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Chapter 3: Q 3.6. (page 100)
Complete the following statement: The descriptive measure is resistant if .......
The descriptive measure is resistant if it is not sensitive to the influence of a few extreme observation.
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Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article 鈥淏ody Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania鈥� (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159-165). Tiger snakes and lowland copperheads are both large snakes confined to the cooler parts of Tasmania. The weights of the male lowland copperhead in Tasmania have a mean of 812.07 g and a standard deviation of 330.24 g; the weights of the male tiger snake in Tasmania have a mean of 743.65 g and a standard deviation of 336.36 g.
a. Determine the z-scores for both a male lowland copperhead snake and a male tiger snake whose weights are 850 g.
b. Under what conditions would it be reasonable to use z-scores to compare the relative standings of the weights of the two snakes?
c. Assuming that a comparison using z-scores is legitimate, relative to the other snakes of its type, which snake is heavier?
Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.
Atlantic Basin Hurricanes. The Tropical Cyclone Report, a publication of the National Hurricane Center, contains comprehensive information on each tropical cyclone, including synoptic history, meteorological statistics, casualties, and damages. A hurricane is a tropical cyclone with winds that have reached a constant speed of or more. During one year, there were Atlantic basin hurricanes. Their maximum wind speeds, in miles per hour (), were as shown in the following table.
Consider these storms a population of interest. Obtain the following parameters for the maximum wind speeds. Use the appropriate mathematical notation for the parameters to express your answers.
a. Mean
b. Standard deviation
c. Median
d. Mode
e. IQR
What condition on a data set is required to apply the Empirical rule?
The data set has mean and standard deviation . Fill in the following blanks:
a. Approximately of the observations lie between_ and _
b. Approximately of the observations lie between_ and _
c. Approximately of the observations lie between _and _
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