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1. METHODS OF REPRESENTATION OF DATA PRESENTED BY : Dr. G Charu Chitra Reader, Dept of Public Health dentistry Rama Dental College 1

2. TABLE OF CONTENT Introduction What do you mean by data Types of statistical data Qualitative data Quantitative data Methods of representation of data Tabulation Drawings/Graphs Presentation of Quantitative data through graphs Histogram Frequency Polygon Frequency Curve Line chart or graph Cumulative frequency diagram Scatter/Dot diagram 2

3. TABLE OF CONTENT Presentation of Qualitative data through graphs Bar diagram Pie/Sector diagram Pictogram/Picture diagram Map diagram / Spot map Summary Conclusion 3

4. INTRODUCTION 4

5. INTRODUCTION DATA : Data, the plural of datum ,are facts expressed in numerical terms . Information in raw or unorganized form (such as alphabets, numbers, or symbols) that refer to, or represent, conditions, ideas, or objects. 5 Indrayan A, Sarmukaddam SB. Medical Biostatistic.1st ed. (Marcel Dekker,Inc . New York) chapter-3.p.66-78

6. INTRODUCTION Contd. Statistical data can be divided into broad categories : Qualitative data Quantitative data 6 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

7. INTRODUCTION Contd. Qualitative Data : Is also called as enumeration data. It represents a particular quality or attribute. These are expressed as numbers without units of measurements. Examples : Religion,Sex,blood group, (Tall/Short) etc 7 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

8. INTRODUCTION Contd. Quantitative Data: Is also called as measurement data. These are expressed as number with or without units of measurements. Example : Height in cm,Weight in kg,Blood pressure (mm of Hg) 8 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

9. NEED FOR PRESENTATION OF DATA The information collected from various sources is called as raw data . It does not lead to any understanding of the situation Hence it should be compiled, classified & presented in a purposive manner to bring out important points clearly and strikingly 9 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

10. PRINCIPLES OF PRESENTATION OF DATA 10

11. PRINCIPLES OF PRESENTATION OF DATA Data should be presented in such a way that data should : arouse interest in reader Become concise without losing important details. Become simple & meaningful Facilitate further statistical analysis Define problem & suggest the solution too. 11 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

12. METHODS OF REPRESENTATION OF DATA 12

13. METHODS OF REPRESENTATION OF DATA There are two important methods for presenting the data: Tabulation Diagrams/Graphs 13 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

14. METHODS OF REPRESENTATION OF DATA Tabulation 14

15. METHODS OF REPRESENTATION OF DATA TABULATION: Tables are simple devices used for presentation of statistical data General principles that are accepted for table construction: Tables should be as simple as possible It should be self-explanatory Each row & column should be labeled concisely & clearly 15 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

16. METHODS OF REPRESENTATION OF DATA TABULATION Contd.: Table must be numbered Title should be clear,concise,and to the point. Tables should not be too large Foot notes be given wherever necessary providing additional information, source or explanatory notes. 16 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

17. TYPES OF TABLES Master Table Simple Table Frequency Distribution Table 17 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

18. TYPES OF TABLES Master Table: They are tables, which contain all the data obtained from a survey. 18 Sl.No . Age Sex Education D M F DMF PI 001 002 003 004 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

19. TYPES OF TABLES Simple Table They are one way tables which supply answers to questions about one characteristic of data only. 19 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

20. TYPES OF TABLES Example of a simple table : Number of students in colleges of RSS Trust in 2011. 20 Name Of College No.Of Students Dental College 540 Nursing College 675 College of Physiotherapy 586 College of Management 1025 Total 2826

21. TYPES OF TABLES Frequency Distribution Table The simplest table is a two column frequency table The first column lists the classes into which the data are grouped The second column lists the frequency for each classification 21 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

22. TYPES OF TABLES Frequency Distribution Table Contd.: Example of a Frequency Distribution table : Anemia in boys and girls of RV Dental College 22 Sex Type Of Anemia Total Mild Moderate Severe Boys 615 85 15 260 Girls 190 120 45 355 Total 350 205 60 615

23. Table Of Content Introduction Methods of representation of data Tabulation Drawings/Graphs Presentation of Quantitative data through graphs Presentation of Qualitative data through graphs Summary Evaluation Of Learning Objective Conclusion 23

