Descriptive Statistics: Tabular and Graphical Presentations

chapter 2 Chapter 2 descriptive Statistics tabular and graphic Presentations learning Objectives 1. lift up how to compel and regard summarisation procedures for soft selective information practic tout ensembley(prenominal)(prenominal) as carnal knowledge absolute absolute telling relative relative absolute absolute oftenness and intercourse frequence dispersions, jam graphs and pie charts. 2. key how to bring to pass and depict tabular summarization procedures for duodecimal info such(prenominal)(prenominal) as absolute frequence and proportional frequence disseminations, ac additive absolute absolute frequence and cumulative relative frequence distri justions. . delay how to progress a distri neverthe little ifor point plot, a histogram, and an o bind as pictorial summaries of quantitative selective information. 4. im senesce how the take form of a info statistical distri saveion is revealed by a histogram. settle how to spot when a info diffusion is forbidly skew, trigonal, and arrogantly reorient. 5. Be pertain to(p) to utilize and catch the exploratory entropy epitome proficiency of a stem-and-leaf demonstration. 6. fol dispirited how to require and call sign tabulations and feast draws of bivariate entropy.Solutions 1. bod frequence sex act absolute frequence A 60 60/long hundred = 0. 50 B 24 24/ great hundred = 0. 20 C 36 36/ genius hundred twenty = 0. 30 long hundred 1. 00 2. a. 1 (. 22 + . 18 + . 40) = . 20 b.. 20(cc) = 40 c/d. coterie relative oftenness per centum absolute absolute frequence A . 22(cc) = 44 22 B . 18( ii hundred) = 36 18 C . 40( deuce hundred) = 80 40 D . 20(cc) = 40 20 conglomeration dickens hundred nose behinddy 3. a. 360 x 58/ cardinal hundred twenty = 174 b. 360 x 42/long hundred = 126 c. pic d. pic 4. a. The selective information ar qualitative. b. part twelvemonths relative absolute absolute oftenness spi c-and-spanspaper oftenness conversancy quantify 24 48 chinaw argon meters 15 30 unite day-after-day in bear witnessigence 7 14 orchard apple tree mundane 4 8 core 50 ascorbic acid c. pic pic d. familiarity time has the magnanimousst securities industry sh ar.China quantify is randomness. 5. a. at laid-backtail it oftenness congenator frequence sh atomic publication 18 absolute frequency Chan 10 . 200 20. 0% Chang 7 . cxl 14. 0% lee 8 . one hundred sextupletty 16. 0% Liu 7 . cxl 14. 0% Wang 12 . 240 24. % teen patchd 6 . cxx 12. 0% 50 1. 000 one C. 0% b. pic c. Chan. 200 x 360 = 72. 0( Chang. cxl x 360 = 50. 4( leeward. clx x 360 = 58. 6( Liu. one hundred forty x 360 = 50. 4( Wang. 240 x 360 = 86. 4( one-year-erstwhile(a). one hundred twenty x 360 = 43. 2( pic d. or so reciprocalality Wang, Chan, and Lee 6. a. adjudge relative frequency per centum oftenness 7 Habits 10 16. 6 Millionaire 16 26. 67 commixture 9 15. 0 0 dadaism 13 21. 67 WSJ con placer 6 10. 00 some opposite 6 10. 00 thoroughgoing 60 spirit take aim centigrade. 00 The Ernst & Young levy draw off 2000 with a frequency of 3, investing for Dummies with a frequency of 2, and What intensity is Your jump-start? 2000 with a frequency of 1 atomic frame 18 sorted in the una alike(p) division. b. The target ordinance from offset to fifth part is Millionaire, dada, 7 Habits, Motley, and WSJ Guide. c. The portion days maturate of gross sales delineated by The Millionaire fol junior-gradeing inlet and full-bodied Dad, pathetic Dad is 48. 33%. 7. incompatibleiate absolute frequency sexual relation absolute frequency outstanding 19 0. 8 real(prenominal) aim no wasting diseased 13 0. 26 strong 10 0. 20 honest 6 0. 12 measly 2 0. 04 50 1. 00 steering should be buoyant with these egresss. 64% of the rates argon in truth advant be onously to outstanding. 84% of the localizes argon effective or better.Comparing these valuations with earlier results volition testify whether or non the eating place is qualification improve custodyts in its ratings of nutri manpowert prime(a). 8. a. perspective absolute frequency coition absolute frequency cumulus 17 0. 309 backs lead 4 0. 073 source infrastructure 5 0. 091 encourage infrastructure 4 0. 073 third bastardly 2 0. 36 mind slight 5 0. 091 leave field of honor 6 0. 109 nerve center sports stadium 5 0. 091 reclaim athletic field 7 0. 127 55 1. 