The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.

1. Organizing Data Graphical and Tabular Descriptive Techniques 2.

9. Nominal Data (Tabular Summary) - 2.

10. Nominal Data (Frequency) 2. Bar Charts are often used to display frequencies… Is there a better way to order these? Would Bar Chart look different if we plotted “relative frequency” rather than “frequency”?

11. Nominal Data (Relative Frequency) 2. Pie Charts show relative frequencies…

14. Example 2.2 Construct a frequency distribution table for these data. Some what None Somewhat Very Very None Very Somewhat Somewhat Very Somewhat Somewhat Very Somewhat None Very None Somewhat Somewhat Very Somewhat Somewhat Very None Somewhat Very very somewhat None Somewhat

15. Solution 2.2 Table 2.2 Frequency Distribution of Stress on Job Stress on Job Tally Frequency ( f ) Very Somewhat None |||| |||| |||| |||| |||| |||| | 10 14 6 Sum = 30

19. Solution 2-2 Table 2.3 Relative Frequency and Percentage Distributions of Stress on Job Stress on Job Relative Frequency Percentage Very Somewhat None 10/30 = .333 14/30 = .467 6/30 = .200 .333(100) = 33.3 .467(100) = 46.7 .200(100) = 20.0 Sum = 1.00 Sum = 100

21. Figure 2.2 Bar graph for the frequency distribution of Table 2.3

23. Table 2.4 Calculating Angle Sizes for the Pie Chart Stress on Job Relative Frequency Angle Size Very Somewhat None .333 .467 .200 360(.333) = 119.88 360(.467) = 168.12 360(.200) = 72.00 Sum = 1.00 Sum = 360

24. Figure 2.4 Pie chart for the percentage distribution of Table 2.5.

26. Frequency Distributions Table 2.7 Weekly Earnings of 100 Employees of a Company Variable Third class Lower limit of the sixth class Upper limit of the sixth class Frequency of the third class Frequency column Weekly Earnings (dollars) Number of Employees f 401 to 600 601 to 800 801 to 1000 1001 to 1200 1201 to 1400 1401 to 1600 9 22 39 15 9 6

41. Write the classes starting with lowest score. Classes Tally Marks Freq. 70 – 78 61 – 69 52 – 60 43 – 51 34 – 42 25 – 33 16 – 24 ///// ///// // /////-// /////-/////-//// /////-/////-/////-// 5 5 0 2 7 14 17

43. Classes Class boundaries Tally Marks Freq. x 70 – 78 61 – 69 52 – 60 43 – 51 34 – 42 25 – 33 16 – 24 69.5 – 78.5 60.5 – 69.5 51.5 – 60.5 42.5 – 51.5 33.5 – 42.5 24.5 – 33.5 15.5 – 24.5 ///// ///// // /////-// /////-/////-//// /////-/////-/////-// 5 5 0 2 7 14 17 74 65 56 47 38 29 20

45. Table 2.9 Home Runs Hit by Major League Baseball Teams During the 2002 Season Team Home Runs Team Home Runs Anaheim Arizona Atlanta Baltimore Boston Chicago Cubs Chicago White Sox Cincinnati Cleveland Colorado Detroit Florida Houston Kansas City Los Angeles 152 165 164 165 177 200 217 169 192 152 124 146 167 140 155 Milwaukee Minnesota Montreal New York Mets New York Yankees Oakland Philadelphia Pittsburgh St. Louis San Diego San Francisco Seattle Tampa Bay Texas Toronto 139 167 162 160 223 205 165 142 175 136 198 152 133 230 187

46. Solution 2-3 Now we round this approximate width to a convenient number – say, 22.

48. Table 2.10 Frequency Distribution for the Data of Table 2.9 Total Home Runs Tally f 124 – 145 146 – 167 168 – 189 190 – 211 212 - 233 |||| | |||| |||| ||| |||| |||| ||| 6 13 4 4 3 ∑ f = 30

51. Solution 2-4 Table 2.11 Relative Frequency and Percentage Distributions for Table 2.10 Total Home Runs Class Boundaries Relative Frequency Percentage 124 – 145 146 – 167 168 – 189 190 – 211 212 - 233 123.5 to less than 145.5 145.5 to less than 167.5 167.5 to less than 189.5 189.5 to less than 211.5 211.5 to less than 233.5 .200 .433 .133 .133 .100 20.0 43.3 13.3 13.3 10.0 Sum = .999 Sum = 99.9%

53. Figure 2.3 Frequency histogram for Table 2.10. 124 - 145 146 - 167 168 - 189 190 - 211 212 - 233 Total home runs 15 12 9 6 3 0 Frequency

54. Figure 2.4 Relative frequency histogram for Table 2.10. 124 - 145 146 - 167 168 - 189 190 - 211 212 - 233 Total home runs .50 .40 .30 .20 .10 0 Relative Frequency

56. Figure 2.5 Frequency polygon for Table 2.10. 124 - 145 146 - 167 168 - 189 190 - 211 212 - 233 15 12 9 6 3 0 Frequency

57. Figure 2.6 Frequency Distribution curve. Frequency x

59. Example 2-5 Construct a frequency distribution table. Calculate the relative frequencies and percentages for all classes. 22.4 19.7 21.6 15.4 21.1 18.2 27.0 21.9 22.1 25.4 23.7 21.7 23.2 19.6 24.9 19.8 17.6 16.0 21.4 25.5 26.7 17.7 16.1 23.8 20.1 23.4 22.5 22.3 21.9 17.1 23.5 23.7 24.4 21.9 22.5 21.2 28.7 15.6 24.3 29.2 19.9 22.7 26.7 26.1 31.2 23.6 24.2 22.7 22.6 20.8

60. Solution 2-5

61. Solution 2-5 Table 2.12 Frequency, Relative Frequency, and Percentage Distributions of Average Travel Time to Work Class Boundaries f Relative Frequency Percentage 15 to less than 18 18 to less than 21 21 to less than 24 24 to less than 27 27 to less than 30 30 to less than 33 7 7 23 9 3 1 .14 .14 .46 .18 .06 .02 14 14 46 18 6 2 Σ f = 50 Sum = 1.00 Sum = 100%

63. Solution 2-6 Table 2.13 Frequency Distribution of Vehicles Owned Vehicles Owned Number of Households ( f ) 0 1 2 3 4 5 2 18 11 4 3 2 Σ f = 40

64. Figure 2.7 Bar graph for Table 2.13.

69. Figure 2.13 Stem-and-leaf display. Leaf for 75 Leaf for 52 Stems 5 6 7 8 9 2 5

71. Figure 2.14 Stem-and-leaf display of test scores. 5 6 7 8 9 2 0 7 5 9 1 8 4 5 9 1 2 6 9 7 1 2 0 7 1 6 3 4 7 6 3 5 2 2 8

72. Figure 2.15 Ranked stem-and-leaf display of test scores. 5 6 7 8 9 0 2 7 1 4 5 8 9 1 1 2 2 5 6 7 9 9 0 1 3 4 6 7 7 2 2 3 5 6 8

74. Solution 2-9 Figure 2.16 Stem-and-leaf display of rents. 6 7 8 9 10 11 12 13 30 75 50 21 50 80 25 50 32 52 15 60 85 65 23 81 35 75 00 91 51 40 75 40 00 10 31 35 80 70

77. Solution 2-10 Figure 2.17 Grouped stem-and-leaf display. 0 – 2 3 – 5 6 – 8 6 * 1 7 9 * 2 6 2 4 7 8 * 1 5 6 9 9 * 3 6 8 2 4 4 5 7 * * 5 6