24. METHODS OF REPRESENTATION OF DATA Diagrams/Graphs 24

25. DIAGRAMS/GRAPHS Diagrams & graphs are one of the most convincing and appealing ways of depicting results. They are extremely useful because: They are attractive to the eyes. Gives a bird’s eye view of the entire data. Has a lasting impression on the mind of the layman Facilitates comparison of data 25 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

26. DIAGRAMS/GRAPHS Principles in the construction of Diagrams & Graphs: Every diagram must be given a title that is self explanatory. It should be simple & consistent with the data. The no. of lines drawn in any graph should not be many. This makes it look clumsy. The scale of presentation for the X-axis & Y-axis should be mentioned 26 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

27. PRESENTATION OF QUANTITATIVE DATA 27

28. PRESENTATION OF QUANTITATIVE DATA Presentation of quantitative data is through graphs. The common graphs in use are: Histogram Frequency Polygon Frequency Curve Line chart or graph Cumulative frequency diagram Scatter/Dot diagram 28 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

29. PRESENTATION OF QUANTITATIVE DATA Histogram 29

30. PRESENTATION OF QUANTITATIVE DATA HISTOGRAM : It’s a pictorial diagram of frequency distribution. The histogram is a series of columns or vertical rectangles, each having as its base one class interval, and the frequency or number of cases in that class as its height The class intervals are given on the X axis and the frequencies along the Y axis. 30 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

31. PRESENTATION OF QUANTITATIVE DATA HISTOGRAM Contd.: There is no space between the cells on a histogram. This graph is not to be confused with a bar chart, which has space between the cells. 31 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

32. HISTOGRAM : Example : The following is the frequency distribution of weights of 30 students of I year dental students of a dental college . Draw a histogram to represent the data. 32 Classes 45-50 50-55 55-60 60-65 65-70 Total Frequency 3 7 12 5 3 30

33. Solution : For drawing a histogram we go through the steps similar to those of a bar graph. They are given below : Step 1 : On a paper, we draw two perpendicular lines and call them horizontal and vertical axes. Step 2 : Along the horizontal axis, we take classes of equal width :45–50, 50–55, ...... As the axis starts from 45–50, we take one interval 40–45 before it and put a kink on axis before that Step 3 : Choose a suitable scale on the vertical axis to represent the frequency. It can start from 0 to 12, with a step of 2, i.e., 0, 2, 4, 6, ...., 12, 14 Step 4 : Draw the rectangles as shown in Fig. 33

34. HISTOGRAM : 34

35. PRESENTATION OF QUANTITATIVE DATA FREQUENCY POLYGON: 35

36. PRESENTATION OF QUANTITATIVE DATA FREQUENCY POLYGON: Its an area diagram of frequency distribution developed over a histogram. The X axis depicts the categories of data and the Y axis depicts the frequency of data in each category. Frequency polygon can be obtained from histogram by joining mid points of blocks or rectangles of the histogram . 36 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

37. FREQUENCY POLYGON: EXAMPLE : The daily earnings of 100 Private dental practioners are given below : 37 Daily Earnings in Rs . 200-300 300-400 400-500 500-600 600-700 700-800 800-900 No. of Dental Clinics 3 12 15 30 25 12 3

38. FREQUENCY POLYGON: 38

39. PRESENTATION OF QUANTITATIVE DATA FREQUENCY CURVE : 39

40. PRESENTATION OF QUANTITATIVE DATA FREQUENCY CURVE : As the number of observations become very large & class intervals very much reduced, the frequency polygon loses its angulation and gives rise to a smooth curve known as frequency curve. Such frequency curves are often encountered when we study the distribution of most of the biological variables. 40 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

41. FREQUENCY CURVE : 41

42. NOTE: Frequency polygon and frequency curves are same except frequency curve is drawn using free hand and frequency polygon is drawn using scale. (Each point is joint using scale) 42 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

43. PRESENTATION OF QUANTITATIVE DATA LINE CHART OR GRAPH 43

44. PRESENTATION OF QUANTITATIVE DATA LINE CHART OR GRAPH Line charts are used to show the trend of events with the passage of time. It is nothing but a frequency polygon presenting variations by a line. The class interval can be a week, a month, a year or 100 years. Scale used can change shape of line diagram but not its trend 44 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

