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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鈥攖he mean or the median鈥攂est describes the surface roughness of the sampled pipe sections? 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% |
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.
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?
Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.
a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?
b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
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