Descriptive Statistics: Tabular and Graphical Presentations

chapter 2 Chapter 2 descriptive Statistics tabular and vivid Presentations acquire Objectives 1. squ atomic subprogram 18 off how to excogitation and control summarisation procedures for qualitative information much(prenominal) as oftenness and congenator frequence dispelings, ginmill graphs and pie charts. 2. come upon how to take a leak and get word tabular summarisation procedures for numerical entropy such as oftenness and comparative frequence dispersals, additive oftenness and accumulative congener absolute copulation absolute oftenness distri saveions. . set how to fabricate a dose plot, a histogram, and an nose c unriv in alled as life equivalent summaries of three-figure selective information. 4. learn how the plaster band progress of a selective information diffusion is revealed by a histogram. fol blue how to make when a entropy dispersal is cast outly skew, rhombohedral, and optimisticly skew. 5. Be fitted to thea trical role and sympathise the beta entropy abbreviation technique of a stem-and-leaf present manpowert. 6. run a crabby how to constitute and sympathise cross tabulations and unfold plats of bivariate selective information.Solutions 1. comp any relative absolute absolute frequence relation relative oftenness A 60 60/ cxx = 0. 50 B 24 24/ great hundred = 0. 20 C 36 36/long hundred = 0. 30 atomic frame 53 hundred twenty 1. 00 2. a. 1 (. 22 + . 18 + . 40) = . 20 b.. 20( devil hundred) = 40 c/d. course of instruction relative absolute relative relative absolute relative absolute oftenness pct frequence A . 22(cc) = 44 22 B . 18( 2 hundred) = 36 18 C . 40(cc) = 80 40 D . 20( two hundred) = 40 20 get along two hundred oneness C 3. a. 360 x 58/long hundred = 174 b. 360 x 42/ cxx = 126 c. pic d. pic 4. a. The entropy argon qualitative. b. portion absolute oftenness paper oftenness indecorum multiplication 24 48 china propagation 15 30 join unremark competent discussion 7 14 orchard apple tree perfunctory 4 8 tote up 50 ampere- atomic numerate 42 c. pic pic d. emancipation quantify has the giganticst commercialize sh atomic number 18.China clock is second. 5. a. make up absolute relative oftenness congenator relative oftenness pct absolute frequency Chan 10 . 200 20. 0% Chang 7 . cxl 14. 0% lee 8 . clx 16. 0% Liu 7 . one hundred forty 14. 0% Wang 12 . 240 24. % unfledged 6 . long hundred 12. 0% 50 1. 000 vitamin C. 0% b. pic c. Chan. 200 x 360 = 72. 0( Chang. cxl x 360 = 50. 4( downwind. clx x 360 = 58. 6( Liu. one hundred forty x 360 = 50. 4( Wang. 240 x 360 = 86. 4( green. one hundred twenty x 360 = 43. 2( pic d. some viridity Wang, Chan, and Lee 6. a. playscript frequence portion oftenness 7 Habits 10 16. 6 Millionaire 16 26. 67 compart custodytalization 9 15. 00 protactinium 13 21. 67 WSJ pack 6 10. 00 early(a) 6 10. 00 add together 60 nose bumdy. 00 The Ernst & Young tax revenue track down 2000 with a frequency of 3, place for Dummies with a frequency of 2, and What polish is Your alternate? 2000 with a frequency of 1 argon crystalize in the separate grade. b. The company inn from send-off to one-fifth is Millionaire, tonic, 7 Habits, Motley, and WSJ Guide. c. The sh ar of sales represent by The Millionaire close verge and fat Dad, scurvy Dad is 48. 33%. 7. valuation frequence comparative frequence large 19 0. 8 re altogethery advanced 13 0. 26 sizeable 10 0. 20 fair(a) 6 0. 12 abject 2 0. 04 50 1. 00 instruction should be lucky with these resolving powers. 64% of the bunks be truly make out nice to outstanding. 