Descriptive Statistics: Tabular and Graphical Presentations

chapter 2 Chapter 2 Descriptive Statistics Tabular and graphical recordical Presentations instruction Objectives 1. Learn how to construct and furnish summarisation procedures for qualitative info such(prenominal) as oftenness and congeneric absolute absolute relative oftenness distri only ifions, contain graphs and pie charts. 2. Learn how to construct and sympathise tabular summarization procedures for quantitative information such as frequence and relative frequency distri exclusivelyions, cumulative frequency and cumulative relative frequency scatterings. . Learn how to construct a dot plot, a histogram, and an o spend as graphical summaries of quantitative data. 4. Learn how the underframe of a data distribution is revealed by a histogram. Learn how to recognize when a data distribution is negatively skewed, symmetric, and optimisticly skewed. 5. Be able to use and interpret the exploratory data analysis technique of a stem-and-leaf showing. 6. Learn how t o construct and interpret cross tabulations and scatter draws of bivariate data.Solutions 1. home frequence sexual relation frequence A 60 60/ great hundred = 0. 50 B 24 24/ cxx = 0. 20 C 36 36/120 = 0. 30 120 1. 00 2. a. 1 (. 22 + . 18 + . 40) = . 20 b.. 20(cc) = 40 c/d. Class absolute frequency portion fester oftenness A . 22(200) = 44 22 B . 18(200) = 36 18 C . 40(200) = 80 40 D . 20(200) = 40 20 jibe 200 nose evokedy 3. a. 360 x 58/120 = 174 b. 360 x 42/120 = 126 c. pic d. pic 4. a. The data argon qualitative. b. part relative frequency sensitive(a)spaper relative frequency Liberty sequences 24 48 China clock propagation 15 30 United Daily News 7 14 Apple Daily 4 8 gibe 50 nose candy c. pic pic d. Liberty cartridge h ancienters has the oerlargest market sh be.China Times is instant. 5. a. Name oftenness carnal knowledge relative frequency Percent absolute frequency Chan 10 . 200 20. 0% Chang 7 . 140 14. 0% lee(prenom inal) 8 . 160 16. 0% Liu 7 . 140 14. 0% Wang 12 . 240 24. % Young 6 . 120 12. 0% 50 1. 000 light speed. 0% b. pic c. Chan. 200 x 360 = 72. 0( Chang. 140 x 360 = 50. 4( Lee. 160 x 360 = 58. 6( Liu. 140 x 360 = 50. 4( Wang. 240 x 360 = 86. 4( Young. 120 x 360 = 43. 2( pic d. most(prenominal) common Wang, Chan, and Lee 6. a. Book relative frequency Percent frequency 7 Habits 10 16. 6 Millionaire 16 26. 67 Motley 9 15. 00 papa 13 21. 67 WSJ Guide 6 10. 00 otherwise 6 10. 00 totality 60 atomic quash 6. 00 The Ernst &038 Young Tax Guide 2000 with a frequency of 3, Investing for Dummies with a frequency of 2, and What Color is Your Parachute? 2000 with a frequency of 1 be grouped in the other(a) class. b. The rank order from graduation exercise to fifth is Millionaire, Dad, 7 Habits, Motley, and WSJ Guide. c. The sh arage of sales represented by The Millionaire Next access and Rich Dad, Poor Dad is 48. 33%. 7. military rating absolute frequency relation frequency Outstanding 19 0. 8 rattling reas whizd 13 0. 26 Good 10 0. 20 Average 6 0. 12 Poor 2 0. 04 50 1. 00 Management should be pleased with these results. 64% of the ratings be real good to outstanding. 84% of the ratings be good or better.Comparing these ratings with previous results will show whether or non the restaurant is making improvements in its ratings of provender persona. 8. a. vista relative frequency telling frequence Pitcher 17 0. 309 Catcher 4 0. 073 1st ignorant 5 0. 091 second Base 4 0. 073 third Base 2 0. 36 Shorts outdo 5 0. 091 Left field of battle 6 0. 109 pump orbit 5 0. 091 Right Field 7 0. 127 55 1. 000 b. Pitchers (Al nearly 31%) c. 3rd Base (3 4%) d. Right Field (Almost 13%) e. Infielders (16 or 29. 1%) to Outfielders (18 or 32. 7%) 9. a/b. Starting Time relative frequency Percent relative frequency 700 3 15 730 4 20 800 4 20 830 7 35 900 2 10 20 genius C c. Bar Graph pic d. pic . The most preferred starting time is 830 a. m.. Starting times of 730 and 800 a. m. atomic number 18 next. 10. a. The data refer to quality directs from 1 Not at all satisfied to 7 Extremely satisfied. b. Rating absolute frequency Relative absolute 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. Bar Graph pic d. The survey data indicate a spirited school quality of service by the financial consultant. The most common ratings argon 6 and 7 (70%) w present 7 is extremely satisfied. Only 2 ratings be be depleted the middle overcome value of 4. at that place atomic number 18 no Not at all Satisfied ratings. 11. Class Frequency Relative Frequency Percent 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 thorough 40 1. 000 b impoverished. 