Descriptive Statistics - Tabular and Graphical Presentations Part 2

Chapter 2 20. a. Off-Course Income ($1000s) 0-4,999 5,000-9,999 10,000-14,999 15,000-19,999 20,000-24,999 25,000-29,999 30,000-34,999 35000-39,999 40,000-44,999 45,000-49,999 Over 50,000 Total b. Frequency 30 9 4 0 3 2 0 0 1 0 1 50 Percent Frequency 60 18 8 0 6 4 0 0 2 0 2 100 Histogram of Off-Course Income Note: The first class is labeled 5000 and provides the golfers who had an off-course income in the range 0 to 4999 or less than 5000. These were the golfers with less than $5 million in off-course income. c. Off-course income is skewed to the right. Only Tiger Woods earns over $50 million. d. Considering the top 50 golfers, the majority (60%) earn less than $5 million in off-course income per year. 60% + 18% = 78% earn less than $10 million. Five golfers (10%) earn between $20 million and $30 million. Tiger Woods with $99.8 million and Phil Mickelson with $40.2 million in offcourse income are clearly the leaders in this income category. Descriptive Statistics: Tabular and Graphical Presentations 21. a/b. Computer Usage (Hours) 0.0 2.9 3.0 5.9 6.0 8.9 9.0 - 11.9 12.0 - 14.9 Total Frequency 5 28 8 6 3 50 Relative Frequency 0.10 0.56 0.16 0.12 0.06 1.00 c. 30 Frequency 25 20 15 10 5 0 0-2.9 3-5.9 6-8.9 9-11.9 12-14.9 Computer Usage (Hours) d. 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 14.9 hour range. Chapter 2 22. 23. 24. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 Leaf Unit = .1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 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 Descriptive Statistics: Tabular and Graphical Presentations 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 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. a. 7 5 9 8 3 6 9 5 6 8 10 0 4 4 11 1 5 12 13 7 14 5 5 Chapter 2 b. Observations such as the following can be made using the stem-and-leaf display.  The daily rate varies from $75 to $145  Typical mid-priced daily rates are $95 to $115 with the average daily rate around $100.  A daily rate in excess of $115 should be considered relatively high. High daily rates of $137 and $145 were found at three ski resorts. 28. a. 2 1 4 2 6 7 3 0 1 1 1 2 3 3 5 6 7 7 4 0 0 3 3 3 3 3 4 4 4 6 6 7 9 5 0 0 0 2 2 5 5 6 7 9 6 1 4 6 6 7 2 b. Most frequent age group: 40-44 with 9 runners c. 43 was the most frequent age with 5 runners d. 4/40 = 10% of the runners were “20-something.” With only 10% of the registrants “20-something,” the article pointed out that surprisingly few registrants were in this age group. One suggested reason was that “20-somethings” don’t have the time to train for a 13.1 mile race. For “20-somethings,” college, starting careers, and starting families may take priority over training for long distance races. 29. a. y x 1 2 Total A 5 0 5 B 11 2 13 C 2 10 12 Total 18 12 30 Descriptive Statistics: Tabular and Graphical Presentations b. y 1 x Total A 100.0 0.0 100.0 B 84.6 15.4 100.0 C 16.7 83.3 100.0 c. y x d. 2 1 2 A 27.8 0.0 B 61.1 16.7 C 11.1 83.3 Total 100.0 100.0 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. 56 40 y 24 8 -8 -24 -40 -40 -30 -20 -10 0 x 10 20 30 40 Chapter 2 b. 31. a. There is a negative relationship between x and y; y decreases as x increases. Row Percentages: Household Income ($1000s) Education Level Under 25 25.0-49.9 50.0-74.9 Not H.S. Graduate 42.23 34.73 13.94 H.S. Graduate 22.25 31.00 22.75 Some College 13.99 26.20 Bachelor's Degree 6.42 Beyond Bach. Deg. Total 75.0-99.9 5.41 100 or More 3.68 Total 100.00 11.93 12.07 100.00 23.31 16.20 20.30 100.00 15.19 20.66 18.72 39.02 100.00 3.71 10.60 16.29 15.87 53.54 100.00 17.77 25.08 20.64 13.90 22.62 100.00 There are six percent frequency distributions in this table with row percentages. The first five give the percent frequency distribution of income for each educational level. The total row provides an overall percent frequency distribution for household income. The second row, labeled H.S. Graduate, is the percent frequency distribution for households headed by high school graduates. The fourth