1. Presentation of Data Prepared by: Ms. Bernabeth Jo T. Tendero

2. Textual Presentation Presented in paragraph or in sentences Includes : - enumeration of important characteristics - emphasizing the most significant features - highlighting the most striking attributes of the set of data (Basilia Ebora Blay)

3. Textual Presentation Disadvantage: Readers sometimes get bored (Basilia Ebora Blay)

4. Tabular Presentation Very effective and efficient means of organizing and summarizing data A lot of information can be seen in one table Makes comparison of figures quick under each category (Luis A. Tattao)

5. Parts of a Tables Block (Age Bracket) Fat Content of Diet Extremely LowFairly LowModerately Low 15 – 240.730.670.15 25 – 350.860.750.21 36 – 440.940.810.26 45 – 541.401.320.75 55 – 641.621.410.78 Table 6. Fat Content of Diet by Age Bracket Table Number Table Heading

6. Parts of the Table Table heading – includes the table number and the title Body – main part of the table containing the figures being presented

7. Parts of a Tables Block (Age Bracket) Fat Content of Diet Extremely LowFairly LowModerately Low 15 – 240.730.670.15 25 – 350.860.750.21 36 – 440.940.810.26 45 – 541.401.320.75 55 – 641.621.410.78 Table 6. Fat Content of Diet by Age Bracket Table Number Table Heading Stubs and Classes

8. Parts of the Table Table heading – includes the table number and the title Body – main part of the table containing the figures being presented Stubs or classes – the categories describing the data, usually found at the left-hand side of the table

9. Parts of a Tables Block (Age Bracket) Fat Content of Diet Extremely LowFairly LowModerately Low 15 – 240.730.670.15 25 – 350.860.750.21 36 – 440.940.810.26 45 – 541.401.320.75 55 – 641.621.410.78 Table 6. Fat Content of Diet by Age Bracket Table Number Table Heading Stubs and Classes Caption

10. Parts of the Table Table heading – includes the table number and the title Body – main part of the table containing the figures being presented Stubs or classes – the categories describing the data, usually found at the left-hand side of the table Caption – designations of the information contained in columns, usually found at the top of the column. (Luis A. Tattao)

11. Frequency Distribution Table A summary table in which data are arranged into conveniently established, numerically ordered class grouping or categories A tabular presentation of data grouped into classes together with the number of observations in each class (Luis A. Tattao)

12. Steps in Constructing a Frequency Distribution Table 1.Determine the Range, R: Range = Highest Value – Lowest Value 2.Determine the approximate number of class intervals, k k = 1 + 3.3 log N N = population or the total number of observation 3.Obtain the class width, C

13. Steps in Constructing a Frequency Distribution Table 4. For Class Intervals (CI) Use the lowest score as the lower limit (LL) of the first interval, add (C-1) to it to obtain the upper limit (UL) of the first interval LL = LL of the previous interval + C UL = LL + (C-1)

14. Example Age of Patients in Hospital X, June 2004 2528273032253126296 31202132185053605054 45403725202732242930 252410121528

15. Solution: 1.Determine the Range, R: R = 60 - 6 = 54 2.k = 1 + 3.3 log N = 1 + 3.3 log 36 = 6.1358 6

16. Solution 3.Obtain the class width, C = 9 4.Class Intervals 6 is the LL of the 1 st interval UL = 6 + (9-1) = 14 of the 1 st interval

17. Solution 2 nd interval LL = 6 + 9 = 15 UL = 15 + 8 = 23 Compute for the other intervals

18. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years)Tally MarksFrequency 60 – 68 I 1 51 – 59 II 2 42 – 50 III 3 33 – 41 II 2 24 – 32 IIIII – IIIII – IIIII – IIIII 20 15 – 23 IIIII 5 6 – 14 III 3 N = 36

19. Assignment Construct the frequency distribution table for the student’s scores in a statistics quiz 5645452388 6787776669 2563955556 6767676833 4555444999 2224434343 9554869277 3358892

20. Answer to Assignment 1.Determine the Range, R: R = 9 – 2 = 7 2.k = 1 + 3.3 log N = 1 + 3.3 log 77 = 7.2254 7

21. Solution 3.Obtain the class width, C = 1 4.Class Intervals Since there is only the class width is only 1 that means the frequency distribution table is ungrouped.

