Data presentation Lecture

To arrange the data in such a way that it should create interest in the reader’s mind at the first sight.
To present the information in a compact and concise form without losing important details.

1. PRESENTATION OF DATA AB.RAJAR. ASSOCIATE PROFESSOR. COMMUNITY HEALTH SCIEMCES.

2. PRESENTATION OF DATA: PRINCIPALS OF DATA PRESENTATION: To arrange the data in such a way that it should create interest in the reader’s mind at the first sight. To present the information in a compact and concise form without losing important details. To present the data in a simple form so as to draw the conclusion directly by viewing at the data. To present it in such away that it can help in further statistical analysis.

3. Presentation of data Tabular Graphical Simple table complex table For quantitative data For qualitative data 1. Histogram 1. Bar chart 2. Frequency polygon 2. Pictogram 3. Frequency curve 3. Pie chart 4. Line chart 4. Map diagram 5. Normal distribution curve 6. Cumulative distribution curve 7.Scatter diagram

4. Ungrouped vs. Grouped Data Data can be classified as grouped or ungrouped. Ungrouped data: are data that are not organized, or if arranged, could only be from highest to lowest or lowest to highest. Grouped data: are data that are organized and arranged into different classes or categories .

5. Methods of presentation of data Numerical presentation Graphical presentation Mathematical presentation

6. Methods of Presentation of Data

7. Textual Presentation of Data Data can be presented using paragraphs or sentences. It involves enumerating important characteristics, emphasizing significant figures and identifying important features of data.

8. Textual Presentation of Data Example. You are asked to present the performance of your section in the Bio-statistics test. The following are the test scores of your class:

9. Solution First, arrange the data in order for you to identify the important characteristics. This can be done in two ways : rearranging from lowest to highest or using the stem-and-leaf plot. Below is the rearrangement of data from lowest to highest:

10. Textual Presentation of Data With the rearranged data, pertinent data worth mentioning can be easily recognized. The following is one way of presenting data in textual form. In the Statistics class of 40 students , 3 obtained the perfect score of 50. Sixteen students got a score of 40 and above, while only 3 got 19 and below. Generally, the students performed well in the test with 23 or 70% getting a passing score of 38 and above.

11. Another way of rearranging data is by making use of the stem-and-leaf plot. What is a stem-and-leaf plot? Stem-and-leaf Plot is a table which sorts data according to a certain pattern. It involves separating a number into two parts. In a two-digit number , the stem consists of the first digit , and the leaf consists of the second digit. While in a three-digit number , the stem consists of the first two digits , and the leaf consists of the last digit. In a one-digit number , the stem is zero .

12. Below is the stem-and-leaf plot of the ungrouped data given in the example. Utilizing the stem-and-leaf plot , we can readily see the order of the data. Thus, we can say that the top ten got scores 50, 50, 50, 49, 48, 46, 46, 46,45, and 45 and the ten lowest scores are 9, 17, 18, 20, 23,23,24,25,26, and 27.

13. Exercise: Prepare a stem-and-leaf plot and present in textual form. The ages of 40 teachers in a public school

14. SOLUTION:

15. TABULATION

16. Tabulation Tables are the devices, that are used to present the data in a simple form . It is probably the first step before the data is used for analysis or interpretation . General principals of designing tables The tables should be numbered e.g. table 1, table 2 etc. A title must be given to each table, which should be brief and self explanatory. The headings of columns or rows should be clear and concise. The data must be presented according to size or importance chronologically, alphabetically, or geographically.

17. Tabulation If percentages or averages are to be compared, they should be placed as close as possible. No table should be too large Most of the people find a vertical arrangement better than a horizontal one because, it is easier to scan the data from top to bottom than from left to right Foot notes may be given, where necessary, providing explanatory notes or additional information. Types of tables 1) Simple tables :Measurements of single set are presented 2) Complex tables :Measurements of multiple sets are presented

18. TABULAR PRESENTATION OF DATA MCPegollo/Basic Statistics/SRSTHS http://www.sws.org.ph/youth.htm Table Number Table Title Column Header Row Classifier Body Source Note Below is a sample of a table with all of its parts indicated:

19. Simple Table When characteristics with values are presented in the form of table, it is known as simple table e.g. Table 4.4 Infant mortality rate of selected countries in 2004 Name of country Infant mortality rate Pakistan 90 Bangladesh 60 Sri Lanka 26 India 60

