1. Understanding Basic Statistics Chapter One Organizing Data

2. Statistics is The study of how to: collect organize analyze interpret numerical information from data

3. Types of Data Quantitative data are numerical measurements –example: number of siblings Qualitative data involve non-numerical observations –example: brand of computer

4. Population all measurements or observations of interest Example: incomes of all residents of a county

5. Sample part of a population used to represent the population Example: incomes of selected residents

6. Methods of Producing Data Sampling: drawing subsets from the population Experimention: impose a change and measure the result Simulation: numerical facsimile of real-world phenomena Census: using measurements from entire population

7. Potential Problems Strong opinions may be overepresented if responses are voluntary. A hidden bias may exist in the way data is collected. There may be hidden effects of other variables. There is no guarantee that results can be generalized.

8. Levels of Measurement Nominal Ordinal Interval Ratio

9. Nominal Measurement Data is put into categories only. Example: eye color

10. Ordinal Measurement Data can be ordered. Differences cannot be calculated or interpreted. Example: class rank

11. Interval Measurement Data can be ordered. Differences between data values can be compared. Example: temperature

12. Ratio Measurement Data can be ordered. Differences and ratios between data values can be compared. Example: time

13. Simple Random Sample of n measurements: every sample of size n has equal chance of being selected every item in the population has equal chance of being included

14. Not random sampling: asking for volunteers to respond to a survey choosing the first five customers in a store

15. Random sampling: drawing names “from a hat” using a random number table to select sample using a random number generator

16. Sampling techniques Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Convenience Sampling

17. Stratified Sampling Population is divided into groups Random samples are drawn from each group

18. Systematic Sampling Population is arranged in sequential order. Select a random starting point. Select every “kth” item.

19. Cluster Sampling Population is divided into sections Some sections are randomly selected Every item in selected sections is included in sample

20. Convenience Sampling Use whatever data is readily available. Risk severe bias.

21. Which sampling technique is described? College students are waiting in line for registration. Every eighth person in line is surveyed. Systematic sampling

22. Which sampling technique is described? College students are waiting in line for registration. Students are asked to volunteer to respond to a survey. Convenience sampling

23. Which sampling technique is described? In a large high school, students from every homeroom are randomly selected to participate in a survey Stratified sampling

24. Which sampling technique is described? An accountant uses a random number generator to select ten accounts for audit. Simple random sampling

25. Which sampling technique is described? To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are surveyed. Cluster sampling

26. Bar Graph bars of uniform width uniformly spaced may be vertical or horizontal lengths represent quantities being compared

27. Pareto Chart tool of quality control start with a bar chart arrange bars in decreasing order of frequency frequently used to investigate causes of problems

28. Circle Graph (Pie Chart) shows division of whole into component parts label parts with appropriate percentages of the whole

29. Time Plot Shows data values in chronological order time on horizontal scale other variable on vertical scale connect data points with line segments

30. Histogram Differences from a bar chart: bars touch width of bars represents quantity

31. To construct a histogram from raw data: Decide on the number of classes (5 to 15 is customary) and find a convenient class width. Organize the data into a frequency table. Find the class boundaries and the class midpoints. Tally data and determine the freqency Sketch the histogram.

32. Computing the class width 1.Compute: 2.Increase the value computed to the next highest whole number

33. Class Width Raw Data: 10.2 18.7 22.3 20.0 6.3 17.8 17.1 5.0 2.4 7.9 0.3 2.5 8.5 12.5 21.4 16.5 0.4 5.2 4.1 14.3 19.5 22.5 0.0 24.7 11.4 Use 5 classes. 24.7 – 0.0 5 = 4.94 Round class width up to 5.

34. Computing Class Width difference between the lower class limit of one class and the lower class limit of the next class

35. Finding Class Widths # of miles Class Width 0.0 - 4.95 5.0 - 9.95 10.0 - 14.95 15.0 - 19.95 20.0 - 24.95

36. Class Boundaries (Upper limit of one class + lower limit of next class) divided by two

37. Finding Class Boundaries # of miles fclass boundaries 0.0 - 4.96 5.0 - 9.954.95 - 9.95 10.0 - 14.94 15.0 - 19.95 20.0 - 24.95

38. Finding Class Boundaries # of miles fclass boundaries 0.0 - 4.96 5.0 - 9.954.95 - 9.95 10.0 - 14.949.95 - 14.95 15.0 - 19.95 20.0 - 24.95

39. # of miles fclass boundaries 0.0 - 4.96 5.0 - 9.954.95 - 9.95 10.0 - 14.949.95 - 14.95 15.0 - 19.9514.95 - 19.95 20.0 - 24.95 Finding Class Boundaries

40. # of miles fclass boundaries 0.0 - 4.96 ?? 5.0 - 9.954.95 - 9.95 10.0 - 14.949.95 - 14.95 15.0 - 19.9514.95 - 19.95 20.0 - 24.9519.95 - 24.95 Finding Class Boundaries

41. # of miles fclass boundaries 0.0 - 4.96 ?? - 4.95 5.0 - 9.954.95 - 9.95 10.0 - 14.949.95 - 14.95 15.0 - 19.9514.95 - 19.95 20.0 - 24.9519.95 - 24.95 Finding Class Boundaries

42. # of miles fclass boundaries 0.0 - 4.96 0.05 - 4.95 5.0 - 9.954.95 - 9.95 10.0 - 14.949.95 - 14.95 15.0 - 19.9514.95 - 19.95 20.0 - 24.9519.95 - 24.95 Finding Class Boundaries

