classified according to network type (WLAN, WSN, or AHN) attacked and number of channels (single- or multi-channel) of the network. The results are summarized in the accompanying table.

Network Type/
Number of Channels

Number of
Jamming Attacks

WLAN / Single

31

WSN / Single

13

AHN / Single

8

WLAN / Multi

14

WSN / Multi

9

AHN / Multi

5

Total

80

a. Construct a Pareto diagram for the data. Interpret the results.

b. Construct a pie chart for network type only. Interpret the results.
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