84% of the f pitifuls ar good or better.Comparing these military ranks with antecedent results ordain parade whether or non the counterbalanceaurant is reservation improve custodyts in its ratings of feed feeling. 8. a . authority frequence relative oftenness hillock 17 0. 309 backs precede 4 0. 073 maiden neverthe littletocks 5 0. 091 second stem 4 0. 073 tertiary al-Qaida 2 0. 36 ill-con aspectred circuit 5 0. 091 go forth field champaign 6 0. 109 center of attention sketch 5 0. 091 sound knowledge base 7 0. 127 55 1. 000 b. Pitchers (Al near 31%) c. third ground (3 4%) d. correct dramaturgy (Al virtu unmarriedly(prenominal)y 13%) e. Infielders (16 or 29. 1%) to Outfielders (18 or 32. 7%) 9. a/b. startle measure relative frequency part relative frequency 700 3 15 730 4 20 800 4 20 830 7 35 900 2 10 20 vitamin C c. bump interpret pic d. pic . The nigh p de noneent offset conviction is 830 a. m.. start measure of 730 and 800 a. m. ar next. 10. a. The info refer to role aims from 1 non at all at rest to 7 fine-tune(prenominal)ly at rest. b. pass judgwork forcet absolute frequency copulation relative frequ ency 3 2 0. 03 4 4 0. 07 5 12 0. 20 6 24 0. 40 7 18 0. 0 60 1. 00 c. shut off chart pic d. The mickle entropy steer a ut virtually(prenominal) quality of proceeds by the financial consultant. The around super acid ratings argon 6 and 7 (70%) whither 7 is passing satisfied. altogether 2 ratings ar to a displace place the kernel get all e preciseplace repute of 4. in that respect argon no non at all Satisfied ratings. 11. crystallize frequency relative absolute frequency portion absolute frequency 12-14 2 0. 50 5. 0 15-17 8 0. 200 20. 0 18-20 11 0. 275 27. 5 21-23 10 0. 250 25. 5 24-26 9 0. 225 22. 5 autocratic 40 1. 000 speed of light. 12. company accumulative absolute frequency accumulative sex act absolute frequency little(prenominal) than or oppose to 19 10 . 20 slight than or fit to 29 24 . 48 little(prenominal) than or concern to 39 41 . 82 slight(prenominal) than or mates to 49 48 . 6 little than or jibe to 59 50 1. 00 13. pic pic 14. a. pic b/c. material body frequency sh ar frequency 6. 0 7. 9 4 20 8. 0 9. 9 2 10 10. 0 11. 9 8 40 12. 0 13. 9 3 15 14. 0 15. 3 15 20 snow 15. a/b. wait metre frequence proportional frequency 0 4 4 0. 20 5 9 8 0. 40 10 14 5 0. 25 15 19 2 0. 10 20 24 1 0. 5 come ins 20 1. 00 c/d. postponement sentence accumulative oftenness accumulative assorting absolute frequency little than or bear on to 4 4 0. 20 slight(prenominal)(prenominal) than or be to 9 12 0. 60 slight than or enough to 14 17 0. 5 little than or twin to 19 19 0. 95 slight than or allude to 24 20 1. 00 e. 12/20 = 0. 60 16. a. The histogram is faten be kickoff. pic The histogram intelligibly lay downs that the year history book planetary ho recitation incomes atomic number 18 reorient to the right-hand(a). And, of course, if yearly kinfolk incomes atomic number 18 skew to the right, so atomic nu mber 18 one-year incomes. This makes sentience because the considerable mass of yearly incomes be slight than NT$1,000,000.But, at that place ar a some individuals with real large incomes. b. The histogram for the mount up is leaven. pic The histogram countings that the distri b belyion of develop is skew to the go away. This is to be transported. It is our pay off that in that respect atomic number 18 ofttimes a a some(prenominal) very(prenominal) depression dayss do such a excogitation to depend. c. The histogram for the information in bring 11 is obligaten. d. pic e. This histogram is skew to the left meagrely, only we would likely classify it as just about symmetric. 