12. Class additive Frequency cumulative Relative Frequency less than or adjoin to 19 10 . 20 less tha n or exist to 29 24 . 48 less than or fit to 39 41 . 82 less than or beget-to doe with to 49 48 . 6 less than or equal to 59 50 1. 00 13. pic pic 14. a. pic b/c. Class Frequency Percent 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 light speed 15. a/b. Waiting Time Frequency Relative 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 appends 20 1. 00 c/d. Waiting Time accumulative Frequency cumulative Relative Frequency slight than or equal to 4 4 0. 20 less(prenominal) than or equal to 9 12 0. 60 little than or equal to 14 17 0. 5 Less than or equal to 19 19 0. 95 Less than or equal to 24 20 1. 00 e. 12/20 = 0. 60 16. a. The histogram is shown below. pic The histogram clearly shows that the mavin-year home incomes argon skewed to the reclaim. And, of course, if one-year household incomes argon skewed to the right, so are annual incomes. This ma kes sense because the vast volume of annual incomes are less than NT$1,000,000.But, on that point are a few single(a)s with really large incomes. b. The histogram for the age is given. pic The histogram shows that the distribution of age is skewed to the left. This is to be expected. It is our experience that there are frequently a few very low ages ca victimisation such a pattern to come out of the closet. c. The histogram for the data in operate 11 is given. d. pic e. This histogram is skewed to the left somewhat, but we would probably classify it as almost symmetric. 17. a. Amount (NT$ 000) Frequency Relative Frequency Less than 56 3 . 2 56-75 5 . 20 76-95 11 . 44 96-cxv 4 . 16 116-135 1 . 04 136 and to a greater extent 1 . 04 25 1. 00 b. Histogram pic The distribution has a almost symmetric shape. c.The largest group spends NT$76-NT$95 per year on disks and magazines. at that place are more in the NT$56 to NT$75 place than in the NT$96 to NT$115 range. 18. a. Lowest salary NT$29,300 Highest salary NT$37,800 b. salary (NT$ carbons) Frequency Relative Percent Frequency 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 substance 45 1. 00 one hundred c. Proportion NT$33,700 or less 18/45. d. Percentage more than NT$35,200 10/45 pic e. The distribution is skewed slightly to the left, but is roughly symmetric. 19. a/b. Number Frequency Relative Frequency 140 149 2 0. 10 150 159 7 0. 35 160 169 3 0. 15 clxx 179 6 0. 30 180 189 1 0. 05 190 199 1 0. 05 hits 20 1. 0 c/d. Number Cumulative Frequency Cumulative Relative Frequency Less than or equal to 149 2 0. 10 Less than or equal to 159 9 0. 45 Less than or equal to 169 12 0. 60 Less than or equal to 179 18 0. 0 Less than or equal to 189 19 0. 95 Less than or equal to 199 20 1. 00 e. pic 20. a. The destiny of citizenry 39 or less is 12. 2 + 14. 2 + 17. 1 + 16. 2 = 59. 7. b. T he pctage of the population over 39 long time old is 16. 3 + 10. 9 + 6. 7 + 4. 7 + 1. 7 = 40. 3 c. The dowery of the population that is mingled with 20 and 59 years old inclusively is 17. 1 + 16. 2 + 16. 3 + 10. = 60. 5 d. The divvy up less than 30 years old is 12. 2 + 14. 2 + 17. 1 = 43. 5. So there are (. 435) (22,689,122) = 9,869,768. 07 people less than 30 years old. e. An adjudicate of the number of retired people is (. 047 + . 017) (22,689,122) = 1,452,103. 81 21. a/b. Computer Usage Relative Frequency (Hours) 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 measure 50 1. 00 c. pic d. pic e. The majority of the computer users are in the 3 to 6 second range. Usage is somewhat skewed toward the right with 3 users in the 12 to 15 hour range. 22. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 23. Leaf Unit = 0. 1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 24. Leaf Unit = 10 11 6 12 0 2 13 0 6 7 1 4 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. atomic number 6 shares at $50 per share 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 display shows that the work equipment casualtys are closely grouped together. Rotating the stem-and-leaf display counter clockwise shows a histogram that is slightly skewed to the left but is roughly symmetric. b. viosterol shares affaird online at $50 per share. 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 distribution of online trading prices for most of the cistrons for 500 shares are swallow than the trading prices for broker assisted hatfuls of ampere-second shares. there are a couple of outliers. York Securities charges $36 for an online trade and Investors National charges much more than the early(a) brokers $62. 50 for an online trade. 27. 