Descriptive Statistics: Tabular and Graphical Presentations

chapter 2 Chapter 2 Descriptive Statistics Tabular and Graphical Presentations keying Objectives 1. Learn how to bring about and interpret summarization procedures for qualitative data much(prenominal) as relative absolute frequency and relative frequency distri nonwithstandingions, bar graphs and pie charts. 2. Learn how to construct and interpret tabular summarization procedures for quantitative data such as frequency and relative frequency diffusions, cumulative frequency and cumulative relative frequency scatterings. . Learn how to construct a dot plot, a histogram, and an ogive as graphical summaries of quantitative data. 4. Learn how the shape of a data distribution is revealed by a histogram. Learn how to recognize when a data distribution is negatively skewed, symmetric, and positively skewed. 5. Be able to do and interpret the exploratory data analysis technique of a stem-and-leaf display. 6. Learn how to construct and interpret cross tabulations and scatter diagr ams of bivariate data.Solutions 1. sectionalization relative frequency comparative oftenness A 60 60/long hundred = 0. 50 B 24 24/120 = 0. 20 C 36 36/120 = 0. 30 120 1. 00 2. a. 1 (. 22 + . 18 + . 40) = . 20 b.. 20(cc) = 40 c/d. assort absolute frequency per centum frequence A . 22( two hundred) = 44 22 B . 18(cc) = 36 18 C . 40(200) = 80 40 D . 20(200) = 40 20 heart and soul 200 snow 3. a. 360 x 58/120 = 174 b. 360 x 42/120 = 126 c. pic d. pic 4. a. The data ar qualitative. b. per centum relative frequency Newspaper absolute frequency Liberty beats 24 48 China Times 15 30 united Daily News 7 14 Apple Daily 4 8 rack up 50 vitamin C c. pic pic d. Liberty Times has the largest market shargon.China Times is second. 5. a. Name Frequency relational Frequency Percent Frequency Chan 10 . 200 20. 0% Chang 7 . one hundred forty 14. 0% downwind 8 . 160 16. 0% Liu 7 . 140 14. 0% Wang 12 . 240 24. % Young 6 . 120 12. 0% 50 1. 000 coulom b. 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 parking lot Wang, Chan, and Lee 6. a. Book Frequency Percent Frequency 7 Habits 10 16. 6 Millionaire 16 26. 67 Motley 9 15. 00 Dad 13 21. 67 WSJ slide by 6 10. 00 Other 6 10. 00 Total 60 light speed. 00 The Ernst & 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 category. b. The rank commit from first to fifth is Millionaire, Dad, 7 Habits, Motley, and WSJ Guide. c. The per centum of sales represented by The Millionaire Next Door and Rich Dad, scurvy Dad is 48. 33%. 7. judge Frequency carnal knowledge Frequency Outstanding 19 0. 8 Very Good 13 0. 26 Good 10 0. 20 Average 6 0. 12 Poor 2 0. 04 50 1. 00 way should be pleased with these allow for s. 64% of the ratings be rattling good to outstanding. 84% of the ratings are good or better.Comparing these ratings with previous results will plant whether or not the restaurant is making improve manpowerts in its ratings of food quality. 8. a. lieu Frequency comparative Frequency Pitcher 17 0. 309 Catcher 4 0. 073 1st Base 5 0. 091 2nd Base 4 0. 073 3rd Base 2 0. 36 pithystop 5 0. 091 left over(p) Field 6 0. 109 Center Field 5 0. 091 Right Field 7 0. 127 55 1. 000 b. Pitchers (Al about 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 Frequency Percent Frequency 700 3 15 730 4 20 800 4 20 830 7 35 900 2 10 20 100 c. Bar Graph pic d. pic . The most preferred beginning time is 830 a. m.. Starting times of 730 and 800 a. m. are next. 10. a. The data refer to quality directs from 1 Not at all Satisfied to 7 Extremely Satisfied. b. evaluate Frequency Relative 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 pursue data indicate a advanced quality of service by the financial consultant. The most habitual ratings are 6 and 7 (70%) where 7 is extremely satisfied. Only 2 ratings are on a lower floor the spirit scale value of 4. thither are 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 Total 40 1. 000 100. 12. Class Cumulative Frequency Cumulative Relative Frequency slight than or liken to 19 10 . 20 little(prenominal) than or play off to 29 24 . 48 less than or live to 39 41 . 82 less than or equal 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 20 100 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 Totals 20 1. 00 c/d. Waiting Time Cumulative Frequency Cumulative Relative Frequency less(prenominal) than or equal to 4 4 0. 20 less(prenominal) than or equal to 9 12 0. 60 Less 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 appearancen below. pic The histogram clearly shows that the yearbook base incomes are skewed to the right. And, of course, if annual househ senescent incomes are skewed to the right, so are annual incomes. This makes good sense because the vast majority of annual incomes are less than NT$1,000,000.But, in that respect are a hardly a(prenominal) individuals with very large incomes. b. The histogram for the age is given. pic The histogram shows that the distribution of age is skewed to the left. This is to be ex pected. It is our experience that there are frequently a few very low ages causing such a pattern to appear. c. The histogram for the data in Exercise 11 is given. d. pic e. This histogram is skewed to the left slightly, but we would probably classify it as just about symmetric. 