Descriptive Statistics: Tabular and Graphical Presentations

chapter 2 Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Learning Objectives 1. Learn how to construct and interpret summarization procedures for qualitative data such as : frequency and relative frequency distributions, bar graphs and pie charts. 2. Learn how to construct and interpret tabular summarization procedures for quantitative data such as: frequency and relative frequency distributions, cumulative frequency and cumulative relative frequency distributions. . 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 use and interpret the exploratory data analysis technique of a stem-and-leaf display. 6. Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data.Solutions: 1. |Class | Frequency |Relative Frequency | |A |60 |60/120 = 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(200) = 40 c/d. Class |Frequency |Percent Frequency | |A |. 22(200) = 44 | 22 | |B |. 18(200) = 36 | 18 | |C |. 40(200) = 80 | 40 | |D |. 20(200) = 40 | 20 | |Total |200 |100 | 3. a. 360 ° x 58/120 = 174 ° b. 360 ° x 42/120 = 126 ° c. [pic] d. [pic] 4. a. The data are qualitative. b. | |Percent Frequency | |Newspaper |Frequency | | |Liberty Times |24 |48 | |China Times |15 |30 | |United Daily News |7 |14 | |Apple Daily |4 |8 | |Total: |50 |100 | c. [pic] [pic] d. Liberty Times has the largest market share.China Times is second. 5. a. |Name |Frequency |Relative Frequency |Percent Frequency | |Chan |10 |. 200 |20. 0% | |Chang |7 |. 140 |14. 0% | |Lee |8 |. 160 |16. 0% | |Liu |7 |. 140 |14. 0% | |Wang |12 |. 240 |24. % | |Young |6 |. 120 |12. 0% | | |50 |1. 000 |100. 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 common: 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 Guide |6 | |10. 00 | | |Other |6 | |10. 00 | | |Total: |60 | |100. 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 are grouped in the â€Å"Other† category. b. The rank order from first to fifth is: Millionaire, Dad, 7 Habits, Motley, and WSJ Guide. c. The percent of sales represented by The Millionaire Next Door and Rich Dad, Poor Dad is 48. 33%. 7. |Rating |Frequency |Relative 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 | Management should be plea sed with these results. 64% of the ratings are very good to outstanding. 84% of the ratings are good or better.Comparing these ratings with previous results will show whether or not the restaurant is making improvements in its ratings of food quality. 8. a. |Position |Frequency |Relative Frequency | |Pitcher |17 |0. 309 | |Catcher | 4 |0. 073 | |1st Base | 5 |0. 091 | |2nd Base | 4 |0. 073 | |3rd Base | 2 |0. 36 | |Shortstop | 5 |0. 091 | |Left Field | 6 |0. 109 | |Center Field | 5 |0. 091 | |Right Field | 7 |0. 127 | | |55 |1. 000 | b. Pitchers (Almost 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 | |7:00 |3 | |15 | | |7:30 |4 | |20 | | |8:00 |4 | |20 | | |8:30 |7 | |35 | | |9:00 |2 | |10 | | | |20 | |100 | | c. Bar Graph [pic] d. [pic] . The most preferred starting time is 8:30 a. m.. Starting times of 7:30 and 8:00 a. m. are next. 10. a. The data refer to quality levels from 1 â€Å"Not at all Satisfied† to 7 â€Å"Extremely Satisfied. † b. |Rating |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 survey data indicate a high quality of service by the financial consultant. The most common ratings are 6 and 7 (70%) where 7 is extremely satisfied. Only 2 ratings are below the middle scale value of 4. There are no â€Å"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 | |less than or equal to 19 |10 | . 20 | |less than or equal to 29 |24 | . 48 | |less than or equal to 39 |41 | . 82 | |less than or equal to 49 |48 | . 6 | |less t han 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 than or equal to 4 |4 |0. 20 | |Less 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 shown below. [pic] The histogram clearly shows that the annual household incomes are skewed to the right. And, of course, if annual household incomes are skewed to the right, so are annual incomes. This makes sense because the vast majority of annual incomes are less than NT$1,000,000.But, there are a few individuals with very large incomes. b. The histogram for the age is given. [pic] The histogram shows that the distribution of age is skewed to the left. This is to be expected. It is our experience that there are frequently a few very low ages causing such a pattern to appear. c. The histogram for the data in Exercise 11 is given. d. [pic] e. This histogram is skewed to the left slightly, but we would probably classify it as roughly symmetric. 17. a. |Amount (NT$ ‘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 more | 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 more in the NT$56 to NT$75 range than in the NT$96 to NT$115 range. 18. a. Lowest s alary: 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 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 | |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 o r equal to 199 |20 |1. 00 | e. [pic] 20. a. The percentage of people 39 or less is 12. 2 + 14. 2 + 17. 1 + 16. 2 = 59. 7. b. The percentage of the population over 39 years old is 16. 3 + 10. 9 + 6. 7 + 4. 7 + 1. 7 = 40. 3 c. The percentage of the population that is between 20 and 59 years old inclusively is 17. 1 + 16. 2 + 16. 3 + 10. = 60. 5 d. The percentage 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 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 | | |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 pr ices for broker assisted 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: $62. 