45. LINE CHART OR GRAPH EXAMPLE: The table below shows daily temperatures for Bangalore City, recorded for 6 days, in degrees Fahrenheit. 45 Temperature in Bangalore City Day Temperature 1 43 2 53 3 50 4 57 5 59 6 67

46. LINE CHART OR GRAPH 46 Temperature In Bangalore City

47. PRESENTATION OF QUANTITATIVE DATA CUMULATIVE FREQUENCY DIAGRAM/OGIVE 47

48. PRESENTATION OF QUANTITATIVE DATA CUMULATIVE FREQUENCY DIAGRAM/OGIVE: Its also a representation of continuous and ordered data In this case, the frequency of data in each category represents the sum of the data from the category and from the preceding category. Cumulative frequencies are plotted opposite the group limits of the attribute or variable. These points are joined by a smooth free hand curve to get a cumulative frequency diagram or “ ogive ”. 48 Dixit JV.Principles and practice of biostatistics.4th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24

49. PRESENTATION OF QUANTITATIVE DATA Example : A Professor arranged the marks gained by all year 10 pupils in a Anatomy test in a table as shown below: 49 Marks Frequency of pupils 11-20 2 21-30 11 31-40 19 41-50 36 51-60 42 61-70 31 71-80 13 81-90 6

50. CUMULATIVE FREQUENCY DIAGRAM/OGIVE: This table shows the number of pupils (called the frequency) who gained marks in the various mark bands, eg 31-40. For example, the number of pupils who scored between 21 and 30 marks was 11. No pupil scored fewer than 11 marks or more than 90 marks. 50

51. CUMULATIVE FREQUENCY DIAGRAM/OGIVE: To create a cumulative total for the frequency of pupils in each group (called the cumulative frequency) a third column is created as shown below: 51 Marks Frequency Cumulative Total Cumulative frequency 11-20 2 2 2 21-30 11 2+11 13 31-40 19 13+19 32 41-50 36 32+36 68 51-60 42 68+42 110 61-70 31 110+31 141 71-80 13 141+13 154 81-90 6 154+6 160

52. CUMULATIVE FREQUENCY DIAGRAM/OGIVE: The cumulative frequency column makes it easy to see at a glance that 68 pupils scored 50 marks or fewer, and that 32 pupils scored 40 marks or fewer. 52 Cumulative Frequency Graph for year 10 anatomy results

53. PRESENTATION OF QUANTITATIVE DATA SCATTER/DOT DIAGRAM: 53

54. PRESENTATION OF QUANTITATIVE DATA SCATTER/DOT DIAGRAM: These show relationship between two variables Also called as correlation diagram Perpendicular drawn from each scatter point on x & y axis gives value of two variables associated with it. Depending on the clustering of scatter points this diagram can provide evidence of positive, negative or no correlation 54 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384

55. SCATTER/DOT DIAGRAM: Example The Prosthodontics and Periodontics results of ten dental students are shown in the table below: 55 Name Sal Kim Bill Tom Gita Alex Bev Ken Alen Jo Prostho 20 71 60 52 80 32 47 90 49 80 Perio 30 80 65 50 81 38 40 87 55 70

56. SCATTER/DOT DIAGRAM : To see whether there is a correlation between the Prostho and Perio marks, you could plot a scatter diagram. The Prostho mark is on the horizontal scale and the corresponding Perio mark on the vertical scale. Bill's Prostho mark was 60 and his Perio mark was 65, so his results are represented by the orange point at coordinates (60, 65). 56

57. SCATTER/DOT DIAGRAM : 57 Prosthodontics Mark Periodontics Marks

58. SCATTER PLOT Things to look for: If the points cluster in a band running from lower left to upper right, there is a positive correlation (if x increases, y increases). If the points cluster in a band from upper left to lower right, there is a negative correlation (if x increases, y decreases). 58

59. Imagine drawing a straight line or curve through the data so that it "fits" as well as possible. The more the points cluster closely around the imaginary line of best fit, the stronger the relationship that exists between the two variables. If it is hard to see where you would draw a line, and if the points show no significant clustering, there is probably no correlation. 59

60. Table Of Content Introduction Methods of representation of data Tabulation Drawings/Graphs Presentation of Quantitative data through graphs Presentation of Qualitative data through graphs Summary Evaluation Of Learning Objective Conclusion 60