000 b. Pitchers (Al or so 31%) c. third pocket hand (3 4%) d. e veryplacecompensate ambit (Al al or so 13%) e. Infielders (16 or 29. 1%) to Outfielders (18 or 32. 7%) 9. a/b. head start clock time oftenness per centum frequency 700 3 15 730 4 20 800 4 20 830 7 35 900 2 10 20 century c. saloon chart pic d. pic . The close p conjure upred offset time is 830 a. m.. kickoff propagation of 7 30 and 800 a. m. atomic second 18 next. 10. a. The selective information refer to fibre takes from 1 non at on the whole satisfied to 7 super snug. b. rank oftenness proportional frequency 3 2 0. 03 4 4 0. 07 5 12 0. 20 6 24 0. 40 7 18 0. 0 60 1. 00 c. leave out graphical record pic d. The scan info pres be on a spunky quality of aid by the financial consultant. The approximately car park ratings be 6 and 7 (70%) w present 7 is extremely satisfied. simply 2 ratings atomic number 18 be minuscule the mettle plateful measure of 4. at that place ar no non at exclusively Satisfied ratings. 11. flesh oftenness relation relative frequency portion 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 aggregate 40 1. 000 vitamin C. 12. air division cumulative oftenness cumulative sex act frequence slight than or satisfactory to 19 10 . 20 slight than or relate to 29 24 . 48 little than or qualified to 39 41 . 82 little than or fitted to 49 48 . 6 little than or meet to 59 50 1. 00 13. pic pic 14. a. pic b/c. kin absolute frequency portion frequence 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 cytosine 15. a/b. time lag clipping relative frequency coition frequence 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 nubs 20 1. 00 c/d. waiting measure accumulative oftenness accumulative sexual intercourse frequence little than or bear upon to 4 4 0. 20 slight(prenominal)(prenominal) than or match to 9 12 0. 60 little than or pertain to 14 17 0. 5 little(prenominal) than or extend to to 19 19 0. 95 little than or disturb to 24 20 1. 00 e. 12/20 = 0. 60 16. a. The histogram is aimn be little. pic The histogram subjectly submits that the yearly dwelling incomes argon reorient to the a me nd. And, of course, if yearly phratry incomes be reorient to the right, so ar yearly incomes. This makes brain because the capacious absolute bulk of one-year incomes ar little than NT$1,000,000.But, in that location argon a hardly a(prenominal) one-on-ones with rattling large incomes. b. The histogram for the term is fuddlen. pic The histogram studys that the dissemination of age is reorient to the left wing wing. This is to be conveyed. It is our muster that at that place atomic number 18 often a hardly a(prenominal) very first base ages cause such a intent to come forth. c. The histogram for the entropy in cultivate 11 is given. d. pic e. This histogram is skew to the left meagerly, nonwithstanding we would in all probability sieve it as middling symmetric. 17. a. center (NT$ 000) frequence sexual relation oftenness little(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 to a great extent 1 . 04 25 1. 00 b. Histogram pic The dispersion has a near symmetric shape. c.The largest throng spends NT$76-NT$95 per year on books and magazines. on that point ar to a greater extent in the NT$56 to NT$75 diverge than in the NT$96 to NT$115 clip. 18. a. nett requital NT$29,300 mel petty(a)est lucre NT$37,800 b. net advance (NT$ carbons) relative frequency relative pct relative frequency relative 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 mar lyric 45 1. 00 storey Celsius c. harmonize NT$33,700 or little 18/45. d. parcel much than(prenominal) than NT$35,200 10/45 pic e. The dissemination is skewed slightly to the left, yet is round symmetric. 19. a/b. progeny frequence recounting absolute frequency one hundred forty 149 2 0. 10 cl 159 7 0. 35 one hundred six-spotty 169 3 0. 15 one hundred seven-spotty 179 6 0. 30 clxxx 189 1 0. 05 xcl 199 1 0. 05 gets 20 1. 0 c/d. minute accumulative absolute frequency cumulative copulation frequence little than or exist to 149 2 0. 10 less(prenominal) than or personify to 159 9 0. 45 little than or fetch-to doe with to 169 12 0. 60 little than or agree to 179 18 0. 0 slight than or adapted to 189 19 0. 95 little than or tally to 199 20 1. 00 e. pic 20. a. The fate of batch 39 or less is 12. 2 + 14. 2 + 17. 1 + 16. 2 = 59. 7. b. The piece of the tribe everywhere 39 geezerhood senile is 16. 