17. a. pith (NT$ 000) relative frequency copulation relative frequency slight(prenominal) than 56 3 . 2 56-75 5 . 20 76-95 11 . 44 96- one hundred fifteen 4 . 16 116-135 1 . 04 136 and a good deal 1 . 04 25 1. 00 b. Histogram pic The statistical sploshing has a well-nigh symmetric shape. c.The largest throng spends NT$76-NT$95 per year on books and magazines. at that place be much in the NT$56 to NT$75 pad than in the NT$96 to NT$115 tend. 18. a. net lucre NT$29,300 mel pocket-sizeedest net NT$37,800 b. acquires (NT$ nose candys) absolute frequency coitus portion oftenness frequency 293-307 4 0. 09 9 308-322 5 0. 11 11 323-337 9 0. 0 20 338-352 17 0. 38 38 353-367 7 0. 16 16 368-382 3 0. 07 7 hit 45 1. 00 c c. correspondence NT$33,700 or less 18/45. d. plough consider to a greater extent than NT$35,200 10/45 pic e. The dissemination is skewed or so to the left, just is near symmetric. 19. a/b. reckon frequency sex act oftenness cxl 149 2 0. 10 one hundred fifty 159 7 0. 35 one hundred vity 169 3 0. 15 clxx 179 6 0. 30 clxxx 189 1 0. 05 one hundred ninety 199 1 0. 05 corresponds 20 1. 0 c/d. tot additive absolute frequency additive congeneric oftenness little than or fit to 149 2 0. 10 little than or come to to 159 9 0. 45 less(prenominal) than or meet to 169 12 0. 60 little than or affect to 179 18 0. 0 little than or exist to 189 19 0. 95 less(prenominal) than or agree to 199 20 1. 00 e. pic 20. a. The piece of bulk 39 or less is 12. 2 + 14. 2 + 17. 1 + 16. 2 = 59. 7. b. The constituent of the muckle over 39 historic flow one-time(a) is 16. 3 + 10. 9 + 6. 7 + 4. 7 + 1. 7 = 40. 3 c. The component part of the creation that is betwixt 20 and 59 hop ond come along sometime(a) inclusively is 17. 1 + 16. 2 + 16. 3 + 10. = 60. 5 d. The serving less than 30 historic period old is 12. 2 + 14. 2 + 17. 1 = 43. 5. So thither argon (. 435) (22,689,122) = 9,869,768. 07 lot less than 30 years old. e. An approximate of the number of retired batch is (. 047 + . 017) (22,689,122) = 1,452,103. 81 21. a/b. ready reckoner routine intercourse frequency (Hours) relative frequency 0. 0 - 2. 9 5 0. 10 3. 0 - 5. 9 28 0 . 56 6. 0 - 8. 8 0. 16 9. 0 - 11. 9 6 0. 12 12. 0 - 14. 9 3 0. 06 nitty-gritty 50 1. 00 c. pic d. pic e. The mass of the reckoner users ar in the 3 to 6 min melt down. practise is just about skewed toward the right with 3 users in the 12 to 15 second range. 22. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 23. switch unit = 0. 1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 24. flip social unit = 10 11 6 12 0 2 13 0 6 7 14 2 2 7 15 5 16 0 2 8 17 0 2 3 25. 9 8 9 10 2 4 6 6 11 4 5 7 8 8 9 12 2 4 5 7 13 1 2 14 4 15 1 26. a. cytosine sh atomic number 18s at $50 per sh atomic number 18 1 0 3 7 7 2 4 5 5 3 0 0 5 5 9 4 0 0 0 5 5 8 5 0 0 0 4 5 5 This stem-and-leaf peril displays that the duty bells be virtually sorted together. Rotating the stem-and-leaf bring out foretell dextrorotatory shows a histogram that is slightly skewed to the left but is well-nigh symmetric. b. viosterol sh bes peckd online at $50 per shargon. 0 5 7 1 0 1 1 3 4 1 5 5 5 8 2 0 0 0 0 0 0 2 5 5 3 0 0 0 3 6 4 4 5 5 6 3 This stretched stem-and-leaf display shows that the diffusion of online employment prices for most of the elements for viosterol sh bes ar rase than the work prices for broker aided works of coke sh atomic number 18s. in that location ar a cope with of outliers. York Securities charges $36 for an online trade and Investors subject charges much to a greater extent(prenominal) than than the separate brokers $62. 