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Chapter 3: Q. 3.150 (page 136)
Explain why minimum and maximum observations are added to the three quartiles to describe better the variation in a data set.
The minimum and maximum observations are added because their difference denotes the variation in data.
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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.
Simple data sets have been given for you to try locating the descriptive metrics mentioned in this section. For each data set separately.
(a) Calculate the quartiles,
(b) calculate the interquartile range
(c)compile a five-number summary.
Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article “Body Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania” (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?
We have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set.
Obtain the quartiles, determine the inter quartile range, find the five-number summary.
Magazine Ads. Advertising researchers F. Shuptrine and D. McVicker wanted to determine whether there were significant differences in the readability of magazine advertisements. Thirty magazines were classified based on their educational level-high, mid, or low-and then three magazines were randomly selected from each level. From each magazine, six advertisements were randomly chosen and examined for readability. In this particular case, readability was characterized by the numbers of words, sentences, and words of three syllables or more in each ad. The researchers published their findings in the article "Readability Levels of Magazine Ads" (Journal of Adrertiving Reseanch, Vol. ). The number of words of three syllables or more in each ad are provided on the Weissstats site.
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