APPENDIX D 773 the data are not at all accurate. And what about that person who smokes 50 cigarettes (or 2.5 packs) a day? What are they thinking? 21. Systolic: x = 127.6 mm Hg; median = 124.0 mm Hg. Diastolic: x = 73.6 mm Hg; median = 75.0 mm Hg. Given that systolic and diastolic blood pressures measure different characteristics, a comparison of the measures of center doesn’t make sense. Because the data are matched, it would make more sense to investigate whether there is an association or correlation between systolic blood pressure measurements and diastolic blood pressure measurements. 23. Males: x = 69.5 beats per minute; median = 66.0 beats per minute. Females: x = 82.1 beats per minute; median = 84.0 beats per minute. The pulse rates of males appear to be lower than those of females. 25. ANSUR I 1988: x = 78.49 kg and median = 77.70 kg. ANSUR II 2012: x = 85.52 kg and median = 84.60 kg. It does appear that males have become heavier. (TI data: ANSUR I 1988: x = 78.82 kg and median = 77.70 kg. ANSUR II 2012: x = 84.53 kg and median = 84.00 kg.) 27. x = 98.20°F; median = 98.40°F. These results suggest that the mean is less than 98.6°F. 29. x = 34.6 minutes, which is reasonably close to the mean of 31.4 minutes obtained by using the original list of values. 31. x = 55.1 years. The mean from the frequency distribution is quite close to the mean of 55.2 years obtained by using the original list of values. 33. 3.14; yes 35. a. 70 years b. n - 1 37. 504 lb is an outlier. Median: 285.5 lb; mean: 294.4 lb; 10% trimmed mean: 285.4 lb; 20% trimmed mean: 285.8 lb. The median, 10% trimmed mean, and 20% trimmed mean are all quite close, but the untrimmed mean of 294.4 lb differs from them because it is strongly affected by the inclusion of the outlier. 39. 0.247% 41. The median found using the given expression is 30.5 minutes. The median of the 1000 times from Data Set 31 is 30.0 minutes. The difference is 0.5 minute. Section 3-2 1. 9.58 cm is in the general ballpark of the standard deviation of 7.10 cm calculated using the 153 heights. The range rule of thumb does not necessarily give an estimate of s that is very accurate. 3. 50.41 cm2 5. Range = 76.0; s2 = 755.4; s = 27.5. Because the jersey numbers are really just replacements for names, they are at the nominal level of measurement, so the results are meaningless. 7. Range = $4550 million; s2 = 2,825,670 1million dollars22; s = $1681 million dollars. Because the data are from celebrities with the highest net worth, the measures of variation are not at all typical for all celebrities. Because all of the amounts end with 0, it appears that they are rounded to the nearest ten million dollars, so it would make sense to round the results to the nearest million dollars, as is done here. 9. Range = 44.0 attacks; s2 = 132.7 attacks2; s = 11.5 attacks. The measures of variation are blind to any trend for these timeseries data. 5. The scatterplot does not show any pattern. There does not appear to be correlation between magnitude and depth. Chapter 3 Answers Section 3-1 1. The term average is not used in statistics. The term mean should be used for the result obtained by adding all of the sample values and dividing the total by the number of sample values. 3. They use different approaches for providing a value (or values) of the center or middle of the sorted list of data. 5. x = 47.8; median = 60.0; mode = none; midrange = 49.0. The resulting statistics are meaningless because the jersey numbers are nominal data that are just replacements for names, and they do not measure or count anything. 7. x = $2281 million; median= $1450 million; mode = $1000 million; midrange = $3225 million. Apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population of net worth of all celebrities. The numbers all end in 0, and they appear to be rounded estimates (which is the reason for rounding to the nearest whole number). 9. x = 76.4 attacks; median = 77.5 attacks; mode = no mode; midrange = 76.0 attacks. The data are time-series data, but the measures of center do not reveal anything about a trend consisting of a pattern of change over time. 11. x = $198.2; median = $200.0; mode = $250; midrange = $175.0. The lowest price is a relevant statistic for someone planning to buy one of the smart thermostats. 13. x = 32.6 mg; median= 39.5 mg; mode = 0 mg; midrange = 27.5 mg. Americans consume some brands much more often than others, but the 20 brands are all weighted equally in the calculations, so the statistics are not necessarily representative of the population of all cans of the same 20 brands consumed by Americans. 15. x = 1.2; median = 1.0; mode = 1; midrange = 1.5. The statistics are meaningless because the data are at the nominal level of measurement with the numbers being replacements for “right” and “left.” Because the measurements were made in 1988, they are not necessarily representative of the current population of all Army women. 17. x = $365.3; median = $200.0; mode = $500; midrange = $1269.5. The amounts of $1500 and $2500 appear to be outliers. 19. x = 2.8 cigarettes; median = 0.0 cigarettes; mode = 0 cigarettes; midrange = 25.0 cigarettes. Because the selected subjects report the number of cigarettes smoked, it is very possible that
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