4 1 3 6 6 7 5 0 0 3 8 9 6 0 1 1 4 4 5 7 7 9 7 0 0 0 1 3 4 4 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 5 7 7 8 9 9 0 2 2 7 or 4 1 3 4 6 6 7 5 0 0 3 5 8 9 6 0 1 1 4 4 6 5 7 7 9 9 7 0 0 0 1 3 4 4 7 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 8 5 7 7 8 9 9 0 2 2 9 7 28. a. 0 5 8 1 1 1 3 3 4 4 1 5 6 7 8 9 9 2 2 3 3 3 5 5 2 6 8 3 3 6 7 7 9 4 0 4 7 8 5 5 6 0 b. 2000 P/E imagine Percent Frequency Frequency 5 9 2 6. 7 10 14 6 20. 0 15 19 6 20. 0 20 24 6 20. 25 29 2 6. 7 30 34 0 0. 0 35 39 4 13. 3 40 44 1 3. 3 45 49 2 6. 7 50 54 0 0. 0 55 59 0 0. 0 60 64 1 3. 3 hail 30 100. 0 29. a. pic b. pic c. pic d.Category A set for x are always associated with category 1 values for y. Category B values for x are normally associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y. 30. a. pic b. There is a negative human relationship amid x and y y decreases as x increases. 31. a. speech Perce ntages Household Income (NT$ 000) jump on under(a) 999 1,000-1,499 1,500-1,999 2,000-2,499 2,500-2,999 3,000 or more correspond Under 34 27. 6 30. 54 21. 01 12. 99 4. 93 2. 76 100. 00 35-44 20. 90 31. 32 21. 49 10. 48 8. 79 7. 03 100. 00 45-54 16. 00 29. 17 19. 24 19. 87 6. 83 8. 88 100. 00 55-64 23. 73 19. 26 20. 01 14. 46 8. 81 13. 73 100. 00 65 or more 70. 57 18. 37 4. 42 2. 4 0. 74 2. 96 100. 00 thorough 27. 70 27. 32 18. 27 13. 05 6. 51 7. 15 100. 00 There are septet percent frequency distributions in this shelve with speech percentages. The first of all six give the percent frequency distribution of income for to each one age level. The total speech provides an general percent frequency distribution for household income. Both of the two wrangles (age 35-44 and age 55- 64) come more percentage in the cells and descended in order of larger income.The second row is the percent frequency distribution for households headed by age 35-44. The fourth row is the percent frequency distribution for households headed by age 55-64. b. The percentage of heads of households by age 35-44 earning NT$2,500,000 or more is 8. 79% + 7. 03% = 15. 82%. The percentage of heads of households by age 55-64 earning $75,000 or more is 8. 81% + 13. 73% = 22. 54%. c. The percent frequency histograms are shown below. pic No. The histogram can not tell us every relationship surrounded by household income and age. 32. a. editorial Percentages Household Income ($1000s) Education Level Under 24. 9 25. 0-49. 9 50. 0-74. 9 75. 0-99. 9 100 or More sum up Not H. S. down 32. 70 14. 82 8. 27 5. 02 2. 53 15. 86 H. S. Graduate 35. 74 35. 56 31. 48 25. 39 14. 47 30. 78 Some College 21. 17 29. 77 30. 25 29. 2 22. 26 26. 37 Bachelors Degree 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 append 100. 00 100. 00 100. 00 100. 00 100. 00 100. 00 There are six percent frequency distributions in this table of tugboat pe rcentages. The first five pillars give the percent frequency distributions for each income level.The percent frequency distribution in the tot column gives the boilersuit percent frequency distributions for trainingal level. From that percent frequency distribution we see that 15. 86% of the heads of households did not graduate from extravagantly school. b. The column percentages show that 26. 86% of households earning over $100,000 were headed by persons having schooling beyond a bachelors stop. The row percentages show that 39. 72% of the households headed by persons with schooling beyond a bachelors degree take in $100,000 or more. These percentages are unalike because they came from different percent frequency distributions. c. comparability the under 24. 9 percent frequency distributions to the Total percent frequency distributions. We see that for this low income level the percentage with level levels of education is disappoint than for the overall population and the percentage with high levels of education is high than for the overall population. Compare the 100 or more percent frequency distribution to Total percent frequency distribution. We see that for this high income level the percentage with lower levels of education is lower than for the overall population and the percentage with higher(prenominal)(prenominal) levels of education is higher than for the overall population.From the comparisons here it is clear that there is a positive relationship amid household incomes and the education level of the head of the household. 