22. Table 1. Frequency Distribution of the students’ scores in a quiz in Statistics ScoresFrequency 98 87 79 612 514 411 39 27

23. Class Mark (x) Midpoint of a class interval Example: 60 – 68

24. Class Boundaries A.k.a. exact limits Obtained by subtracting 0.5 from the LL and adding 0.5 to UL Example: 60 – 68 60 – 0.5 = 59.5 68 + 0.5 = 68.5 Class Boundary: 59.5 – 68.5

25. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years)Tally MarksFrequency 60 – 68 I 1 51 – 59 II 2 42 – 50 III 3 33 – 41 II 2 24 – 32 IIIII – IIIII – IIIII – IIIII 20 15 – 23 IIIII 5 6 – 14 III 3 N = 36 Calculate the class mark and the class boundaries of this FDT

26. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years)FrequencyClass MarkClass Boundary 60 – 6816459.5 – 68.5 51 – 5925550.5 – 59.5 42 – 5034641.5 – 50.5 33 – 4123732.5 – 41.5 24 – 32202823.5 – 32.5 15 – 2351914.5 – 23.5 6 – 143105.5 – 14.5 N = 36

27. Relative frequency (rf) Percentage of frequency Written in decimal form

28. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years)Frequency 60 – 681 51 – 592 42 – 503 33 – 412 24 – 3220 15 – 235 6 – 143 N = 36

29. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years) FrequencyClass MarkClass Boundary Relative Frequency 60 – 6816459.5 – 68.50.0278 51 – 5925550.5 – 59.50.0556 42 – 5034641.5 – 50.50.0833 33 – 4123732.5 – 41.50.0556 24 – 32202823.5 – 32.50.5556 15 – 2351914.5 – 23.50.1389 6 – 143105.5 – 14.50.0833 N = 36

30. Less than Cumulative frequency (<cf) Obtained by cumulating frequency from top to bottom

31. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years) FrequencyClass MarkClass Boundary Relative Frequency 60 – 6816459.5 – 68.50.0278 51 – 5925550.5 – 59.50.0556 42 – 5034641.5 – 50.50.0833 33 – 4123732.5 – 41.50.0556 24 – 32202823.5 – 32.50.5556 15 – 2351914.5 – 23.50.1389 6 – 143105.5 – 14.50.0833 N = 36

32. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years) FrequencyClass MarkClass Boundary Relative Frequency Less than cumulative frequency (<cf) 60 – 6816459.5 – 68.50.02781 51 – 5925550.5 – 59.50.05563 42 – 5034641.5 – 50.50.08336 33 – 4123732.5 – 41.50.05568 24 – 32202823.5 – 32.50.555628 15 – 2351914.5 – 23.50.138933 6 – 143105.5 – 14.50.083336 N = 36

33. More than cumulative frequency (>cf) Obtained by cumulating the frequency from bottom to top

34. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years) FrequencyClass Mark Class Boundary Relative Frequency Less than cumulative frequency (<cf) More than comulative frequency (>cf) 60 – 6816459.5 – 68.50.02781 36 51 – 5925550.5 – 59.50.05563 35 42 – 5034641.5 – 50.50.08336 32 33 – 4123732.5 – 41.50.05568 30 24 – 32202823.5 – 32.50.555628 10 15 – 2351914.5 – 23.50.138933 5 6 – 143105.5 – 14.50.083336 2 N = 36

35. Practice Weights (in lbs.) of First Year High School Students in XYZ School 10510712094107105 9511510685105117 1038696949699 100115 9910785 868786859589 96851178695116

36. R = 120 – 35 = 35 k = 1 + 3.3 log 36 = 6.14 = 6 C = 35/6 = 5.8 = 6 Weight (in lbs.) FrequencyClass Mark Class Boundary Relative Frequency Less than cumulative frequency (<cf) More than comulative frequency (>cf) 85 – 901087.584.5 – 90.527.7810 36 91 – 96893.590.5 – 96.522.2218 26 97 – 102399.5 96.5 – 102.5 8.3321 18 103 – 1088105.5 102.5 – 108.5 22.2229 15 109 – 1140111.5 108.5 – 114.5 029 7 115 – 1207117.5 114.5 – 120.5 19.4436 7 N = 36