row, labeled Bachelor's Degree, is the percent frequency distribution for households headed by bachelor's degree recipients. b. The percentage of households headed by high school graduates earning $75,000 or more is 11.93% + 12.07 = 24.00%. The percent of households headed by bachelor's degree recipients earning $75,000 or more is 18.72% + 39.02% = 57.74%. c. The percent frequency histogram for high school graduates. Descriptive Statistics: Tabular and Graphical Presentations The percent frequency distribution for college graduates with a bachelor’s degree. The histograms show that households headed by a college graduate with a bachelor’s degree earn more than households headed by a high school graduate. Yes, there is a positive relationship between education level and income. 32. a. Column Percentages: Household Income ($1000s) Education Level Under 25 25.0-49.9 Not H.S. Graduate 32.10 18.71 9.13 5.26 2.20 13.51 H.S. Graduate 37.52 37.05 33.04 25.73 16.00 29.97 Some College 21.42 28.44 30.74 31.71 24.43 27.21 Bachelor's Degree 6.75 11.33 18.72 25.19 32.26 18.70 Beyond Bach. Deg. 2.21 4.48 8.37 12.11 25.11 10.61 100.00 100.00 100.00 100.00 100.00 100.00 Total 50.0-74.9 75.0-99.9 100 or More Total 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 "Total" column gives the overall percent frequency distributions for educational level. From that percent frequency distribution we see that 13.51% of the heads of households did not graduate from high school. b. The column percentages show that 25.11% of households earning $100,000 or more were headed by persons having schooling beyond a bachelor's degree. The row percentages show that 53.54% 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 and provide different kinds of information. c. Compare the "under 25" 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 higher than for the overall population and the percentage with higher levels of education is lower than for the overall population. Chapter 2 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 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 Too Fast Fine 35 65 40 60 75 125 Gender Male Female Total Total 100 100 200 The female golfers have the highest percentage saying the greens are too fast: 40/100 = 40%. Male golfers have 35/100 = 35% saying the greens are too fast. b. Among low handicap golfers, 1/10 = 10% of the women think the greens are too fast and 10/50 = 20% of the men think the greens are too fast. So, for the low handicappers, the men show a higher percentage who think the greens are too fast. c. Among the higher handicap golfers, 39/51 = 43% of the woman think the greens are too fast and 25/50 = 50% of the men think the greens are too fast. So, for the higher handicap golfers, the men show a higher percentage who think the greens are too fast. d. 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 aggregated, 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. 5 Year Average Return . Fund Type 0-9.99 Total 1 25 1 0 40-49.99 0 50-59.99 DE 0 27 FI 9 1 0 0 0 0 10 IE 0 2 3 2 0 1 8 Total 10 28 4 2 0 1 45 b. 10-19.99 20-29.99 5 Year Average Return 0-9.99 10-19.99 20-29.99 30-39.99 40-49.99 50-59.99 Total 30-39.99 Frequency 10 28 4 2 0 1 45 Descriptive Statistics: Tabular and Graphical Presentations c. Fund Type DE FI IE Total Frequency 27 10 8 45 d. The right margin shows the frequency distribution for the fund type variable and the bottom margin shows the frequency distribution for the 5 year average return variable. e. Higher returns are associated with International Equity funds and lower returns are associated with Fixed Income funds. 35. a. Expense Ratio (%) Fund Type 0-0.24 0.25-0.49 0.50-0.74 0.75-0.99 1.00-1.24 1.25-1.49 DE 1 1 3 5 10 7 Total 27 FI 2 4 3 0 0 1 10 IE 0 0 1 2 4 1 8 Total 3 5 7 7 14 9 45 b. Expense Ratio (%) 0-0.24 0.25-0.49 0.50-0.74 0.75-0.99 1.00-1.24 1.25-1.49 Total c. Frequency 3 5 7 7 14 9 45 Percent 6.7 11.1 15.6 15.6 31.0 20.0 100 Higher expense ratios are associated with Domestic Equity funds and lower expense ratios are associated with Fixed Income fund