Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes: a. ?Determine the value of the sample standard deviation for each sample, interpret these values, and then contrast variability in the two samples. [Hint:?xi=237.?0 ?for the urban sample and =128.4 for the farm sample, and ?x2i = 10,079 for the urban sample and 1617.94 for the farm sample.] b?. ?Compute the fourth spread for each sample and compare. Do the fourth spreads convey the same message about variability that the standard deviations do? Explain. c. ?The authors of the cited article also provided endotoxin concentrations in dust bag dust: Construct a comparative boxplot (as did the cited paper) and compare and contrast the four samples.

Answer: Step1: The given data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes: 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 Step2: a). To determine the value of the sample standard deviation for each sample. U (u u) F (f f) 6 241.4916 4 20.7936 5 273.5716 14 29.5936 11 111.0916 11 5.9536 33 131.3316 9 0.1936 4 307.6516 9 0.1936 5 273.5716 8 0.3136 80 3417.5716 4 20.7936 18 12.5316 20 130.8736 35 181.1716 5 12.6736 17 20.6116 8.9 0.1156 23 2.1316 21 154.7536 9.2 0.4096 3 30.9136 2 43.0336 0.3 68.2276 2 2 u = (u u) = f = (f f) = 237 4972. 128.4 518.836 u f Mean u = n Mean f = n = 128.4 15 = 237 f = 8.56 11 u = 21.5454 2 (uu) (ff) Variance u = Variance f = n 1 n 1 = 4972 = 518.836 111 151 u2 = 497.2 f2 = 37.0598 u = 497.2 f = 37.0598 u = 22.30 f = 6.09 Here we conclude that the variability in endotoxin concentration is far greater in urban homes than in farm homes. Step3: b). To compute the fourth spread for each sample and compare. The sample of urban homes: First we have to arrange the data ascending order. U: 4.0 5.0 5.0 6.0 11 17 18 23 33 35 80 First we have to find median. Median = 17 ( if n is odd, the median is the middle value. That is 17 is median) Consider lower half of the data. Select the data before median. 4.0 5.0 5.0 6.0 11 Therefore, lower fourth = 5.0 ( here n is odd, so lower fourth is the middle value) Consider upper half data that. Select the data after the median. 18 23 33 35 80 Therefore, upper fourth = 33 ( here n is odd, so upper fourth is the middle value) The ourth spread for urban homes: Fourth spread = upper fourth - lower fourth = 33 - 5 = 28 Therefore, fourth spread for urban homes is 28. The sample of farm homes: Arrange the data ascending order. 0.3 2.0 3 4 4 5 8 8.9 9 9 9.2 11 14 20 21 We have to find median. Median = 8.9 ( if n is odd, the median is the middle value. That is 8.9 is the median) Consider lower half of the data. Select the data before median. 0.3 2 3 4 4 5 8 Therefore, lower fourth = 4 ( here n is odd, so lower fourth is the middle value) Consider upper half data that. Select the data after the median. 9 9 9.2 11 14 20 21 Therefore, upper fourth = 11 ( here n is odd, so upper fourth is the middle value) The f ourth spread for farm homes: Fourth spread = upper fourth - lower fourth = 11 - 4 = 7 Therefore, fourth spread for farm homes is 7. Here we conclude that the variability in endotoxin concentration is far greater in urban homes than in farm homes. Step4: c). Consider the box plots below. The endotoxin concentration in urban homes generally exceeds that in farm homes, whether measured by settled dust or bag dust. The endotoxin concentration in bag dust generally exceeds that of settled dust, both in urban homes and in farm homes. Settled dust in farm homes shows far less variability than any other scenario.