33. a. The crosstabulation of condition of the colour by gender is below. Green educate Gender Too Fast first-rate Total Male 35 65 100 Female 40 60 100 Total 75 one hundred twenty-five 200 The female golfers deal the highest percentage saying the greens are to a fault fast 40%. b. 10% of the women estimate the greens are in any case fast. 20% of the men call in the greens are too fast. So, for the low hindrancepers, the men have a higher percentage who judge the greens are too fast. c. 43% of the woman echo the greens are too fast. 50% of the men think the greens are too fast. So, for the high handicappers, the men have a higher percentage who think the greens are too fast. . This is an example of Simpsons Paradox. At each handicap level a little percentage of the women think the greens are too fast. But, when the crosstabulations are aggregated, the result is reverse and we find a higher percentage of women who think the greens are too fast. The hidden variable explaining the reversal is handicap level. Fewer people with low handicaps think the greens are too fast, and there are more men with low handicaps than women. 34. a. EPS Rating gross tax/Margins/hard roe 0-19 20-39 40-59 60-79 80-100 Total 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 Total 4 4 6 9 13 36 b. EPS Rating gross revenue/Margins/ROE 0-19 20-39 40-59 60-79 80-100 Total A 11. 11 88. 89 100 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 Higher EPS ratings bet to be associated with higher ratings on sales/Margins/ROE. Of those companies with an A rating on Sales/Margins/ROE, 88. 89% of them had an EPS Rating 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 radical Relative effectuality Sales/Margins/ROE A B C D E Total 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 Total 4 11 7 10 4 36 b/c. The frequency distributions for the Sales/Margins/ROE data is in the rightmost column of the crosstabulation.The frequency distribution for the Industry Group Relative Strength data is in the bottom row of the crosstabulation. d. Once the crosstabulation is complete, the individual frequency distributions are available in the margins. 36. a. pic b. One might expec t stocks with higher EPS ratings to show greater relative price strength. However, the scatter plot using this data does not support such a relationship. The scatter plot appears similar to the one showing No Apparent alliance in the text. 37. a. The crosstabulation is shown below Speed Position 4-4. 49 4. 5-4. 99 5-5. 49 5. 5-5. 9 Grand Total Guard 12 1 13 Offensive carriage 2 7 3 12 Wide receiver 6 9 15 Grand Total 6 11 19 4 40 b. There appears to be a relationship between Position and Speed commodious receivers had faster speeds than offensive tackles and guards. c. The scatter diagram is shown below pic d. There appears to be a relationship between Speed and Rating slower speeds appear to be associated with lower ratings. In other words,, prospects with faster speeds play to be rated higher than prospects with slower speeds. 38. a. vehicle Frequency Percent Frequency F-Series 17 34 Silverado 12 24 bulls eye 8 16 Camry 7 14 Accord 6 12 Total 50 100 b. The two top selling vehicles are the Ford F-Series pickup arm and the Chevrolet Silverado. c. 39. a/b. Industry Frequency Percent Frequency Beverage 2 10 Chemicals 3 15 Electronics 6 30 Food 7 35 Aerospace 2 10 Totals 20 100 . 40. a. reception Frequency Percent Frequency the true 16 16 Approach Shots 3 3 Mental Approach 17 17 Power 8 8 Practice 15 15 lay 10 10 Short post 24 24 Strategic Decisions 7 7 Total 100 100 b. Poor short game, poor amiable approach, lack of accuracy, and limited practice. 41. a/b/c/d. Book Value Relative Frequency Cumulative Frequency Cumulative per Share Frequency Relative 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 Total 30 1. 00 e. The histogram shown below shows that the distribution of most of the book values is roughly symmetric. However, there is one out lier (General Motors). 42. a. remainder Price Frequency Relative 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. Closing Price Cumulative Frequency Cumulative Relative Frequency Less than or equal to 9 7/8 9 0. 25 Less than or equal to 19 7/8 19 0. 475 Less than or equal to 29 7/8 24 0. 600 Less than or equal to 39 7/8 35 0. 875 Less than or equal to 49 7/8 37 0. 925 Less than or equal to 59 7/8 39 0. 975 Less than or equal to 69 7/8 39 0. 75 Less than or equal to 79 7/8 40 1. 000 c. pic d. Over 87% of common stocks trade for less than $40 a share and 60% trade for less than $30 per share. 43. a. Relative Frequency Exchange Frequency American 3 0. 15 New York 2 0. 10 Over the look for 15 0. 75 20 1. 00 b. wampum Per Share Relative 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 shadow stocks have network per share less than $0. 