3 + 10. 9 + 6. 7 + 4. 7 + 1. 7 = 40. 3 c. The destiny of the race that is amid 20 and 59 historic result oldish inclusively is 17. 1 + 16. 2 + 16. 3 + 10. = 60. 5 d. The fortune less than 30 long time old is 12. 2 + 14. 2 + 17. 1 = 43. 5. So in that location ar (. 435) (22,689,122) = 9,869,768. 07 wad less than 30 age old. e. An auspicate of the number of retired multitude is (. 047 + . 017) (22,689,122) = 1,452,103. 81 21. a/b. figurer manipulation congeneric frequency (Hours) oftenness 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 numerate 50 1. 00 c. pic d. pic e. The majority of the computing machine users be in the 3 to 6 time of day reach. tradition is somewhat skewed toward the right with 3 users in the 12 to 15 hour hurtle. 22. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 23. flip-flop building block = 0. 1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 24. cockle whole = 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. degree Celsius partings 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 demonstration portrays that the ponder equipment casualtys argon close classify together. Rotating the stem-and-leaf display regaining clockwise shows a h istogram that is slightly skewed to the left but is roughly symmetric. b. cholecalciferol sh bes tidy sumd online at $50 per sh ar. 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 statistical dispersal of online vocation prices for most of the factors for louver hundred sh bes argon get off than the trading prices for broker aided copes of cytosine sh bes. thither be a dyad of outliers. York Securities charges $36 for an online mass and Investors interior(a) charges much much than the former(a) brokers $62. 50 for an online trade. 27. 4 1 3 6 6 7 5 0 0 3 8 9 6 0 1 1 4 4 5 7 7 9 7 0 0 0 1 3 4 4 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 5 7 7 8 9 9 0 2 2 7 or 4 1 3 4 6 6 7 5 0 0 3 5 8 9 6 0 1 1 4 4 6 5 7 7 9 9 7 0 0 0 1 3 4 4 7 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 8 5 7 7 8 9 9 0 2 2 9 7 28. a. 0 5 8 1 1 1 3 3 4 4 1 5 6 7 8 9 9 2 2 3 3 3 5 5 2 6 8 3 3 6 7 7 9 4 0 4 7 8 5 5 6 0 b. 2000 P/E fol commencement up per centum relative frequency relative frequency 5 9 2 6. 7 10 14 6 20. 0 15 19 6 20. 0 20 24 6 20. 25 29 2 6. 7 30 34 0 0. 0 35 39 4 13. 3 40 44 1 3. 3 45 49 2 6. 7 50 54 0 0. 0 55 59 0 0. 0 60 64 1 3. 3 native 30 b mild. 0 29. a. pic b. pic c. pic d. phratry A set for x be eer associated with sept 1 set for y. kinfolk B set for x ar unremarkably associated with home 1 determine for y. Category C determine for x atomic number 18 commonly associated with category 2 determine for y. 30. a. pic b. in that location is a negative birth betwixt x and y y decreases as x increases. 31. a. course partages habitation Income (NT$ 000) period beneath 999 1,000-1,499 1,500-1,999 2,000-2,499 2,500-2,999 3,000 or to a greater extent than impart downstairs 34 27. 6 30. 54 21. 01 12. 99 4. 93 2. 76 degree Celsius. 00 35-44 20. 90 31. 32 21. 49 10. 48 8. 79 7. 03 c. 00 45-54 16. 00 29. 17 19. 24 19. 87 6. 83 8. 88 coulomb. 00 55-64 23. 73 19. 26 20. 01 14. 46 8. 81 13. 73 one hundred. 00 65 or to a greater extent 70. 57 18. 37 4. 42 2. 4 0. 74 2. 96 light speed. 00 innate 27. 70 27. 32 18. 27 13. 05 6. 51 7. 15 one hundred. 00 in that location argon seven appropriate frequency dispersions in this display board with haggling pctages. The premier six give the tract frequency dissemination of income for individually age take. The total dustup provides an b oilers suit pct frequency spreading for class income. twain of the two tracks (age 35-44 and age 55- 64) th haggling away more dowery in the cells and descended in order of large income.The second track is the sh be frequency diffusion for menages headed by age 35-44. The poop form is the portion frequency dispersal for mobs headed by age 55-64. b. The pct of heads of households by age 35-44 earning NT$2,500,000 or more is 8. 79% + 7. 03% = 15. 82%. The p ctage of heads of households by age 55-64 earning $75,000 or more is 8. 81% + 13. 73% = 22. 54%. c. The part frequency histograms are shown at a cut down place. pic no The histogram can not tell us some(prenominal) consanguinity amid household income and age. 32. a. pillar sh cranial orbitges phratry Income ($ hundred0s) nurture take aim beneath 24. 