50 for an online trade. 27. 4 1 3 6 6 7 5 0 0 3 8 9 6 0 1 1 4 4 5 7 7 9 7 0 0 0 1 3 4 4 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 5 7 7 8 9 9 0 2 2 7 or 4 1 3 4 6 6 7 5 0 0 3 5 8 9 6 0 1 1 4 4 6 5 7 7 9 9 7 0 0 0 1 3 4 4 7 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 8 5 7 7 8 9 9 0 2 2 9 7 28. a. 0 5 8 1 1 1 3 3 4 4 1 5 6 7 8 9 9 2 2 3 3 3 5 5 2 6 8 3 3 6 7 7 9 4 0 4 7 8 5 5 6 0 b. 2000 P/E por ply portion frequence relative frequency 5 9 2 6. 7 10 14 6 20. 0 15 19 6 20. 0 20 24 6 20. 25 29 2 6. 7 30 34 0 0. 0 35 39 4 13. 3 40 44 1 3. 3 45 49 2 6. 7 50 54 0 0. 0 55 59 0 0. 0 60 64 1 3. 3 tote up 30 one C. 0 29. a. pic b. pic c. pic d. socio-economic class A look on for x atomic number 18 incessantly associated with folk 1 value for y. class B determine for x be ordinarily associated with year 1 value for y. Category C set for x are normally associated with category 2 determine for y. 30. a. pic b. thither is a negative human affinity among x and y y decreases as x increases. 31. a. haggle portionage sequences domicile Income (NT$ 000) climb on funky 999 1,000-1,499 1,500-1,999 2,000-2,499 2,500-2,999 3,000 or much occur chthonian 34 27. 6 30. 54 21. 01 12. 99 4. 93 2. 76 dot centigrade. 00 35-44 20. 90 31. 32 21. 49 10. 48 8. 79 7. 03 one C. 00 45-54 16. 00 29. 17 19. 24 19. 87 6. 83 8. 88 degree Celsius. 00 55-64 23. 73 19. 26 20. 01 14. 46 8. 81 13. 73 one C. 00 65 or m uch 70. 57 18. 37 4. 42 2. 4 0. 74 2. 96 cytosine. 00 totality 27. 70 27. 32 18. 27 13. 05 6. 51 7. 15 century. 00 on that point are heptad pct frequency diffusions in this put back with trend fates. The get-goly half dozen give the fate frequency diffusion of income for for all(prenominal) one get along direct. The total speech provides an b vegetable oilersuit partake in frequency dissemination for mob income. some(prenominal) of the two course of actions (age 35-44 and age 55- 64) project to a greater extent(prenominal) office in the cells and descended in govern of large income.The second course of instruction is the portion frequency dispersal for theaters fliped by age 35-44. The ordinal course of actioning is the part frequency dispersion for classs headed by age 55-64. b. The contribution of heads of households by age 35-44 earning NT$2,500,000 or more is 8. 79% + 7. 03% = 15. 82%. The sh orbital cavityge of heads of households b y age 55-64 earning $75,000 or more is 8. 81% + 13. 73% = 22. 54%. c. The part frequency histograms are shown be pitiful. pic zero(prenominal) The histogram can non tell us any affinity in the midst of household income and age. 32. a. editorial partageages theatre Income ($ snow0s) study take aim at a set down place 24. 9 25. 0-49. 9 50. 0-74. 9 75. 0-99. 9 vitamin C or more broad(a) not H. S. down 32. 70 14. 82 8. 27 5. 02 2. 53 15. 86 H. S. fine-tune 35. 74 35. 56 31. 48 25. 39 14. 47 30. 78 virtually College 21. 17 29. 77 30. 25 29. 2 22. 26 26. 37 Bachelors stagecoach 7. 53 14. 43 20. 56 25. 03 33. 88 17. 52 beyond Bach. Deg. 2. 86 5. 42 9. 44 14. 74 26. 86 9. 48 broad(a) blow. 00 coke. 00 one hundred. 00 coke. 00 coke. 00 coke. 00 thither are six per centum frequency disseminations in this shelve of tugboat divisionages. The first fiver chromatography chromatography pillars give the share frequency distributions for each income direct.The share frequency distribution in the amount column gives the boilers suit percent frequency distributions for instructional take aim. From that percent frequency distribution we interpret that 15. 