20. FREQUENCY DISTRIBUTION TABLE.

21. FREQUENCY DISTRIBUTION TABLE A frequency distribution table is a table which shows the data arranged into different classes(or categories) and the number of cases(or frequencies) which fall into each class. The following is an illustration of a frequency distribution table for ungrouped data:

22. Sample of a Frequency Distribution Table for Ungrouped Data: Table 1.1 Frequency Distribution for the Ages of 50 Students Enrolled in Statistics

23. Sample of a Frequency Distribution Table for Grouped Data: Table 1.2 Frequency Distribution Table for the Quiz Scores of 50 Students in Geometry.

24. Lower Class Limits are the smallest numbers that can actually belong to different classes RATING FREQUENCY 0-2 1 3-5 2 6-8 13 9-11 15 12-14 19 Total 50

25. Lower Class Limits. are the smallest numbers that can actually belong to different classes RATING FREQUENCY -2 1 3 -5 2 6 -8 13 9 -11 15 12 -14 19 Total 50 Lower Class Limits

26. Upper Class Limits. are the largest numbers that can actually belong to different classes. RATING FREQUENCY 0-2 1 3-5 2 6-8 13 9-11 15 12-14 19 Total 50

27. Upper Class Limits. are the largest numbers that can actually belong to different classes. RATING FREQUENCY 0- 2 1 3- 5 2 6- 8 13 9- 11 15 12- 14 19 Total 50 Upper Class Limits

28. Class Boundaries are the numbers used to separate classes , but without the gaps created by class limits. Class boundaries or true limits are the points that demarcate upper limit of one class and lower limit of the next.

29. Class Boundaries. number separating classes RATING FREQUENCY 0-2 1 3-5 2 6-8 13 9-11 15 12-14 19

30. Class Boundaries. N umber separating classes 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency - 0.5 2.5 5.5 8.5 11.5 14.5 Class Boundaries

31. Class Midpoints. The Class Mark or Class Midpoint is the respective average of each class limits

32. 0 - 1 2 20 3 - 4 5 14 6 - 7 8 15 9 - 10 11 2 12 - 13 14 1 Rating Frequency Class Midpoints Class Midpoints. midpoints of the classes

33. Class Width. is the difference between two consecutive lower class limits or two consecutive class boundaries. 3 0 - 2 20 3 3 - 5 14 3 6 - 8 15 3 9 - 11 2 3 12 - 14 1 Rating Frequency Class Width

34. SIMPLE FREQUENCY DISTRIBUTION ( f ) SCORE f SCORE f SCORE f 22 1 48 1 69 1 23 1 49 2 74 1 32 1 53 1 75 1 34 2 54 2 76 1 37 2 56 2 83 1 38 1 57 1 84 1 44 1 63 1 85 2 45 1 64 1 87 2 46 1 64 4 98 3 47 2 66 1 Total 42 Table:2 // Simple frequency distribution of students score in High school .

35. GROUPED FREQUENCY DISTRIBUTION Class Interval f 20-29 2 30-39 6 40-49 8 50-59 6 60-69 8 70-79 3 80-89 6 90-99 3 Total 42 Table:3 // Group frequency distribution of students score in High school .

36. CUMULATIVE FREQUENCY DISTRIBUTION ( Cumf ) Class Interval f Cum f 20-29 2 2 30-39 6 8 40-49 8 16 50-59 6 22 60-69 8 30 70-79 3 33 80-89 6 39 90-99 3 42 Table:4 // Cumulative frequency distribution of student’s score in High school . Cumualtive: Incorporating all current and previous data up to the present or at time of measuring or collecting .(By Addition )

37. RELATIVE FREQUENCY DISTRIBUTION (RF/P) CI f RF 20-29 2 4.8 30-39 6 14.3 40-49 8 19.0 50-59 6 14.3 60-69 8 19.0 70-79 3 7.1 80-89 6 14.3 90-99 3 7.1 Total 42 100% Table:5// Relative frequency distribution of student’s score in High school .

