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94Chapter 3Statistics for Describing, Exploring, and Comparing DataBasic Skills and ConceptsStatistical Literacy and Critical Thinking1. Measures of CenterIn what sense are the mean, median, mode, and midrange measuresof “center”?2. AverageA headline in USA Todaystated that “Average family income drops 2.3%.” Whatis the role of the term averagein statistics? Should another term be used in place of average?3. MedianIn an editorial, the Poughkeepsie Journalprinted this statement: “The medianprice—the price exactly in between the highest and lowest—...” Does that statement cor-rectly describe the median? Why or why not?4. Nominal DataWhen the Indianapolis Colts recently won the Super Bowl, the numberson the jerseys of the active players were 29, 41, 50, 58, 79, ..., 10 (listed in the alphabeticalorder of the player’s names). Does it make sense to calculate the mean of those numbers? Whyor why not?In Exercises 5–20, find the (a) mean,(b) median,(c) mode,and (d) midrangethe given sample data. Then answer the given questions.5. Number of English WordsA simple random sample of pages from Merriam-Webster’sCollegiate Dictionary, 11th edition,was obtained. Listed below are the numbers of words de-fined on those pages. Given that this dictionary has 1459 pages with defined words, estimatethe total number of defined words in the dictionary. Is that estimate likely to be an accurateestimate of the number of words in the English language?6. Tests of Child Booster SeatsThe National Highway Traffic Safety Administration51633643346273395379for3-2
conducted crash tests of child booster seats for cars. Listed below are results from those tests,with the measurements given in hic (standard head injury conditionunits). According to thesafety requirement, the hic measurement should be less than 1000 hic. Do the results suggestthat all of the child booster seats meet the specified requirement?7. Car Crash CostsThe Insurance Institute for Highway Safety conducted tests with crashesof new cars traveling at 6 mi/h. The total cost of the damages was found for a simple randomsample of the tested cars and listed below. Do the different measures of center differ very much?8. FICO ScoresThe FICO credit rating scores obtained in a simple random sample arelisted below. As of this writing, the reported mean FICO score was 678. Do these sampleFICO scores appear to be consistent with the reported mean?9. TV SalariesListed below are the top 10 annual salaries (in millions of dollars) of TV per-sonalities (based on data from OK!magazine). These salaries correspond to Letterman, Cowell,Sheindlin, Leno, Couric, Lauer, Sawyer, Viera, Sutherland, and Sheen. Given that these arethe top 10salaries, do we know anything about the salaries of TV personalities in general? Aresuch top 10lists valuable for gaining insight into the larger population?10. Phenotypes of PeasBiologists conducted experiments to determine whether a defi-ciency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the pheno-type codes, where and Can the measures of center be obtained for these values? Do the results make