43. Computing Class Midpoints lower class limit + upper class limit 2

44. # of miles fclass midpoints 0.0 - 4.96 2.45 5.0 - 9.95 10.0 - 14.94 15.0 - 19.95 20.0 - 24.95 Finding Class Midpoints

45. # of miles fclass midpoints 0.0 - 4.96 2.45 5.0 - 9.957.45 10.0 - 14.94 15.0 - 19.95 20.0 - 24.95 Finding Class Midpoints

46. # of miles fclass midpoints 0.0 - 4.96 2.45 5.0 - 9.957.45 10.0 - 14.9412.45 15.0 - 19.9517.45 20.0 - 24.9522.45 Finding Class Midpoints

47. Tallying the Data # of miles tally frequency 0.0 - 4.9|||| |6 5.0 - 9.9||||5 10.0 - 14.9||||4 15.0 - 19.9||||5 20.0 - 24.9||||5

48. # of miles f 0.0 - 4.96 5.0 - 9.95 10.0 - 14.94 15.0 - 19.95 20.0 - 24.95 Constructing the Histogram f | | | | | | 65432106543210 -------------- -0.05 4.95 9.95 14.95 19.95 24.95 mi.

49. Grouped Frequency Table # of miles f 0.0 - 4.96 5.0 - 9.95 10.0 - 14.94 15.0 - 19.95 20.0 - 24.95 Class limits: lower - upper

50. Relative Frequency Relative frequency = f = class frequency n total of all frequencies

51. Relative Frequency f = 6 = 0.24 n 25 f = 5 = 0.20 n 25

52. # of miles f relative frequency 0.0 - 4.9 6 0.24 5.0 - 9.9 50.20 10.0 - 14.9 40.16 15.0 - 19.9 50.20 20.0 - 24.9 50.20 Relative Frequency Histogram | | | | | |.24.20.16.12.08.04 0 -------------- -0.05 4.95 9.95 14.95 19.95 24.95 mi. Relative frequency f/n

53. Common Shapes of Histograms Symmetric f When folded vertically, both sides are (more or less) the same.

54. Common Shapes of Histograms Also Symmetric f

55. Common Shapes of Histograms Uniform f

56. Common Shapes of Histograms Non-Symmetric Histograms skewed. These histograms are skewed.

57. Common Shapes of Histograms Skewed Histograms Skewed leftSkewed right

58. Common Shapes of Histograms Bimodal f The two largest rectangles are separated by at least one class.

59. Stem and Leaf Display Raw Data: 35, 45, 42, 45, 41, 32, 25, 56, 67, 76, 65, 53, 53, 32, 34, 47, 43, 31

60. Stem and Leaf Display First data value = 35 Stem and Leaf Display First data value = 35 234567234567 stems 5leaf

61. Stem and Leaf Display Second data value = 45 Stem and Leaf Display Second data value = 45 234567234567 5 5

62. Stem and Leaf Display Third data value = 42 Stem and Leaf Display Third data value = 42 234567234567 5 5 2

63. Stem and Leaf Display Next data value = 45 Stem and Leaf Display Next data value = 45 234567234567 5 5 2 5

64. Stem and Leaf Display Next data value = 41 Stem and Leaf Display Next data value = 41 234567234567 5 5 2 5 1

65. Stem and Leaf Display Next data value = 32 Stem and Leaf Display Next data value = 32 234567234567 5 2 5 2 5 1

66. Stem and Leaf Display Next data value = 25 Stem and Leaf Display Next data value = 25 234567234567 5 2 5 2 5 1 5

67. Stem and Leaf Display Next data value = 56 Stem and Leaf Display Next data value = 56 234567234567 5 2 5 2 5 1 5 6

68. Stem and Leaf Display Next data value = 67 Stem and Leaf Display Next data value = 67 234567234567 5 2 5 2 5 1 5 6 7

69. Stem and Leaf Display Next data value = 76 Stem and Leaf Display Next data value = 76 234567234567 5 2 5 2 5 1 5 6 7 6

70. Stem and Leaf Display Next data value = 65 Stem and Leaf Display Next data value = 65 234567234567 5 2 5 2 5 1 5 6 7 5 6

71. Stem and Leaf Display Next data value = 53 Stem and Leaf Display Next data value = 53 234567234567 5 2 5 2 5 1 5 6 3 7 5 6

72. Stem and Leaf Display Next data value = 53 Stem and Leaf Display Next data value = 53 234567234567 5 2 5 2 5 1 5 6 3 3 7 5 6

73. Stem and Leaf Display Next data value = 32 Stem and Leaf Display Next data value = 32 234567234567 5 2 2 5 2 5 1 5 6 3 3 7 5 6

74. Stem and Leaf Display Next data value = 34 Stem and Leaf Display Next data value = 34 234567234567 5 2 2 4 5 2 5 1 5 6 3 3 7 5 6

75. Stem and Leaf Display Next data value = 47 Stem and Leaf Display Next data value = 47 234567234567 5 2 2 4 5 2 5 1 7 5 6 3 3 7 5 6

76. Stem and Leaf Display Next data value = 43 Stem and Leaf Display Next data value = 43 234567234567 5 2 2 4 5 2 5 1 7 3 5 6 3 3 7 5 6

77. Stem and Leaf Display Next data value = 31 Stem and Leaf Display Next data value = 31 234567234567 5 2 2 4 1 5 2 5 1 7 3 5 6 3 3 7 5 6

78. Finished Stem and Leaf Display 234567234567 5 2 2 4 1 5 2 5 1 7 3 5 6 3 3 7 5 6