61. PRESENTATION OF QUALITATIVE DATA 61

62. PRESENTATION OF QUALITATIVE DATA Presentation of qualitative data is through diagrams. The common diagrams in use are : Bar diagram Pie or sector diagram Pictogram or Picture diagram Map diagram or spot map 62 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

63. PRESENTATION OF QUALITATIVE DATA BAR DIAGRAM : 63

64. PRESENTATION OF QUANLITATIVE DATA BAR DIAGRAM : Bar diagram is a popular & easy method adopted for visual comparison of the magnitude of different frequency such as morbity,mortality,immunization status of population in different ages, sexes or places There are three types of bar diagrams: Simple bar diagram Multiple bar diagram Proportional bar diagram 64 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

65. PRESENTATION OF QUANLITATIVE DATA Simple bar diagram: It represents only one variable. Example : Age-wise prevalence of dental caries (in percentage) 65 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

66. Simple bar diagram: 66 Age-wise prevalence of dental caries (in percentage)

67. PRESENTATION OF QUANLITATIVE DATA Multiple bar diagram: This diagram is similar to the bar diagram except that for each category of the variable there are set of bars of the same width corresponding to the different sections without any gap in between Example: Prevalence of dental caries based on age & gender 67 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

68. Multiple bar diagram: 68 Prevalence Of Dental Caries Based On Age & Gender

69. PRESENTATION OF QUANLITATIVE DATA Proportional bar diagram: The individual bars are divided into two or more parts. This diagram is used to compare the sub-groups between different major groups of observations. Example: Prevalence of dental caries based on age and gender 69 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

70. Proportional bar diagram : 70 Prevalence of dental caries based on age and gender

71. PRESENTATION OF QUALITATIVE DATA PIE/SECTOR DIAGRAM: 71

72. PRESENTATION OF QUANLITATIVE DATA PIE/SECTOR DIAGRAM: They are so called because the entire graph looks like a pie & its component represent slices cut from a pie. The total angle at the Centre of a circle is equal to 360 & it represents the total frequency. It is divided into different sectors corresponding to the frequencies of the variables in the distribution. Eg .: Distribution of dental disease in 30-40 year olds. 72 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

73. PRESENTATION OF QUANLITATIVE DATA PIE/SECTOR DIAGRAM Contd.: The segments are then shaded with different shades or color and an index is provided for these shade colors This diagram cannot be used to represent two or more data sets. 73 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

74. PIE/SECTOR DIAGRAM: 74 Distribution of dental diseases in 30-40 year olds

75. PRESENTATION OF QUALITATIVE DATA PICTOGRAM OR PICTURE DIAGRAM: 75

76. PRESENTATION OF QUANLITATIVE DATA PICTOGRAM OR PICTURE DIAGRAM: These diagrams are used for a layman man those who cannot understand technical charts like bar charts. Here pictures or symbols are used to present the data. Example: For physically disabled person the symbol of person sitting on wheelchair is used in public places. 76 Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384.

77. Pictogram 77 India Singapore Bangladesh Dentist population Ratio 7500 10000 1,50000

78. PRESENTATION OF QUALITATIVE DATA MAP DIAGRAM OR SPOT MAP: 78

79. PRESENTATION OF QUANLITATIVE DATA MAP DIAGRAM OR SPOT MAP: These maps are used to show geographical distribution of frequencies of a characteristic. It is a map of an area with the location of each case of an illness,death,abnormality or condition identified by a spot ,dot or other symbol on the map 79 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102

80. MAP DIAGRAM OR SPOT MAP: 80

81. CONCLUSION "A picture is worth a thousand words" refers to the notion that a complex idea can be conveyed with just a single still image. Representation of data through charts & diagrams also aptly characterizes one of the main goals of visualization, namely making it possible to absorb large amounts of data quickly. 81

82. REFERENCES Dixit JV.Principles and practice of biostatistics.4 th ed.In:M /s Banarsidas bhanot publishers 2009.chapter-2.Collection and presentation of data.p.5-24 Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p) Ltd.chapter-6.p.88-102 Hiremath SS.Textbook of preventive and community dentistry.1st ed.Elsevier 2007:chapter-48. Biostatistics,p.483-488 82

83. REFERENCES Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house 2009.chapter-14.Research methodology and biostatistics 365-384 Indrayan A, Sarmukaddam SB. Medical Biostatistic.1st ed. (Marcel Dekker,Inc . New York) chapter-3.p.66-78 83

84. 84 THANK YOU !!!!