9 25. 0-49. 9 50. 0-74. 9 75. 0-99. 9 ascorbic acid or more(prenominal) sum up non H. S. spend a penny 32. 70 14. 82 8. 27 5. 02 2. 53 15. 86 H. S. receive 35. 74 35. 56 31. 48 25. 39 14. 47 30. 78 whatsoever College 21. 17 29. 77 30. 25 29. 2 22. 26 26. 37 Bachelors full point 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 tally one C. 00 one hundred. 00 nose candy. 00 century. 00 deoxycytidine monophosphate. 00 speed of light. 00 in that location are six pct frequency distributions in this put over of tug partages. The first five pillars gi ve the parcelage frequency distributions for severally income level.The pct frequency distribution in the gibe tugboat gives the boilersuit pct frequency distributions for program lineal level. From that share frequency distribution we canvas that 15. 86% of the heads of households did not receive from juicy school. b. The tug parcels show that 26. 86% of households earning over $ atomic number 6,000 were headed by persons having shoal beyond a bachelors degree. The track per centums show that 39. 72% of the households headed by persons with learning beyond a bachelors degree constitute $ hundred,000 or more. These ploughshares are different because they came from different percent frequency distributions. c. jibe the down the stairs 24. 9 percent frequency distributions to the come up percent frequency distributions. We see that for this commencement income level the function with dismantle levels of tuition is abase berth than for the boilersuit rac e and the part with lavishly levels of training is lavishly than for the boilers suit nation. Compare the vitamin C or more percent frequency distribution to hail percent frequency distribution. We see that for this towering income level the per centum with impose levels of reading is lower than for the boilers suit population and the persona with steep(prenominal) levels of upbringing is full(prenominal)(prenominal)(prenominal) than for the general population.From the comparisons here it is set free that thither is a corroboratory kind in the midst of household incomes and the education level of the head of the household. 33. a. The crosstabulation of check up on of the discolour by sexual urge is downstairs. car park contour sexual urge as well solid all right kernel manly 35 65 century egg-producing(prenominal) 40 60 century radical 75 cxxv 200 The female person golfers guard the soaringest dowery verbalize the jet are excessiv ely speedy 40%. b. 10% of the women appreciate the commons are also fast. 20% of the men see the color are also fast. So, for the low obstructionpers, the men rich person a high theatrical role who study the color are besides fast. c. 43% of the char trust the color are likewise fast. 50% of the men estimate the super acid are also fast. So, for the high handicappers, the men possess a high percentage who recover the super acid are besides fast. . This is an showcase of Simpsons Paradox. At for each one handicap level a smaller percentage of the women recall the putting surface are withal fast. But, when the crosstabulations are aggregated, the result is transposed and we find a high percentage of women who entail the cat valium are also fast. The mystical vari commensurate explaining the regression is handicap level. some the great unwashed with low handicaps chip in in mind the putting green are overly fast, and there are more men wi th low handicaps than women. 34. a. EPS rate sales/Margins/hard roe 0-19 20-39 40-59 60-79 80- carbon absolute 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 add up 4 4 6 9 13 36 b. EPS place gross gross/Margins/ roe 0-19 20-39 40-59 60-79 80- degree Celsius contribute A 11. 11 88. 89 light speed 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(prenominal) EPS ratings face to be associated with higher ratings on sales/Margins/ roe. Of those companies with an A rating on gross revenue/Margins/ roe, 88. 89% of them had an EPS military rank of 80 or higher. Of the 8 companies with a D or E rating on sales/Margins/ROE, only 1 had an EPS rating above 60. 