17. a. derive (NT$ 000) Frequency Relative Frequency Less than 56 3 . 2 56-75 5 . 20 76-95 11 . 44 96-115 4 . 16 116-135 1 . 04 136 and to a greater extent 1 . 04 25 1. 00 b. Histogram pic The distribution has a roughly symmetric shape. c.The largest group spends NT$76-NT$95 per year on books and magazines. There are to a greater extent than in the NT$56 to NT$75 target than in the NT$96 to NT$115 range. 18. a. Lowest salary NT$29,300 Highest salary NT$37,800 b. Salary (NT$100s) 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 Total 45 1. 00 100 c. Proportion NT$33,700 or l ess 18/45. d. Percentage more(prenominal) 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. 15 170 179 6 0. 30 180 189 1 0. 05 190 199 1 0. 05 Totals 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 pctage of people 39 or less is 12. 2 + 14. 2 + 17. 1 + 16. 2 = 59. 7. b. The region of the population over 39 years old is 16. 3 + 10. 9 + 6. 7 + 4. 7 + 1. 7 = 40. 3 c. The luck of the population that is between 20 and 59 years old inclusively is 17. 1 + 16. 2 + 16. 3 + 10. = 60. 5 d. The per centumage 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 estimate of the number of retired people is (. 047 + . 017) (22,689,122) = 1,452,103. 81 21. a/b. Computer consumption 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 Total 50 1. 00 c. pic d. pic e. The majority of the computer users are in the 3 to 6 hour 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 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. 100 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 trading prices 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. 500 shares traded 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 brokers for 500 shares are lower than the trading prices for broker help trades of 100 shares. There are a couple of outliers. York Securities charges $36 for an online trade and Investors National charges much more than the other brokers $62. 50 for an online trade. 27. 4 1 3 6 6 7 5 0 0 3 8 9 6 0 1 1 4 4 5 7 7 9 7 0 0 0 1 3 4 4 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 5 7 7 8 9 9 0 2 2 7 or 4 1 3 4 6 6 7 5 0 0 3 5 8 9 6 0 1 1 4 4 6 5 7 7 9 9 7 0 0 0 1 3 4 4 7 5 5 6 6 6 7 8 8 8 0 1 1 3 4 4 8 5 7 7 8 9 9 0 2 2 9 7 28. a. 0 5 8 1 1 1 3 3 4 4 1 5 6 7 8 9 9 2 2 3 3 3 5 5 2 6 8 3 3 6 7 7 9 4 0 4 7 8 5 5 6 0 b. 2000 P/E Forecast Percent Frequency Frequency 5 9 2 6. 7 10 14 6 20. 0 15 19 6 20. 0 20 24 6 20. 25 29 2 6. 7 30 34 0 0. 0 35 39 4 13. 3 40 44 1 3. 3 45 49 2 6. 7 50 54 0 0. 0 55 59 0 0. 0 60 64 1 3. 3 Total 30 100. 0 29. a. pic b. pic c. pic d.Category A set for x are always associated with category 1 values for y. Category B values for x are usually associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y. 30. a. pic b. There is a negative affinity between x and y y decreases as x increases. 31. a. Row Percentages Household Income (NT$ 000) Age Under 999 1,000-1,499 1,500-1,999 2,000-2,499 2,500-2,999 3,000 or more Total 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 Total 27. 70 27. 32 18. 27 13. 05 6. 51 7. 15 100. 00 There are seven percent frequency distributions in this table with actors line percentages. The first six give the percent frequency distribution of income for each age level. The total row provides an overall percent frequency distribution for household income. Both of the two rows (age 35-44 and age 55- 64) get to 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 any consanguinity between household income and a ge. 32. a. Column Percentages Household Income ($1000s) Education Level Under 24. 9 25. 0-49. 9 50. 0-74. 9 75. 0-99. 9 100 or More Total Not H. S. Graduate 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 slightly 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 Total 100. 00 100. 00 100. 00 100. 00 100. 00 100. 00 There are six percent frequency distributions in this table of tower percentages. The first 5 columns give the percent frequency distributions for each income level.The percent frequency distribution in the Total column gives the overall percent frequency distributions for educational level. From that percent frequency distribution we see that 15. 86% of the heads of households did not graduate from high school. b. The column percentages show that 26. 86% of households earning over $100,000 were headed by persons having schooling beyond a bachelors degree. The row percentages show that 39. 72% of the households headed by persons with schooling beyond a bachelors degree earned $100,000 or more. These percentages are different because they came from different percent frequency distributions. c.Compare the under 24. 9 percent frequency distributions to the Total percent frequency distributions. We see that for this low income level the percentage with lower levels of education is lower than for the overall population and the percentage with higher levels of education is higher 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 levels of education is higher than for the overall population.From the comparisons here it is clear that there is a positive re lationship between household incomes and the education level of the head of the household. 