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Chapter 3: Problem 87
Explain how the interquartile range is calculated. Give one example.
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Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.
Suppose that on a certain section of \(1-95\) with a posted speed limit of \(65 \mathrm{mph}\), the speeds of all vehicles have a bell-shaped distribution with a mean of \(72 \mathrm{mph}\) and a standard deviation of \(3 \mathrm{mph}\). 4\. Using the empirical rule, find the percentage of vehicles with the following speeds on this section of \(1-95\). i. 63 to \(81 \mathrm{mph}\) Ii. 69 to \(75 \mathrm{mph}\) 4b. Using the empirical rule, find the interval that contains the speeds of \(95 \%\) of vehicles traveling on this section of \(1-95\).
Jeffrey is serving on a six-person jury for a personal-injury lawsuit. All six jurors want to award damages to the plaintiff but cannot agree on the amount of the award. The jurors have decided that each of them will suggest an amount that he or she thinks should be awarded; then they will use the mean of these six numbers as the award to recommend to the plaintiff. a. Jeffrey thinks the plaintiff should receive \(\$ 20,000\), but he thinks the mean of the other five jurors' recommendations will be about \(\$ 12,000 .\) He decides to suggest an inflated amount so that the mean for all six jurors is \(\$ 20,000\). What amount would Jeffrey have to suggest? b. How might this jury revise its procedure to prevent a juror like Jeffrey from having an undue influence on the amount of damages to be awarded to the plaintiff?
A local golf club has men's and women's summer leagues. The following data give the scores for 芒 round of 18 holes of golf for 17 men and 15 women randomly selected from their respective leagues. \begin{tabular}{l|rrrrrrrrr} \hline Men & 87 & 68 & 92 & 79 & 83 & 67 & 71 & 92 & 112 \\ & 75 & 77 & 102 & 79 & 78 & 85 & 75 & 72 & \\ \hline Women & 101 & 100 & 87 & 95 & 98 & 81 & 117 & 107 & 103 \\ & 97 & 90 & 100 & 99 & 94 & 94 & & & \\ \hline \end{tabular} a. Make a box-and-whisker plot for each of the data sets and use them to discuss the similarities and differences between the scores of the men and women golfers. b. Compute the various descriptive measures you have learned for each sample. How do they compare?
The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days. \(\begin{array}{llllllllll}45 & 52 & 48 & 41 & 56 & 46 & 44 & 42 & 48 & 53 \\\ 51 & 53 & 51 & 48 & 46 & 43 & 52 & 50 & 54 & 47 \\ 44 & 47 & 50 & 49 & 52 & & & & & \end{array}\) Prepare a box-and-whisker plot. Comment on the skewness of these data.
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