Exercise 34 presented the following data on endotoxinconcentration in settled dust both for a sample of urbanhomes 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 23.0F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.09.2 3.0 2.0 0.3a. Determine the value of the sample standard deviationfor each sample, interpret these values, and thencontrast variability in the two samples. [Hint:oxi 5 237.0 for the urban sample and 5 128.4 forthe farm sample, and oxi2 5 10,079 for the urbansample and 1617.94 for the farm sample.]b. Compute the fourth spread for each sample and compare.Do the fourth spreads convey the same messageabout variability that the standard deviations do?Explain.c. The authors of the cited article also provided endotoxinconcentrations in dust bag dust:U: 34.0 49.0 13.0 33.0 24.0 24.0 35.0 104.0 34.0 40.0 38.0 1.0F: 2.0 64.0 6.0 17.0 35.0 11.0 17.0 13.0 5.0 27.0 23.028.0 10.0 13.0 0.2Construct a comparative boxplot (as did the cited paper)and compare and contrast the four samples.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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:
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 value of the sample standard deviation
for each sample, interpret these values, and then
contrast variability in the two samples. [Hint:
oxi 5 237.0 for the urban sample and 5 128.4 for
the farm sample, and oxi
2 5 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:
U: 34.0 49.0 13.0 33.0 24.0 24.0 35.0 104.0 34.0 40.0 38.0 1.0
F: 2.0 64.0 6.0 17.0 35.0 11.0 17.0 13.0 5.0 27.0 23.0
28.0 10.0 13.0 0.2
Construct a comparative boxplot (as did the cited paper)
and compare and contrast the four samples.
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