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Chapter 2: Q41E (page 94)
Describe how the mean compares to the median for distribution as follows:
a.Skewed to the left
b.Skewed to the right
c.Symmetric
a. The mean is smaller than the median
b. The mean is greater than the median
c. The mean and median are the same
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Ranking driving performance of professional golfers.Refer to The Sport Journal(Winter 2007) analysis of anew method for ranking the total driving performance ofgolfers on the PGA tour, Exercise 2.52 (p. 97). Recall thatthe method uses both the average driving distance (yards)and driving accuracy (percent of drives that land in thefairway). Data on these two variables for the top 40 PGAgolfers are saved in the accompanying file. A professionalgolfer is practicing a new swing to increase his averagedriving distance. However, he is concerned that his drivingaccuracy will be lower. Is his concern a valid one? Explain.
Construct a relative frequency histogram for the data summarized in the accompanying table.
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.
Groundwater contamination in wells. In New Hampshire, about half the counties mandate the use of reformulated gasoline. This has led to an increase in the contamination of groundwater with methyl tert-butyl ether (MTBE). Environmental Science & Technology (Jan. 2005) reported on the factors related to MTBE contamination in public and private New Hampshire wells. Data were collected for a sample of 223 wells. Three of the variables are qualitative in nature: well class (public or private), aquifer (bedrock or unconsolidated), and detectible level of MTBE (below limit or detect). [Note: A detectible level of MTBE occurs if the MTBE value exceeds .2 micrograms per liter.] The data for 11 selected wells are shown in the accompanying table.
Source: Based on J. D. Ayotte, D. M. Argue, and F. J. McGarry, 鈥淢ethyl tert-Butyl Ether Occurrence and Related Factors in Public and Private Wells in Southeast New Hampshire,鈥� Environmental Science & Technology, Vol. 39, No. 1, Jan. 2005, pp. 9鈥�16
a. Use graphical methods to describe each of the three qualitative variables for all 223 wells.
b. Use side-by-side bar charts to compare the proportions of contaminated wells for private and public well classes.
c. Use side-by-side bar charts to compare the proportions of contaminated wells for bedrock and unconsolidated aquifers.
d. What inferences can be made from the bar charts, parts a鈥揷?
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.
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