33. a. The crosstabulation of condition of the greens by gender is below. Green Condition Gender Too debauched Fine Total Male 35 65 100 Female 40 60 100 Total 75 125 200 The female golfers have the highest percentage saying the greens are overly fast 40%. b. 10% of the women think the greens are to a fault fast. 20% of the men think the greens are too fast. So, for the low stymiepers, the men have a higher percentage who think the greens are too fast. c. 43% of the woman think 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 smaller percentage of the women think the greens are too fast. But, when the crosstabulations are aggregated, the result is reversed and we find a higher percentage of women who think the greens are too fast. The underground 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 Sales/Margins/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 Sales/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 seem 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, further 1 had an EPS rating above 60. 35. a. Industry Group Relative Strength 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. one time the crosstabulation is complete, the individual frequency distributions are available in the margins. 36. a. pic b. One might expect stocks with higher EPS ratings to show greater relative price strength. However, the scatter diagram using this data does not support such a relationship. The scatter diagram appears similar to the one showing No Apparent Relationship in the text. 37. a. The crosstabulation is shown below animate Position 4-4. 49 4. 5-4. 99 5-5. 49 5. 5-5. 9 Grand Total vindication 12 1 13 Offensive tackle 2 7 3 12 coarse receiver 6 9 15 Grand Total 6 11 19 4 40 b. There appears to be a relationship between Position and Speed wide receivers had swift 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 tend to be rated higher than prospects with slower speeds. 38. a. Vehicle Frequency Percent Frequency F-Series 17 34 Silverado 12 24 Taurus 8 16 Camry 7 14 Accord 6 12 Total 50 100 b. The two top selling vehicles are the Ford F-Series Pickup and the Chevrolet Silverado. c. 39. a/b. Industry Frequency Percent Frequency Beverage 2 10 Chemicals 3 15 Electronics 6 30 feed 7 35 Aerospace 2 10 Totals 20 100 . 40. a. Response Frequency Percent Frequency Accuracy 16 16 Approach Shots 3 3 Mental Approach 17 17 Power 8 8 Practice 15 15 Putting 10 10 Short Game 24 24 Strategic Decisions 7 7 Total 100 100 b. Poor short game, poor mental approach, lack of accuracy, and limited practice. 41. a/b /c/d. Book treasure 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 outlier (General Motors). 42. a. Closing 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 th an 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. oer 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 Counter 15 0. 75 20 1. 00 b. Earnings 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 Seventy percent of the night stocks have earnings per share less than $0. 40. It looks like low EPS should be expected for shadow stocks. Price-Earning Ratio Relative Frequency Frequency 0. 00 9. 9 3 0. 15 10. 0 19. 9 7 0. 35 20. 0 29. 9 4 0. 20 30. 0 39. 9 3 0. 15 40. 0 49. 9 2 0. 10 50. 0 59. 9 1 0. 05 20 1. 00 P-E Ratios vary considerably, but there is a significant cluster in the 10 19. 9 range. 44. Relative Frequency Income ($) 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 conjugation Council on Economic Educations claim. However, the degree of difficulty of the questions needs to be taken into cypher ahead 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. 48. a. Satisfaction Score Occupation 30-39 40-49 50-59 60-69 70-79 80-89 Total furniture maker 2 4 3 1 10 Lawyer 1 5 2 1 1 10 Physical 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 m akers seem to have the higher job satisfaction scores while lawyers seem to have the lowest. Fifty percent of the physical therapists have mediocre scores but the rest are quite 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. Fuel Type year Constructed Elec Nat.Gas Oil Propane Other Total 1973 or before 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 Fuel Type Frequency 1973 or before 247 Electricity 149 1974-1979 54 Nat.Gas 317 1980-1986 82 Oil 17 1987-1991 121 Propane 7 Total 504 Other 14 Total 504 c. Crosstabulation of Column Percentages Fuel Type Year Constructed Elec Nat. Gas Oil 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 indwelling gas, 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. All of the buildings using propane are older. Observations from the row percentages crosstabulation Most of the buildings in the CG&E service area use electricity or natural gas. In the period 1973 or before most used natural gas. From 1974-1986, it is fairly 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 comeliness and profit. put ons ($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, stockhol ders equity goes up. The relationship, however, is not very strong. 52. a. Crosstabulation of market value and profit. Profit ($1000s) Market range ($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) Market cheer ($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 positi ve relationship between Market Value and Stockholders Equity. pic pic pic