Solution Found!
Compute the sample median, 25% trimmed mean, 10% trimmed
Chapter 2, Problem 40E(choose chapter or problem)
Compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures. Reference exercise-27 The paper “Study on the Life Distribution of Microdrills” (J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy. a. ?Why can a frequency distribution not be based on the class intervals 0–50, 50–100, 100–150, and so on? b. ?Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, . . . , and then comment on interesting characteristics. c?. ?Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics. d?. ?What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?
Questions & Answers
QUESTION:
Compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures. Reference exercise-27 The paper “Study on the Life Distribution of Microdrills” (J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy. a. ?Why can a frequency distribution not be based on the class intervals 0–50, 50–100, 100–150, and so on? b. ?Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, . . . , and then comment on interesting characteristics. c?. ?Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics. d?. ?What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?
ANSWER:Problem 40E Answer: Step1: We have The paper “Study on the Life Distribution of Micro Drills” (J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy. x 11 59 81 105 161 14 61 84 105 168 20 65 85 112 184 23 67 89 118 206 31 68 91 123 248 36 71 93 136 263 39 74 96 139 289 44 76 99 141 322 47 78 101 148 388 50 79 104 158 513 We need to compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures. Step2: Consider the given data in Ascending Order x 11 59 81 105 161 14 61 84 105 168 20 65 85 112 184 23 67 89 118 206 31 68 91 123 248 36 71 93 136 263 39 74 96 139 289 44 76 99 141 322 47 78 101 148 388 50 79 104 158 513 Sample Median = 25th value + 26th value 91+93 2 = 2 = 184 2 = 92 Therefore,the sample median of the given data is 92. Step3: 1).Consider the given data in Ascending Order x 11 59 81 105 161 14 61 84 105 168 2