1. Understandable Statistics Seventh Edition By Brase and Brase Prepared by: Lynn Smith Gloucester County College Chapter Two Organizing Data

2. A graphical display should: Show the data Induce the viewer to think about the substance of the graphic Avoid distorting the message

3. Bar Graph bars of uniform width uniformly spaced may be vertical or horizontal lengths represent quantities being compared provide title, labels for each bar and lengths of bars

4. 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

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

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

7. Time Series Time series are data sets composed of similar measurements taken at regular intervals over time. A time plot can reveal some features of a time series.

8. Histogram Differences from a bar chart: bars have equal width and always touch width of bars represents quantity heights of bars represent frequency f Measured quantity

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

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

11. 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.

12. Frequency Table Determine class width. Create the classes. May use smallest data value as lower limit of first class and add width to get lower limit of next class. Tally data into classes. Compute midpoints for each class. Determine class boundaries.

13. 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

14. 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

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

16. # of miles fclass widths 0.0 - 4.96 5 5.0 - 9.965 10.0 - 14.945 15.0 - 19.955 20.0 - 24.955 Finding Class Widths

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

18. # 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

19. # 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

20. # 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

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

22. 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

23. 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

24. # 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

25. # 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

26. # 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

27. # 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

28. # 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.

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

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

31. # 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

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

33. Common Shapes of Histograms Also Symmetrical f

34. Common Shapes of Histograms Uniform f

35. Common Shapes of Histograms Non-Symmetrical Histograms skewed. These histograms are skewed.

36. Common Shapes of Histograms Skewed Histograms Skewed leftSkewed right

37. Common Shapes of Histograms Bimodal f The two largest rectangles are approximately equal in height and are separated by at least one class.

38. Frequency Polygon A frequency polygon or line graph emphasizes the continuous rise or fall of the frequencies.

39. Constructing the Frequency Polygon Dots are placed over the midpoints of each class. Dots are joined by line segments. Zero frequency classes are included at each end.

40. Weights (in pounds) f 2 - 46 5 - 75 8 - 104 11 - 135 Constructing the Frequency Polygon f | | | | | | 65432106543210 -------------- 0 3 6 9 12 15 pounds

41. Cumulative Frequency The sum of the frequencies for that class and all previous or later classes

42. Weights (in pounds) f Greater than 1.5 20 Greater than 4.5 14 Greater than 7.5 9 Greater than 10.5 5 Greater than 13.5 0 Cumulative Frequency Table Weights (in pounds) f 2 - 46 5 - 75 8 - 104 11 - 135 20

43. Ogive Graph of a cumulative frequency table

44. Weights (in pounds) f Greater than 1.5 20 Greater than 4.5 14 Greater than 7.5 9 Greater than 10.5 5 Greater than 13.5 0 Constructing the Ogive Cumulative frequency | | | | | | 20 15 10 5 0 ---------- 1.5 4.5 7.5 10.5 13.5 pounds

45. Exploratory Data Analysis A field of statistical study useful in detecting patterns and extreme data values Tools used include histograms and stem- and-leaf displays

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

47. To make a Stem-and-Leaf Display Digits of each data value has two parts: left = “stem,” right = “leaf” Align all stems in vertical column in increasing order with a vertical line to their right. Place all leaves with same stem on same row as the stem. Rearrange in increasing order Label

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

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

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

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

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

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

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

55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

61. 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

62. 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

63. 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

64. 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

65. 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

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

67. Stem and Leaf Display with Leaves Rearranged 234567234567 1 2 2 4 5 1 2 3 5 5 7 5 3 3 6 5 7 6

68. Stem and Leaf Display with Labeling 234567234567 1 2 2 4 5 1 2 3 5 5 7 5 3 3 6 5 7 6 Ages of Employees 2  5 represents 25 years