Chapter 2: 145SE (page 142)
Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.
Short Answer
The standard deviation tells us the variability of the data.
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Chapter 2: 145SE (page 142)
Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.
The standard deviation tells us the variability of the data.
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Consider the following sample of five measurements: 2, 1, 1, 0, 3.
a.Calculate the range, s2, and s.
b.Add 3 to each measurement and repeat part a.
c.Subtract 4 from each measurement and repeat part a.
d.Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?
Using only integers between 0 and 10, construct two data sets with at least 10 observations each that have the same range but different means. Construct a dot plot for each of your data sets, and mark the mean of each data set on its dot diagram.
Refer to Exercise 2.141. Assuming all populations are approximately mound-shaped, for parts a鈥揹, determine whether the values 0, 4, and 12 are outliers.
Treating psoriasis with the 鈥淒octorfish of Kangal.鈥漃soriasis 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 鈥淒octorfish of Kangal.鈥 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.
Compute xbar, s2, and sfor each of the following data sets. If appropriate, specify the units in which your answer is expressed.
a.3, 1, 10, 10, 4
b.8 feet, 10 feet, 32 feet, 5 feet
c.-1, -4, -3, 1, -4, -4
d.1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce
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