37. Contingency Table Has two or more frequencies shown Use to record and analyzed the relationship between 2 or more variables

38. Example Table 3.5. The Contingency Table for the Opinion of Viewers on the New Program Choice/SampleMenWomenChildrenTotal Like the program505645151 Indifferent23161251 Do not like the program435540138 Total11612797340

39. Graphical Presentation Data are presented in a form of graph or a diagram A graph is a geometrical presentation of data A graph must have a figure number and a title. If data came from another source, a source note should be incuded.

40. Advantages of a Graph Helps to visualize certain properties and characteristics of the data at one glance (Tattao) Helps facilitate comparison and interpretation without going through the numerical data (Blay)

41. TYPES OF GRAPH

42. Bar Graph Comparing numbers by means of rectangles of uniform widths but of lengths proportional to the numbers being represented (Tattao) Can be simple or compound Can be vertical or horizontal Used both for qualitative and quantitative data

43. Simple and Vertical

44. Horizontal and Compound

45. Line graph Shows trends and increases and decreases in data sets Obtained by plotting the frequency of the category above the point of the horizontal axis representing that category, and then joining the points with a straight line Also used for both qualitative and quantitative data

47. From Table to Graph Temperatures In NY City DayTemperature 143° F 253° F 350° F 457° F 559° F 667° F

48. From Table to Graph Value of Sarah’s Car YearValue 2001$24,000 2002$22,500 2003$19,700 2004$17,500 2005$14,500 2006$10,000 2007$ 5,800

49. From Table to Graph Sam’s Weight MonthWeight in kg January49 February54 March61 April69 May73

50. Pie Chart Useful when presenting the sizes of components that make up a certain whole entity A circle subdivided into slices that represents various categories Each slice is proportional to the percentages corresponding to that category

51. Constructing Pie Chart Table 3.12. Monthly Expenses of a Filipino Family with Four Children. Monthly ExpensesAmount in Pesos FoodP 9,000 TransportationP 2,000 MiscellaneousP 3,000 TotalP 14,000

52. Constructing Pie Chart 1.Obtain the percentage for each category. Example: Monthly ExpensesAmount in PesosPercentage (%) FoodP 9,00064.3 TransportationP 2,00014.3 MiscellaneousP 3,00021.4 TotalP 14,000100

53. Constructing Pie Chart 2. Convert percentage into degrees using this conversion factor: Example: Monthly Expenses Amount in Pesos Percentage (%) Degrees FoodP 9,00064.3231.5 TransportationP 2,00014.351.5 MiscellaneousP 3,00021.477.0 TotalP 14,000100360

54. Constructing Pie Chart 3. Use protractor to measure the degrees needed to make each slices

55. Pictograph Makes use of symbols Used to compare few discrete data usually of one kind

56. Example of Pictograph

59. Statistical Map Shows the graphical location may contain different symbols on the map Legend tells what symbols represent

60. Statistical Map

61. Histogram Representation of frequency distribution table Rectangles has widths that represent class intervals and areas are proportional to frequencies Constructed by marking off true class boundaries along horizontal axis and erecting over each class interval a rectangle whose height equals the frequency of that class

62. Example of Histogram

63. Table 1. Ages of Patients in Hospital X, June 2004 Age (in years)FrequencyClass MarkClass Boundary 60 – 6816459.5 – 68.5 51 – 5925550.5 – 59.5 42 – 5034641.5 – 50.5 33 – 4123732.5 – 41.5 24 – 32202823.5 – 32.5 15 – 2351914.5 – 23.5 6 – 143105.5 – 14.5 N = 36

64. Frequency Polygon Line graph associated with Frequency Distribution Table Obtained by plotting the Class Mark vs. the Frequency of that class. Points are joined with straight lines.

65. Example of Frequency Polygon

66. Ogive Graphical presentation of the cumulative frequency of an FDT Constructed by plotting lower class boundary of each class vs. the cumulative frequency of the corresponding class. Points are joined with straight lines

67. Example of Ogive