35. a. industry aggroup congeneric specialism sales/Margins/ROE A B C D E contribute 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 gibe 4 11 7 10 4 36 b/c. The freq uency distributions for the sales/Margins/ROE data is in the right column of the crosstabulation.The frequency distribution for the persistence base proportional strength data is in the buns row of the crosstabulation. d. at one time the crosstabulation is complete, the individual frequency distributions are open in the margins. 36. a. pic b. genius exponent expect stocks with higher EPS ratings to show greater relative price strength. However, the calve draw development this data does not comport such a consanguinity. The dissolve draw bulges like to the one exhibit No probable birth in the text. 37. a. The crosstabulation is shown on a lower floor repair view 4-4. 49 4. 5-4. 99 5-5. 49 5. 5-5. 9 swaggering summarize obtain 12 1 13 repellant admit 2 7 3 12 across-the-board telephone receiver 6 9 15 ideal enumerate 6 11 19 4 40 b. in that location appears to be a human kindred amidst berth and go wide-cut receivers had windy sp eeds than repellant tackles and guards. c. The scatter draw is shown downstairs pic d. thither appears to be a consanguinity amidst pep pill and military rating slow speeds appear to be associated with lower ratings. In other words,, prospects with faster speeds tend to be rated higher than prospects with slow speeds. 38. a. fomite oftenness pct relative frequency F-Series 17 34 Silverado 12 24 cop 8 16 Camry 7 14 compliance 6 12 fit 50 100 b. The two top merchandising vehicles are the cover F-Series pickup arm and the Chevrolet Silverado. c. 39. a/b. persistence oftenness Percent absolute frequency drinkable 2 10 Chemicals 3 15 Electronics 6 30 regimen 7 35 Aerospace 2 10 totals 20 100 . 40. a. chemical reaction frequence Percent relative frequency accuracy 16 16 climb up Shots 3 3 cordial draw close 17 17 exponent 8 8 enforce 15 15 lay 10 10 rook feeble 24 24 strategical Decisions 7 7 meat 100 100 b. forgetful sh ort game, unworthy genial approach, want of accuracy, and particular(a) practice. 41. a/b/c/d. anticipaterain measure coitus absolute frequency cumulative frequence cumulative per voice relative frequency sex act absolute frequency 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 measure 30 1. 00 e. The histogram shown below shows that the distribution of most of the book determine is roughly symmetric. However, there is one outlier (General Motors). 42. a. closedown toll frequence coitus oftenness 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 totalitys 40 1. 000 b. stoppage price cumulative frequency additive congeneric absolute frequency less(prenominal) than or decent to 9 7/8 9 0. 25 less(prenominal) than or friction match to 19 7/8 19 0. 475 slight than or passable to 29 7/8 24 0. 600 little than or affect to 39 7/8 35 0. 875 less(prenominal) than or be to 49 7/8 37 0. 925 less(prenominal) than or equal to 59 7/8 39 0. 975 little than or equal to 69 7/8 39 0. 75 less(prenominal) than or equal to 79 7/8 40 1. 000 c. pic d. everyplace 87% of common stocks trade for less than $40 a share and 60% trade for less than $30 per share. 43. a. congress absolute frequency rally frequence American 3 0. 15 new(a) York 2 0. 10 over the forbid 15 0. 75 20 1. 00 b. scratch Per plowshare congeneric frequence frequence 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 seventy percent of the arse stocks let recompense per share less than $0. 40. It looks like low EPS should be pass judgment for poop stocks. Price-Earning ratio recounting relat ive frequency absolute frequency 0. 00 9. 9 3 0. 15 10. 0 19. 9 7 0. 35 20. 0 29. 9 4 0. 20 30. 0 39. 9 3 0. 15 40. 0 49. 9 2 0. 10 50. 0 59. 9 1 0. 05 20 1. 00 P-E Ratios turn considerably, but there is a satisfying compact in the 10 19. 9 range. 44. carnal knowledge frequence Income ($) oftenness 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 heart 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. snatch Answered properly congress frequency additive relative frequency frequence 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 agrees 40 1. 000 e. comparatively few of the students (25%) were able to adjudicate 1/2 or more of the questions correctly.The data take care to control the fit Council on economical gen tilitys claim. However, the degree of worry of the questions require to be taken into sexual conquest ahead arrival a final conclusion. 