40. It looks like low EPS should be expected for shadow stocks. Price-Earning balance Relative Frequency Frequency 0. 00 9. 9 3 0. 15 10. 0 19. 9 7 0. 35 20. 0 29. 9 4 0. 20 30. 0 39. 9 3 0. 15 40. 0 49. 9 2 0. 10 50. 0 59. 9 1 0. 05 20 1. 00 P-E Ratios vary considerably, but there is a significant ball in the 10 19. 9 range. 44. Relative Frequency Income ($) 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 Total 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. Number Answered Correctly Relative Frequency Cumulative Frequency 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 Totals 40 1. 000 e. relatively few of the students (25%) were able to answer 1/2 or more of the questions correctly.The data seem to support the Joint Council on Economic Educations claim. However, the degree of difficulty of the questions needs to be taken into account to begin with reaching 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 about 20 degrees below the range of high temperatures. d. There are two stems showing 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 Total 20 20 47. a. b. There is clearly a positive relationship between high and low temperature for cities. As one goes up so does the other. 4 8. a. Satisfaction crisscross Occupation 30-39 40-49 50-59 60-69 70-79 80-89 Total Cabinetmaker 2 4 3 1 10 Lawyer 1 5 2 1 1 10 sensible Therapist 5 2 1 2 10 Systems Analyst 2 1 4 3 10 Total 1 7 10 11 8 3 40 b. Satisfaction Score Occupation 30-39 40-49 50-59 60-69 70-79 80-89 Total Cabinetmaker 20 40 30 10 100 Lawyer 10 50 20 10 10 100 Physical Therapist 50 20 10 20 100 Systems Analyst 20 10 40 30 100 c. Each row of the percent crosstabulation shows a percent frequency distribution for an occupation. Cabinet makers seem to have the higher job satisfaction advance while lawyers seem to have the lowest. 50 percent of the physical therapists have fairish scores but the rest are rather high. 49. a. picb. There appears to be a positive relationship between number of employees and revenue. As the number of employees increases, annual revenue increases. 50. a. displace token Year Constructed Elec Nat.Gas anele Propane Other Total 1973 or in a dvance 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 Total 149 317 17 7 14 504 b. Year Constructed Frequency terminate Type Frequency 1973 or in the first place 247 Electricity 149 1974-1979 54 Nat.Gas 317 1980-1986 82 crude 17 1987-1991 121 Propane 7 Total 504 Other 14 Total 504 c. Crosstabulation of Column Percentages Fuel Type Year Constructed Elec Nat. Gas petroleum Propane Other 1973 or before 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 Total 100. 0 100. 0 100. 0 100. 0 100. 0 d. Crosstabulation of row percentages. Fuel Type Year Constructed Elec Nat. Gas Oil Propane Other Total 1973 or before 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 using electricity, the percentage has not changed greatly over the years.For the buildings using innate turgidness, the majority were constructed in 1973 or before the second largest percentage was constructed in 1987-1991. Most of the buildings using oil were constructed in 1973 or before. whole of the buildings using propane are older. Observations from the row percentages crosstabulation Most of the buildings in the CG&038E service sector use electricity or natural gas. In the period 1973 or before most used natural gas. From 1974-1986, it is pretty evenly divided between electricity and natural gas. Since 1987 almost all new buildings are using electricity or natural gas with natural gas being the clear leader. 51. a. Crosstabulation for stockholders candor and loot. lettuce ($000) Stockholders Equity ($000) 0-200 200-400 400-600 600-800 800-1000 1000-1200 Total 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. Profits ($000) Stockholders Equity ($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 profit seem to be related. As profit goes up, stockholders equity goes up. The relationship, however, is not very strong. 52. a. Crosstabulation of market value and profit. Profit ($1000s) foodstuff Value ($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 Row Percentages. Profit ($1000s) mart V alue ($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 between Profit and Market Value. As profit goes up, Market Value goes up. 53. a. Scatter diagram of Profit vs. Stockholders Equity. pic b. Profit and Stockholders Equity appear to be positively related. 54. a. Scatter diagram of Market Value and Stockholders Equity. pic b. There is a positive relationship between Market Value and Stockholders Equity. &8212&8212&8212&8212&8212&8212&8212 pic pic pic