50 for an online trade. 27. 4 |1 3 6 6 7 | |5 |0 0 3 8 9 | |6 |0 1 1 4 4 5 7 7 9 | |7 |0 0 0 1 3 4 4 5 5 6 6 6 7 8 8 | |8 |0 1 1 3 4 4 5 7 7 8 9 | |9 |0 2 2 7 | or |4 |1 3 | |4 |6 6 7 | |5 |0 0 3 | |5 |8 9 | 6 |0 1 1 4 4 | |6 |5 7 7 9 9 | |7 |0 0 0 1 3 4 4 | |7 |5 5 6 6 6 7 8 8 | |8 |0 1 1 3 4 4 | |8 |5 7 7 8 9 | |9 |0 2 2 | |9 |7 | 28. a. |0 |5 8 | |1 |1 1 3 3 4 4 | |1 |5 6 7 8 9 9 | |2 |2 3 3 3 5 5 | |2 |6 8 | |3 | | 3 |6 7 7 9 | |4 |0 | |4 |7 8 | |5 | | |5 | | |6 |0 | b. |2000 P/E Forecast | |Percent Frequency | | |Frequency | | |5 – 9 |2 |6. 7 | | |10 – 14 |6 |20. 0 | | |15 – 19 |6 |20. 0 | | |20 – 24 |6 |20. | | |25 – 29 |2 |6. 7 | | |30 – 34 |0 |0. 0 | | |35 – 39 |4 |13. 3 | | |40 – 44 |1 |3. 3 | | |45 – 49 |2 |6. 7 | | | 50 – 54 |0 |0. 0 | | |55 – 59 |0 |0. 0 | | |60 – 64 |1 |3. 3 | | |Total |30 |100. 0 | | 29. a. [pic] b. [pic] c. [pic] d.Category A values for x are always associated with category 1 values for y. Category B values for x are usually associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y. 30. a. [pic] b. There is a negative relationship between x and y; y decreases as x increases. 31. a. Row Percentages: | |Household Income (NT$ ‘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 row 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) have 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 relationship between household income and age. 32. a. Column Percentages: |Household Income ($1000s) | | |Educa tion 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 | |Some College |21. 17 |29. 77 |30. 25 |29. 2 |22. 26 |26. 37 | |Bachelor's 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 column percentages. The first five columns give the percent frequency distributions for each income level.The percent frequency distribution in the â€Å"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 h eaded by persons having schooling beyond a bachelor's degree. The row percentages show that 39. 72% of the households headed by persons with schooling beyond a bachelor's degree earned $100,000 or more. These percentages are different because they came from different percent frequency distributions. c.Compare the â€Å"under 24. 9† percent frequency distributions to the â€Å"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 â€Å"100 or more† percent frequency distribution to â€Å"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.Fr om the comparisons here it is clear that there is a positive relationship 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 Fast |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 too fast: 40%. b. 10% of the women think the greens are too fast. 20% of the men think the greens are too fast. So, for the low handicappers, 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 Simpson's Paradox. At each handicap level a smaller percentage of the women think the greens are too fast. But, when the crosstabulations are aggr egated, the result is reversed 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 | | | |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 â€Å"A† rating on Sales/Margins/ROE, 88. 89% of them had an EPS Rating of 80 or higher. Of the 8 companies with a â€Å"D† or â€Å"E† rating on Sales/Margins/ROE, only 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. Once 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 â€Å"No Apparent Relationship† 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 tackle | |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; wide 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 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 | |Food | 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 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 outlier (General Motors). 42. a. |Closing Price |Frequency |Rel ative 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 Counter |15 |0. 75 | | |20 |1. 00 | b. Earn ings 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 shadow 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 Joint Council on Economic Education’s claim. However, the degree of difficulty of the questions needs to be taken into account before 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 | |Cabinetmaker | | |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 o f the percent crosstabulation shows a percent frequency distribution for an occupation. Cabinet makers 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 rather high. 49. a. [pic]b. 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 Colum n 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 natural gas, the majority were constructed in 1973 or before; the second largest percentage was constructed in 1987-1991. Most of t he 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 stockholder's equity and profit. | |Profits ($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 |10 00-1200 |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. Stockholder's equity and profit seem to be related. As profit goes up, stockholder's equity goes up. The relationship, however, is not very strong. 52. a. Crosstabulation of market value and profit. | |Profit ($1000s) | | | |Market 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) | | | |Market Value ($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. Stockholder's Equity. [pic] b. Profit and Stockholder's Equity appear to be positively related. 54. a. Scatter diagram of Market Value and Stockholder's Equity. [pic] b. There is a positive relationship between Market Value and Stockholder's Equity. ———————– [pic] [pic] [pic]