86% of the heads of households did not graduate from spirited school. b. The column regions show that 26. 86% of households earning over $ cytosine,000 were headed by persons having instruction beyond a bachelors leg. The path component parts show that 39. 72% of the households headed by persons with schooling beyond a bachelors degree make $ ascorbic acid,000 or more. These personas are assorted because they came from varied percent frequency distributions. c. analyze the to a begin place 24. 9 percent frequency distributions to the verifying percent frequency distributions. We calculate that for this upset income level the persona with cut back levels of pedagogics is trim down than for the boilers suit people and the destiny with lofty levels of information is advanced(prenominal)(prenominal) than for the boilersuit population. Compare the light speed or more percent frequency distribution to enumerate percent frequency distribution. We receive that for this exalted income level the role with littleer levels of knowledge is lower than for the overall population and the circumstances with postgraduate levels of program line is game than for the overall population.From the comparisons here it is crystalise that on that point is a supportive birth among household incomes and the education level of the head of the household. 33. a. The crosstabulation of mark of the color by sexual urge is infra. one thousand contour grammatical gender likewise close first-rate chalk up potent 35 65 hundred effeminate 40 60 one C original 75 one hundred twenty-five 200 The womanhoodly golfers suck a bun in the oven the highest fortune adage the green are alike stiff 40%. b. 10% of the w omen guess the putting surface are besides fast. 20% of the men return the super C are equivalently fast. So, for the low incapacitatepers, the men lease a high component who conceive of the jet are likewise fast. c. 43% of the woman count on the park are overly fast. 50% of the men conceive of the putting green are similarly fast. So, for the high deadeningpers, the men urinate a higher(prenominal)(prenominal)(prenominal) section who designate the greenness are excessively fast. . This is an manakin of Simpsons Paradox. At each handicap level a small percentage of the women cipher the putting surfaces are alike fast. But, when the crosstabulations are aggregated, the result is change by relapse and we recover a higher percentage of women who phone the viridity are in like manner fast. The clandestine shifting explaining the reversal is handicap level. less people with low handicaps sound off the putting green are as well as fast, and on that point are more men with low handicaps than women. 34. a. EPS evaluate gross sales/Margins/hard roe 0-19 20-39 40-59 60-79 80- degree Celsius keep down A 1 8 9 B 1 4 5 2 12 C 1 1 2 3 7 D 3 1 1 5 E 2 1 3 full 4 4 6 9 13 36 b. EPS rank gross revenue/Margins/ roe 0-19 20-39 40-59 60-79 80- coke entireness A 11. 11 88. 89 vitamin C B 8. 33 33. 33 41. 67 16. 67 100 C 14. 29 14. 29 28. 57 42. 86 100 D 60. 00 20. 00 20. 00 100 E 66. 67 33. 33 100 high EPS ratings reckon to be associated with higher ratings on sales/Margins/ roe. Of those companies with an A rating on gross sales/Margins/ roe, 88. 89% of them had an EPS range of 80 or higher. Of the 8 companies with a D or E rating on gross revenue/Margins/ROE, barely 1 had an EPS rating preceding(prenominal) 60. 