statistics the number of words in the English language

| January 30, 2017

Question
Find the (a)mean, (b) median, (c) mode, and (d) midrange for the given sample data. Then answer the given questions.

a) Number of English WordsA simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, was obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1459 pages with defined words, estimate the total number of defined words in the dictionary. Is that estimate likely to be an accurate estimate of the number of words in the English language?

51 63 36 43 34 62 73 39 53 79

b) Tests of Child Booster SeatsThe National Highway Traffic Safety Administration 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 condition units). According to the safety requirement, the hic measurement should be less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?

774 649 1210 546 431 612

c) Car Crash CostsThe Insurance Institute for Highway Safety conducted tests with crashes of new cars traveling at 6 mi/h. The total cost of the damages was found for a simple random sample of the tested cars and listed below. Do the different measures of center differ very much?

$7448 $4911 $9051 $6374 $4277

d) FICO ScoresThe FICO credit rating scores obtained in a simple random sample are listed below. As of this writing, the reported mean FICO score was 678. Do these sample FICO scores appear to be consistent with the reported mean?

714 751 664 789 818 779 698 836 753 834 693 802

e) TV SalariesListed below are the top 10 annual salaries (in millions of dollars) of TV personalities (based on data from OK! magazine). These salaries correspond to Letterman, Cowell, Sheindlin, Leno, Couric, Lauer, Sawyer, Viera, Sutherland, and Sheen. Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general? Are such top 10 lists valuable for gaining insight into the larger population?

38 36 35 27 15 13 12 10 9.6 8.4

f) Phenotypes of PeasBiologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where

1

smooth-yellow,

2

smooth-green,

3

wrinkled-yellow,

4

wrinkled-green

Can the measures of center be obtained for these values? Do the results make sense?

2 1 1 1 1 1 1 4 1 2 2 1 2 3 3 2 3 1 3 1 3 1 3 2 2

g) Space Shuttle FlightsListed below are the durations (in hours) of a simple random sample of all flights (as of this writing) of NASA’s Space Transport System (space shuttle). The data are from Data Set 10 in Appendix B. Is there a duration time that is very unusual? How might that duration time be explained?

73 95 235 192 165 262 191 376 259 235 381 331 221 244 0

h) Freshman 15According to the “freshman 15” legend, college freshmen gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshmen included in a study (“Changes in Body Weight and Fat Mass of Men and Women in the First Year of College: A Study of the ‘Freshman 15,’” by Hoffman, Policastro, Quick, and Lee, Journal of American College Health, Vol. 55, No. 1). Positive values correspond to students who gained weight and negative values correspond to students who lost weight. Do these values appear to support the legend that college

students gain 15 pounds (or 6.8 kilograms) during their freshman year? Why or why not?

11 3 0 -2 3 -2 -2 5 -2 7 2 4 1 8 1 0 -5 2

i) Change in MPG MeasureFuel consumption is commonly measured in miles per gallon. The Environmental Protection Agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. For example, the first car was measured at 16 mi/gal under the old standards and 15 mi/gal under the new 2008 standards, so the amount of the decrease is 1 mi/gal. Would there be much of an error if, instead of retesting all older cars using the new 2008 standards, the mean amount of decrease is subtracted

from the measurement obtained with the old standard?

1 2 3 2 4 3 4 2 2 2 2 3 2 2 2 3 2 2 2 2

j) NCAA Football Coach SalariesListed below are the annual salaries for a simple random sample of NCAA football coaches (based on data from USA Today). How do the mean and median change if the highest salary is omitted?

$150,000 $300,000 $350,147 $232,425 $360,000 $1,231,421 $810,000 $229,000

k) Playing Times of Popular SongsListed below are the playing times (in seconds) of songs that were popular at the time of this writing. (The songs are by Timberlake, Furtado, Daughtry, Stefani, Fergie, Akon, Ludacris, Beyonce, Nickelback, Rihanna, Fray, Lavigne, Pink, Mims, Mumidee, and Omarion.) Is there one time that is very different from the others?

448 242 231 246 246 293 280 227 244 213 262 239 213 258 255 257

l) SatellitesListed below are the numbers of satellites in orbit from different countries. Does one country have an exceptional number of satellites? Can you guess which country has the most satellites?

158 17 15 18 7 3 5 1 8 3 4 2 4 1 2 3 1 1 1 1 1 1 1 1

m) Years to Earn Bachelor’s DegreeListed below are the lengths of time (in years) it took for a random sample of college students to earn bachelor’s degrees (based on data from the U.S. National Center for Education Statistics). Based on these results, does it appear that it is common to earn a bachelor’s degree in four years?

4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5 6 6 8 9 9 13 13 15

n) Car EmissionsEnvironmental scientists measured the greenhouse gas emissions of a sample of cars. The amounts listed below are in tons (per year), expressed as equivalents. Given that the values are a simple random sample selected from Data Set 16 in Appendix B, are these values a simple random sample of cars in use? Why or why not?

7.2 7.1 7.4 7.9 6.5 7.2 8.2 9.3

o) BankruptciesListed below are the numbers of bankruptcy filings in Dutchess County, New York State. The numbers are listed in order for each month of a recent year (based on data from the Poughkeepsie Journal ). Is there a trend in the data? If so, how might it be explained?

59 85 98 106 120 117 97 95 143 371 14 15

p) Radiation in Baby TeethListed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s,” by Mangano, et al., Science of the Total Environment). How do the different measures of center compare? What, if anything, does this suggest about the distribution of the data?

155

142

149

130

151

163

151

142

156

133

138

161

128

144

172

137

151

166

147

163

145

116

136

158

114

165

169

145

150

150

150

158

151

145

152

140

170

129

188

156

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