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34 CHAPTER 1 Overview and Descriptive Statistics

EXERCISES Section 1.3 (33–43)

33. The May 1, 2009 issue of The Montclarian reported the fol- lowing home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):

590 815 575 608 350 1285 408 540 555 679

a. Calculate and interpret the sample mean and median. b. Suppose the 6th observation had been 985 rather than

1285. How would the mean and median change? c. Calculate a 20% trimmed mean by first trimming the two

smallest and two largest observations. d. Calculate a 15% trimmed mean.

34. Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article “Dust Sampling Methods for Endotoxin—An Essential, But Underestimated Issue” (Indoor Air, 2006: 20–27) considered various issues associated with determin- ing endotoxin concentration. The following data on concen- tration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the cited article.

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0 F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

a. Determine the sample mean for each sample. How do they compare?

b. Determine the sample median for each sample. How do they compare? Why is the median for the urban sample so different from the mean for that sample?

c. Calculate the trimmed mean for each sample by deleting the smallest and largest observation. What are the corre- sponding trimming percentages? How do the values of these trimmed means compare to the corresponding means and medians?

35. The minimum injection pressure (psi) for injection molding specimens of high amylose corn was determined for eight different specimens (higher pressure corresponds to greater processing difficulty), resulting in the following observa- tions (from “Thermoplastic Starch Blends with a Polyethylene-Co-Vinyl Alcohol: Processability and Physical Properties,” Polymer Engr. and Science, 1994: 17–23):

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A trimmed mean with a moderate trimming percentage—someplace between 5% and 25%
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