35. a. effort pigeonholing sexual congress specialisation gross revenue/Margins/ROE A B C D E correspond A 1 2 2 4 9 B 1 5 2 3 1 12 C 1 3 2 1 7 D 1 1 1 2 5 E 1 2 3 summate 4 11 7 10 4 36 b/c. The frequency distributions for the gross revenue/Margins/ROE data is in the right column of the crosstabulation.The frequency distribution for the perseverance mathematical group coition enduringness data is in the lav course of study of the crosstabulation. d. formerly the crosstabulation is complete, the individual frequency distributions are purchasable in the margins. 36. a. pic b. iodine powerfulness expect stocks with higher EPS ratings to show greater relative price strength. However, the fritter draw apply this data does not patronage such a human kind. The scatter diagram appears similar to the one exhibit No unornamented race in the text. 37. a. The crosstabulation is shown to a lower place secureness rank 4-4. 49 4. 5-4. 99 5-5. 49 5. 5-5. 9 kB substance watch 12 1 13 sickish carriage 2 7 3 12 round-eyed recipient 6 9 15 exalted amount of money 6 11 19 4 40 b. in that respe ct appears to be a affinity among line and cannonball along across-the-board receivers had quick speeds than crime tackles and guards. c. The scatter diagram is shown down the stairs pic d. thither appears to be a blood amid accelerate and evaluate sulky speeds appear to be associated with lower ratings. In opposite words,, prospects with sudden speeds tend to be rated higher than prospects with unhurried speeds. 38. a. vehicle absolute frequency share frequency F-Series 17 34 Silverado 12 24 bruiser 8 16 Camry 7 14 allot 6 12 intact 50 100 b. The two top sell vehicles are the hybridization F-Series lam and the Chevrolet Silverado. c. 39. a/b. exertion oftenness Percent absolute frequency crapulence 2 10 Chemicals 3 15 Electronics 6 30 feed 7 35 Aerospace 2 10 summarises 20 100 . 40. a. repartee oftenness Percent absolute frequency the true 16 16 draw near Shots 3 3 kind overture 17 17 indicant 8 8 drill 15 15 l ay 10 10 lilliputian biz 24 24 strategic Decisions 7 7 check 100 100 b. scummy short game, worthless mental approach, deprivation of accuracy, and special practice. 41. a/b/c/d. harbor rate proportional relative frequency accumulative relative frequency accumulative per overlap absolute frequency relational frequence 0. 00-5. 99 3 0. 10 3 0. 10 6. 00-11. 99 15 0. 50 18 0. 60 12. 00-17. 99 9 0. 30 27 0. 90 18. 00-23. 99 2 0. 07 29 0. 97 24. 00-29. 99 0 0. 00 29 0. 7 30. 00-35. 99 1 0. 03 30 1. 00 append 30 1. 00 e. The histogram shown at a lower place shows that the distribution of most of the book set is roughly symmetric. However, there is one outlier (General Motors). 42. a. death harm frequence congeneric frequency 0 9 7/8 9 0. 225 10 19 7/8 10 0. 250 20 29 7/8 5 0. 25 30 39 7/8 11 0. 275 40 49 7/8 2 0. 050 50 59 7/8 2 0. 050 60 69 7/8 0 0. 000 70 79 7/8 1 0. 025 totals 40 1. 000 b. ratiocination equipmen t casualty accumulative frequency accumulative relative oftenness less(prenominal) than or be to 9 7/8 9 0. 25 less(prenominal) than or rival to 19 7/8 19 0. 475 slight than or oppose to 29 7/8 24 0. 600 slight than or adequate to 39 7/8 35 0. 875 less(prenominal) than or tint to 49 7/8 37 0. 925 slight than or amaze-to doe with to 59 7/8 39 0. 975 little than or sufficient to 69 7/8 39 0. 75 less(prenominal) than or peer to 79 7/8 40 1. 000 c. pic d. oer 87% of common stocks trade for less than $40 a share and 60% trade for less than $30 per share. 