a. a. Jay L. Devore Probability and Statistics

Type 3 350 361 362 364 364 365 366 371 377 377 377 379 380 380 392 a. Construct a comparative boxplot, and comment on simi- larities and differences. b. Construct a comparative dotplot a dotplot for each sam- ple with a common scale. Comment on similarities and differences. c. Does the comparative boxplot of part a give an inform- ative assessment of similarities and differences? Explain your reasoning. 76. The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange, which is the average of the smallest and largest observations, and the midfourth, which is the average of the two fourths.Which of these five measures of center are resistant to the effects of out- liers and which are not? Explain your reasoning. 77. The authors of the article “Predictive Model for Pitting Corrosion in Buried Oil and Gas Pipelines” Corrosion, 2009: 332–342 provided the data on which their investiga- tion was based. a. Consider the following sample of 61 observations on maximum pitting depth mm of pipeline specimens buried in clay loam soil. 0.41 0.41 0.41 0.41 0.43 0.43 0.43 0.48 0.48 0.58 0.79 0.79 0.81 0.81 0.81 0.91 0.94 0.94 1.02 1.04 1.04 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.19 1.19 1.27 1.40 1.40 1.59 1.59 1.60 1.68 1.91 1.96 1.96 1.96 2.10 2.21 2.31 2.46 2.49 2.57 2.74 3.10 3.18 3.30 3.58 3.58 4.15 4.75 5.33 7.65 7.70 8.13 10.41 13.44 Construct a stem-and-leaf display in which the two largest values are shown in a last row labeled HI. b. Refer back to a, and create a histogram based on eight classes with 0 as the lower limit of the first class and class widths of .5, .5, .5, .5, 1, 2, 5, and 5, respectively. c. The accompanying comparative boxplot from Minitab shows plots of pitting depth for four different types of soils. Describe its important features. 78. Consider a sample and suppose that the values of , s 2 , and s have been calculated. a. Let for . How do the values of s 2 and s for the y i ’ s compare to the corresponding values for the x i ’ s? Explain. b. Let for . What are the values of the sample variance and sample standard deviation for the z i ’ s? 79. Let and denote the sample mean and variance for the sample and let and denote these quanti- ties when an additional observation is added to the sample. a. Show how can be computed from and . b. Show that so that can be computed from , , and . c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16 th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard devi- ation for all 16 elongation observations? 80. Lengths of bus routes for any particular transit system will typically vary from one route to another. The article “Planning of City Bus Routes” J. of the Institution of Engineers, 1995: 211–215 gives the following information on lengths km for one particular system: Length Frequency 6 23 30 35 32 Length Frequency 48 42 40 28 27 Length Frequency 26 14 27 11 2 402,45 352,40 302,35 282,30 262,28 242,26 222,24 202,22 182,20 162,18 142,16 122,14 102,12 82,10 62,8 s n 2 x n x n1 1 s n1 1 2 ns n1 1 2 5 n 2 1s n 2 1 n n 1 1 x n1 1 2 x n 2 x n1 1 x n x n1 1 x n1 1 s n1 1 2 x n1 1 x 1 , c , x n s n 2 x n i 5 1, c , n z i 5 x i 2 x s i 5 1, c , n y i 5 x i 2 x x x 1 , x 2 , c , x n Maximum pit depth 14 12 10 8 6 4 2 C CL SCL SYCL Soil type Comparative boxplot for Exercise 77 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.