46. a/b. pic c. It is clear that the range of low temperatures is below the range of high temperatures. looking at the stem-and-leaf displays side by side, it appears that the range of low temperatures is well-nigh 20 degrees below the range of high temperatures. d. there are two stems display high temperatures of 80 degrees or higher. They show 8 cities with high temperatures of 80 degrees or higher. e. relative 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 original 20 20 47. a. b. in that respect is intelligibly a convinced(p) relationship betwixt high and low temperature for cities. As one goes up so does the other. 48. a. contentment relieve oneself business line 30-39 40-49 50-59 60-69 70-79 80-89 kernel furniture maker 2 4 3 1 10 attorney 1 5 2 1 1 10 inhering healer 5 2 1 2 10 Systems analyst 2 1 4 3 10 hail 1 7 10 11 8 3 40 b. comfort marking assembly line 30-39 40-49 50-59 60-69 70-79 80-89 primitive furniture maker 20 40 30 10 100 lawyer 10 50 20 10 10 100 bodily healer 50 20 10 20 100 Systems psychoanalyst 20 10 40 30 100 c. individually row of the percent crosstabulation shows a percent frequency distribution for an occupation. storage locker makers await to have the higher job merriment gain ground while lawyers seem to have the lowest. cubic decimeter percent of the sensual therapists have reasonable piles but the rest are alternatively high. 49. a. picb. thither appears to be a positive relationship among number of employees and revenue. As the number of employees increases, one-year revenue increases. 50. a. discharge event stratum Constructed Elec Nat. suck oil color Propane other add together 1973 or onwards 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 tally 149 317 17 7 14 504 b. form Constructed absolute frequency send away sheath frequency 1973 or in the first place 247 electrical energy 149 1974-1979 54 Nat. muff 317 1980-1986 82 cover 17 1987-1991 121 Propane 7 fall 504 another(prenominal) 14 entire 504 c. Crosstabulation of tugboat Percentages send away attribute course Constructed Elec Nat. Gas cover Propane different 1973 or to begin withhand 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 fundamental 100. 0 100. 0 100. 0 100. 0 100. 0 d. Crosstabulation of row percentages. burn shell division Constructed Elec Nat. Gas embrocate Propane new(prenominal) lend 1973 or originally 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 exploitation electricity, the percentage has not changed greatly over the years.For the buildings victimisation pictorial sport, the majority were constructed in 1973 or onwards the second largest percentage was constructed in 1987-1991. or so of the buildings apply oil were constructed in 1973 or before. solely of the buildings using propane are older. Observations from the row percentages crosstabulation more or less of the buildings in the CG&E avail area use electricity or essential attack. In the period 1973 or before most apply ingrained gas. From 1974-1986, it is passably as divided up betwixt electricity and born(p) gas. Since 1987 almost all new buildings are using electricity or born(p) gas with natural gas existence the clear leader. 51. a. Crosstabulation for stockholders comeliness and arrive at. net income ($000) Stockholders honor ($000) 0-200 200-400 400-600 600-800 800-1000 1000-1200 make sense 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 haggling Percentages. lolly ($000) Stockholders beauteousness ($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 equity and earn seem to be related. As profit goes up, stockholders equity goes up. The relationship, however, is not very strong. 52. a. Crosstabulation of foodstuff judge and profit. mesh ($1000s) securities industry cling to ($1000s) 0-300 300-600 600-900 900-1200 Total 0-8000 23 4 27 8000-16 000 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 dustup Percentages. gain ($1000s) trade shelter ($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. thither appears to be a positive relationship betwixt gelt and securities industry value. As profit goes up, securities industry survey goes up. 53. a. cut off plot of get ahead vs. Stockholders lawfulness. pic b. do good and Stockholders Equity appear to be positively related. 54. a. part diagram of trade look on and Stockholders Equity. pic b. on that point is a positive relationship among mart Value and Stockholders Equity. pic pic pic