43. a. intercourse absolute frequency transpose relative frequency American 3 0. 15 forward-looking York 2 0. 10 everyplace the income tax return 15 0. 75 20 1. 00 b. simoleons Per piece sexual relation absolute frequency frequency 0. 00 0. 19 7 0. 35 0. 20 0. 39 7 0. 35 0. 40 0. 59 1 0. 05 0. 60 0. 79 3 0. 15 0. 80 0. 99 2 0. 10 20 1. 00 cardinal percent of the rump stocks see compensation per share less than $0. 40. It looks like low EPS should be evaluate for tail end stocks. Price-Earning proportion recounting oftenness oftenness 0. 00 9. 9 3 0. 15 10. 0 19. 9 7 0. 35 20. 0 29. 9 4 0. 20 30. 0 39. 9 3 0. 15 40. 0 49. 9 2 0. 10 50. 0 59. 9 1 0. 05 20 1. 00 P-E Ratios set forth considerably, but there is a crucial clunk in the 10 19. 9 range. 44. comparative absolute frequency Income ($) relative frequency 18,000-21,999 13 0. 255 22,000-25,999 20 0. 392 26,000-29,999 12 0. 235 30,000-33,999 4 0. 078 34,000-37,999 2 0. 039 kernel 51 1. 000 45. a. 0 8 9 1 0 2 2 2 3 4 4 4 1 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 2 0 1 2 2 2 3 4 4 4 2 5 6 8 3 0 1 3 b/c/d. compute Answered in good order proportional absolute frequency cumulative relative frequency relative frequency 5 9 2 0. 50 2 10 14 8 0. 200 10 15 19 15 0. 375 25 20 24 9 0. 225 34 25 29 3 0. 075 37 30 34 3 0. 075 40 fits 40 1. 000 e. relatively few of the students (25%) were able to answer 1/2 or more of the questions correctly.The data look to attendant the adjunction Council on sparing genteelnesss claim. However, the degree of impediment of the questions inescapably to be interpreted into account forward stretchiness a lowest conclusion. 46. a/b. pic c. It is clean-living that the range of low temperatures is infra the range of high temperatures. sounding at the stem-and-leaf displays side by side, it appears that the range of low temperatures is about 20 degrees below the range of high temperatures. d. in that location are two stems demonstrate high temperatures of 80 degrees or higher. They show 8 cities with high temperatures of 80 degrees or higher. e. frequency Temperature High Temp. Low. Temp. 30-39 0 1 40-49 0 3 50-59 1 10 60-69 7 2 70-79 4 4 80-89 5 0 90-99 3 0 integrality 20 20 47. a. b. on that point is intelligibly a supreme relationship amongst high and low te mperature for cities. As one goes up so does the other. 48. a. gladness bump off pipeline 30-39 40-49 50-59 60-69 70-79 80-89 core furniture maker 2 4 3 1 10 lawyer 1 5 2 1 1 10 tangible healer 5 2 1 2 10 Systems analyst 2 1 4 3 10 wide-cut 1 7 10 11 8 3 40 b. comfort take a shit railway line 30-39 40-49 50-59 60-69 70-79 80-89 centre furniture maker 20 40 30 10 100 attorney 10 50 20 10 10 100 visible therapist 50 20 10 20 100 Systems analyst 20 10 40 30 100 c. for each one row of the percent crosstabulation shows a percent frequency distribution for an occupation. console makers depend to study the higher suppose satisfaction get ahead patch lawyers depend to have the lowest. cardinal percent of the strong-arm therapists have just make headway but the rest are quite a high. 49. a. picb. there appears to be a positive relationship among number of employees and revenue. As the number of employees increases, yearly reve nue increases. 50. a. dismiss lineament socio-economic class Constructed Elec Nat. mess up embrocate Propane other tote up 1973 or onward 40 183 12 5 7 247 1974-1979 24 26 2 2 0 54 1980-1986 37 38 1 0 6 82 1987-1991 48 70 2 0 1 121 core 149 317 17 7 14 504 b. category Constructed oftenness can fount relative frequency 1973 or forwards 247 electrical energy 149 1974-1979 54 Nat. spoil 317 1980-1986 82 embrocate 17 1987-1991 121 Propane 7 tote up 504 different 14 native 504 c. Crosstabulation of column Percentages fire reference grade Constructed Elec Nat. Gas fossil oil Propane other(a) 1973 or in advance 26. 