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Chapter 2: Q41E (page 94)
Describe how the mean compares to the median for distribution as follows:
a.Skewed to the left
b.Skewed to the right
c.Symmetric
a. The mean is smaller than the median
b. The mean is greater than the median
c. The mean and median are the same
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Treating psoriasis with the “Doctorfish of Kangal.”Psoriasis is a skin disorder with no known cure and noproven effective pharmacological treatment. An alternative treatment for psoriasis is ichthyotherapy, also known as therapy with the “Doctorfish of Kangal.” Fish from the hot pools of Kangal, Turkey, feed on the skin scales of bathers, reportedly reducing the symptoms of psoriasis. In one study, 67 patients diagnosed with psoriasis underwent 3 weeks of ichthyotherapy (Evidence-Based Research in Complementary and Alternative Medicine,December 2006). The Psoriasis Area Severity Index (PASI) of each patient was measured both before and after treatment. (The lower the PASI score, the better is the skin condition.) Box plots of the PASI scores, both before (baseline) and after 3 weeks of ichthyotherapy treatment, are shown in the accompanying diagram.
a.Find the approximate 25th percentile, the median, and the 75th percentile for the PASI scores before treatment.
b.Find the approximate 25th percentile, the median, and the 75th percentile for the PASI scores after treatment.
c.Comment on the effectiveness of ichthyotherapy in treating psoriasis.
Nuclear power plants.According to the Nuclear Energy Institute (NEI), 62 nuclear power plants were operating in the United States in 2015. The table at top of the next column lists the 30 states that operate nuclear power
plants, the number of plants in each state, and whether the state has passed legislation supporting nuclear energy expansion (regulated) or not (deregulated).
a.Find the mean, median, and mode of the number of power plants per state. Interpret these values.
b.Repeat part afor the regulated states only.
c.Repeat part afor the deregulated states only.
d.Compare the results, parts band c.What inference can you make about the impact that state regulation has on the number of nuclear power plants?
e.Eliminate the state with the largest number of power plants from the data set and repeat part a.What effect does dropping this measurement have on the measures of central tendency found in part a?
f.Arrange the 30 values in the table from lowest to highest. Next, eliminate the lowest two values and the highest two values from the data set and find the mean of the remaining data values. The result is called a 10% trimmed meanbecause it is calculated after removing the highest 10% and the lowest 10% of the data values. What advantages does a trimmed mean have over the regular arithmetic mean?
State | Status | Number of Power Plants |
Alabama | Regulated | 2 |
Arizona | Regulated | 1 |
Arkansas | Regulated | 1 |
California | Regulated | 1 |
Connecticut | Deregulated | 1 |
Florida | Regulated | 3 |
Georgia | Regulated | 2 |
Illinois | Deregulated | 6 |
Iowa | Deregulated | 1 |
Kansas | Regulated | 1 |
Louisiana | Regulated | 2 |
Maryland | Deregulated | 1 |
Massachusetts | Deregulated | 1 |
Michigan | Deregulated | 3 |
Minnesota | Regulated | 2 |
Mississippi | Regulated | 1 |
Missouri | Regulated | 1 |
Nebraska | Regulated | 2 |
New Hampshire | Deregulated | 1 |
New Jersey | Deregulated | 3 |
New York | Deregulated | 4 |
North Carolina | Regulated | 3 |
Ohio | Deregulated | 2 |
Pennsylvania | Deregulated | 5 |
South Carolina | Regulated | 4 |
Tennessee | Regulated | 2 |
Texas | Deregulated | 2 |
Virginia | Regulated | 2 |
Washington | Regulated | 1 |
Wisconsin | Deregulated | 1 |
Calculate the range, variance, and standard deviation for the following samples:
a.39, 42, 40, 37, 41
b.100, 4, 7, 96, 80, 3, 1, 10, 2
c.100, 4, 7, 30, 80, 30, 42, 2
Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.
a.Would you consider 400 sags per week unusual, statistically? Explain.
b.Would you consider 100 swells per week unusual, statistically? Explain.
Spreading rate of spilled liquid.A contract engineer atDuPont Corp. studied the rate at which a spilled volatileliquid will spread across a surface (Chemical EngineeringProgress, January 2005). Assume 50 gallons of methanol
spills onto a level surface outdoors. The engineer used derived empirical formulas (assuming a state of turbulent-freeconvection) to calculate the mass (in pounds) of the spillafter a period of time ranging from 0 to 60 minutes. The calculatedmass values are given in the table. Is there evidenceto indicate that the mass of the spill tends to diminish astime increases?
Support your answer with a scatterplot.
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