(a)

Scenario: An article considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the article:

Homes
Urban 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0
Farm 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

Problem: Determine the value of the sample standard deviation for each sample. for the urban sample and for the farm sample. for the urban sample and for the farm sample. Interpret these values. Contrast variability in the two samples.

Process: ...

Answer: 22.30 and 6.09. The endotoxin concentration in an urban home typically deviates from the mean by an amount that is more than the average endotoxin concentration in urban homes, and the endotoxin concentration in a farm home typically deviates from the mean by an amount that is less than the average endotoxin concentration in farm homes. The variability in endotoxin concentration is far greater in urban homes than in farm homes.

(b)

Problem: 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.

Process: The fourth spread is the interquartile range. The first quartile () is the median number between the lowest data point () and the median of the data set (). The third quartile () is the median number between the median of the data set () and the highest data point (). The interquartile range is the difference between the third quartile and the first quartile.

Answer: 28 and 7. Yes, The fourth spreads do communicate the same message as the standard deviations did.

(c)

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