38. Table (III): Distribution of 20 lung cancer patients at the chest department of Alexandria hospital and 40 controls in May 2008 according to smoking Complex frequency distribution Table

39. Table (IV): Distribution of 60 patients at the chest department of Alexandria hospital in May 2008 according to smoking & lung cancer

40. GRAPHICAL PRESENTATION

41. Charts and Diagrams Charts and diagrams are useful methods of presenting simple data . They have powerful impact on imagination of people. Gives information at a glance . Diagrams are better retained in memory than statistical table. However graphs cannot be substituted for statistical table, because the graphs cannot have mathematical treatment where as tables can be treated mathematically. Whenever graphs are compared , the difference in the scale should be noted. It should be remembered that a lot of details and accuracy of original data is lost in charts and diagrams, and if we want the real study, we have to go back to the original data.

42. Common diagrams Pie chart Simple bar diagram Multiple bar diagram Component bar diagram or subdivided bar diagram Histogram Frequency polygon Frequency curve O give curve Scatter diagram Line diagram Pictogram Statistical maps

43. Bar charts The data presented is categorical Data is presented in the form of rectangular bar of equal breadth . Each bar represent one variant /attribute . Suitable scale should be indicated and scale starts from zero. The width of the bar and the gaps between the bars should be equal throughout. The length of the bar is proportional to the magnitude/ frequency of the variable. The bars may be vertical or horizontal .

44. SIMPLE BAR CHARTS

45. MULTIPLE BAR CHARTS Also called compound bar charts More then one sub-attribute of variable can be expressed

46. COMPONENT BAR CHARTS When there are many categories on X-axis (more than 5) and they have further subcategories, then to accommodate the categories, the bars may be divided into parts, each part representing a certain item and proportional to the magnitude of that particular item

47. COMPONENT BAR CHART

48. Histogram Used for Quantitative, Continuous, Variables . It is used to present variables which have no gaps e.g age, weight, height, blood pressure, blood sugar etc. It consist of a series of blocks. The class intervals are given along horizontal axis and the frequency along the vertical axis.

49. HISTOGRAM Figure (2): Distribution of 100 cholera patients at (place) , in (time) by age

50. Frequency polygon Frequency polygon is an area diagram of frequency distribution over a histogram. It is a linear representation of a frequency table and histogram, obtained by joining the mid points of the histogram blocks. Frequency is plotted at the central point of a group

51. Line Graph Year MMR 1960 50 1970 45 1980 26 1990 15 2000 12 Figure (1): Maternal mortality rate of (country), 1960-2000

52. Line diagram Line diagrams are used to show the trend of events with the passage of time. Line diagram showing the malaria cases reported throughout the word excluding African region during 1972-78 10 8 6 4 2 1972 73 74 75 76 77 78 1972 73 74 75 76 77 78 Cases

53. Pie charts Most common way of presenting data The value of each category is divided by the total values and then multiplied by 360 and then each category is allocated the respective angle to present the proportion it has. It is often necessary to indicate percentages in the segment as it may not be sometimes very easy virtually, to compare the areas of segments

54. Pie charts

55. Pie charts Question-: In a DHQ Hospital 120 Doctors are working.60 doctors went to Lahore to attend a workshop.20 doctors went on long leave.30 doctors were retired. Show this data by Pie chart.

56. Pictogram Popular method of presenting data to those who cannot understand orthodox charts. Small pictures or symbols are used to present the data,e.g a picture of a doctor to represent the population physician. Fraction of the picture can be used to represent numbers smaller than the value of whole symbol

57. Statistical maps When statistical data refers to geographic or administrative areas, it is presented either as statistical map or dot map. The shaded maps are used to present data of varying size. The areas are shaded with different color or different intensities of the same color, which is indicated in the key.

58. Scatter diagram Scatter diagrams show the relationship between the two variables e.g a positive correlation/ association between the intake of fat and sugar in the average diets of 41 countries. If the dots cluster round a straight line, it shows evidence of a relationship of a linear nature. If there is no such cluster, it is probable that there is no relationship between the variables.

59. MATHAMETICAL PRESENTATION.

60. Mathematical presentation Summery statistics. Measures of location 1- Measures of central tendency 2- Measures of non central locations (Quartiles, Percentiles ) Measures of dispersion

61. 1- Measures of central tendency (cont.)

62. Measures of central tendency (cont.) MEAN. MODE. MEDIAN.

63. Measures of dispersion

64. Measures of dispersion Range Variance Standard deviation Semi-interquartile range Coefficient of variation “Standard error”