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Chapter 2: Q35E (page 94)
Calculate the mean and median of the following grade point averages:
3.2, 2.5, 2.1, 3.7, 2.8, 2.0
The mean is 2.71.
The median is 2.65.
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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.
Rankings of research universities.Based on factors (e.g., academic reputation, financial aid offerings, overall cost, and success of graduates in the post-college job market) that actual college freshmen said were most important to their college decision, College Choice developed their 2015 Rankings of National Research Universities. Data for the top 50 universities are saved in the TOPUNIVfile. Several are listed in the accompanying table above.
a) The average financial aid awarded values were determined by recording the financial aid awarded to each freshman who attended the university in 2015. Does this statistic represent a population or sample mean? Interpret this value for Harvard University.
b) The median salary during early career values were determined by recording the salaries of a random selection of alumni with 0 to 5 years of experience. Does this statistic represent a population or sample median? Interpret this value for Harvard University.
Rank | University | Public/ Private | Academic Reputation Score (100 pt. scale) | Average Financial Aid Awarded | Average Net Cost Attend | Median Salary During Early Career | % High Meaning | %Stem Degrees |
1 | Harvard University | Private | 99 | \(41,555 | \)14,455 | \(61,400 | 65% | 28% |
5 | Yale University | Private | 97 | \)39,771 | \(18,479 | \)60,300 | 68% | 21% |
20 | University of California Berkeley | Public | 79 | \(16,141 | \)16,178 | \(59,500 | 50% | 31% |
23 | University of Virginia | Public | 76 | \)16,834 | \(12,672 | \)54,700 | 52% | 24% |
27 | Carnegie Mellon University | Private | 76 | \(24,263 | \)33,257 | \(64,700 | 46% | 51% |
47 | Pepperdine University | Private | 60 | \)29,926 | \(25,345 | \)48,300 | 51% | 4% |
Question: Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.47 (p. 96). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C). Measures of variation for the permeability measurements (mV) of each sandstone group are displayed in the accompanying Minitab printout.
Descriptive Statistics: PermA, PermB, PermC | ||||||
Variable | N | StDev. | Variance | Minimum | Maximum | Range |
PermA | 100 | 14.48 | 209.53 | 55.20 | 122.40 | 67.20 |
PermB | 100 | 21.97 | 482.75 | 50.40 | 150.00 | 99.60 |
PermC | 100 | 20.05 | 401.94 | 52.20 | 129.00 | 76.80 |
a.Find the range of the permeability measurements for Group A sandstone slices. Verify its value using the minimum and maximum values shown on the printout.
b.Find the standard deviation of the permeability measurements for Group A sandstone slices. Verify its value using the variance shown on the printout.
c.Which condition (A, B, or C) has the more variable permeability data?
Lead in drinking water. The U.S. Environmental Protection Agency (EPA) sets a limit on the amount of lead permitted in drinking water. The EPA Action Level for lead is .015 milligram per liter (mg/L) of water. Under EPA guidelines, if 90% of a water system’s study samples have a lead concentration less than .015 mg/L, the water is considered safe for drinking. I (coauthor Sincich) received a recent report on a study of lead levels in the drinking water of homes in my subdivision. The 90th percentile of the study sample had a lead concentration of .00372 mg/L. Are water customers in my subdivision at risk of drinking water with unhealthy lead levels? Explain.
Question: In business, do nice guys really finish last?Do “nice guys finish last” in the competitive corporate world? In a study published in Nature(March 20, 2008), college students repeatedly played a version of the game “prisoner’s dilemma,” where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units; defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used against each player. A graph of the data
is shown in the accompanying scatterplot. Does it appear that average payoff is associated with punishment use? The researchers concluded that “winners don’t punish.” Do you agree? Explain.
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