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Chapter 2: Q106E (page 125)
A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements are outliers.
a.65
b.21
c.72
d.98
(a) Not an outlier
(b) Outlier
(c) Not an outlier
(d) Outlier
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Surface roughness of oil field pipe.Oil field pipes are internally coated to prevent corrosion. Researchers at the University of Louisiana, Lafayette, investigated the influence that coating may have on the surface roughness of oil field pipes (Anti-corrosion Methods and Materials, Vol. 50, 2003). A scanning probe instrument was used to measure the surface roughness of each in a sample of 20 sections of coated interior pipe. The data (in micrometers) are provided in the table.
(1.72, 2.50, 2.16, 2.13, 1.06, 2.24, 2.3,1 2.03, 1.09, 1.40, 2.57, 2.64, 1.26, 2.05, 1.19, 2.13, 1.27, 1.51, 2.41, 1.95)
a.Find and interpret the mean of the sample.
b.Find and interpret the median of the sample.
c.Which measure of central tendency—the mean or the median—best describes the surface roughness of the sampled pipe sections? Explain.
Question: Construct a scatterplot for the data in the following table.
Variable 1: 5 3 -1 2 7 6 4 0 8
Variable 2: 14 3 10 1 8 5 3 2 12
Answer the following questions about the variability of data sets:
a.What is the primary disadvantage of using the range to compare the variability of data sets?
b.Describe the sample variance using words rather than a formula. Do the same with the population variance.
c.Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.
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.
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% |
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