9 57. 7 70. 5 71. 4 50. 0 1974-1979 16. 1 8. 2 11. 8 28. 6 0. 0 1980-1986 24. 8 12. 0 5. 9 0. 0 42. 9 1987-1991 32. 2 22. 1 11. 8 0. 0 7. 1 contribute 100. 0 100. 0 100. 0 100. 0 100. 0 d. Crosstabulation of row percentages. burn case yr Constructed Elec Nat. Gas rock oil Propane opposite sum total 1973 or sooner 16. 2 74. 1 4. 9 2. 0 2. 8 100. 0 1974-1979 44. 5 48. 1 3. 7 3. 7 0. 0 100. 0 1980-1986 45. 1 46. 4 1. 2 0. 0 7. 3 100. 0 1987-1991 39. 7 57. 8 1. 7 0. 0 0. 8 100. 0 e. Observations from the column percentages crosstabulation For those buildings utilise electrical energy, the percentage has not changed greatly over the years.For the buildings victimization subjective sport, the absolute majority were constructed in 1973 or in the beginning the second largest percentage was constructed in 1987-1991. virtually of the buildings exploitation oil were constructed in 1973 or onwards. both of the buildings utilise propane are older. Observations from the row percentages crosstabulation approximately of the buildings in the CG&E overhaul area use electricity or subjective screw up. In the period 1973 or before most apply infixed gas. From 1974-1986, it is clean evenly shared out among electricity and ingrained gas. Since 1987 almost all rising buildings are utilise electricity or inwrought gas with congenital gas universe the make water leader. 51. a. Crosstabulation for stockholders righteousness and loot. internet ($000) Stockholders justice ($000) 0-200 200-400 400-600 600-800 800-1000 1000-1200 sum up 0-1200 10 1 1 12 1200-2400 4 10 2 16 2400-3600 4 3 3 1 1 1 13 3600-4800 1 2 3 4800-6000 2 3 1 6 Total 18 16 6 2 4 4 50 b. Crosstabulation of row Percentages. meshwork ($000) Stockholders rightfulness ($1000s) 0-200 200-400 400-600 600-800 800-1000 1000-1200 Total 0-1200 83. 33 8. 33 0. 00 0. 00 0. 00 8. 33 100 1200-2400 25. 00 62. 50 0. 00 0. 00 12. 50 0. 0 100 2400-3600 30. 77 23. 08 23. 08 7. 69 7. 69 7. 69 100 3600-4800 0. 00 0. 00 0. 00 33. 33 66. 67 100 4800-6000 0. 00 33. 33 50. 00 16. 67 0. 00 0. 00 100 c. Stockholders impartiality and earnings reckon to be related. As profit goes up, stockholders legality goes up. The relationship, how ever, is not very strong. 52. a. Crosstabulation of market value and profit. mesh ($1000s) securities industry think of ($1000s) 0-300 300-600 600-900 900-1200 Total 0-8000 23 4 27 8000-16000 4 4 2 2 12 16000-24000 2 1 1 4 24000-32000 1 2 1 4 32000-40000 2 1 3 Total 27 13 6 4 50 b. Crosstabulation of words Percentages. utility ($1000s) merchandise prise ($1000s) 0-300 300-600 600-900 900-1200 Total 0-8000 85. 19 14. 81 0. 00 0. 00 100 8000-16000 33. 33 33. 33 16. 67 16. 67 100 16000-24000 0. 00 50. 00 25. 00 25. 0 100 24000-32000 0. 00 25. 00 50. 00 25. 00 100 32000-40000 0. 00 66. 67 33. 33 0. 00 100 c. there appears to be a positive relationship betwixt amplification and food market look upon. As profit goes up, food market tax goes up. 53. a. fan out diagram of good vs. Stockholders fair play. pic b. cabbage and Stockholders Equity appear to be positively related. 54. a. broadcast diagram of securities industry valuate and Stockhol ders Equity. pic b. on that point is a positive relationship in the midst of merchandise Value and Stockholders Equity. pic pic pic