1. Data organization and Presentation

2. Data Organization Making it easy for comparison and analysis of data Arranging data in an orderly sequence or into groups on the basis of similarity. This is the first step of data analysis

3. Ways of arranging data Arrays Frequency tables Stem and leaf plot Tabulations: Simple tables and cross tabulation

4. Arrays Simple arrays Is an arrangement of data in an ascending or descending order. It’s convenient if the number of it is small. Frequency array It’s a series formed on the basis of frequency with which each item is repeated in a series.

5. Example: Consider this data 12,3,5,10,8,3,6,5,7,8,9,10 Simple array 3,3,5,5,6,7,8,8,9,10,10,12 Frequency Array DataFrequency 32 52 61 71 82 91 102 121

6. Frequency distribution tables A frequency distribution table is a table that lists categories of items along with their corresponding frequencies.

7. An example of a frequency distribution table

8. Guidelines for constructing a frequency distribution table The classes must be mutually exclusive. That is, each score must belong to exactly one class. The classes must be exhaustive meaning there should be enough classes to accommodate all data The class size must be uniform throughout The number of classes should be between 5 and 20.

9. Constructing a frequency distribution table The following is a survey of the pocket money of 40 students in a school (pocket money in Ksh per day). Draw a frequency distribution with mid-point, cumulative frequency, and class boundaries 55,63,44,37,50,47,44,57,42,46,33,44,58,40,54,65,39,27,28,56,38,45,70,60,30,35,56,78,55,2 7,50,28,44,28,60,61,31,37,65,43

10. Steps Steps in the construction of Frequency Tables Frequency refers to the number of times an item (or number) occurs. Step 1: list all the data values Step 2: scan the raw data, item by item placing a tally mark next to a value each time it occurs (every 5 th tally mark crosses through a group of 4) Step 3: Count the number of tally marks for each value (frequency) Step 4: Determine the range of the data set i. e Max. Value _Min Value Step 5: Determine class sizes (Class widths) {For grouped data} Class Width(CW)=Range/Number of classes Note: # of classes is to be decided by the researcher but it should be greater than or equals to 5

11. Example Step 5: Determine the frequency for each class by referring to the tally columns and present the results in a table. ClassTally tableFrequency 27-347 35-39 40-44 45-49 50-54 55-59 60-69 70-74 75-79 Total

12. Exercise Add 3 more columns for midpoint, class boundary and cumulative frequency

13. Stem and leaf plot A stem and leaf plot shows us potential patterns in the responses that may not be apparent in the original listing of the data

14. Example - drawing a stem and leaf Answer :- (1) Identify the largest and the smallest value (38 and 72) (2) put values into preliminary diagram: Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 set these data into a stem and leaf plot stem leaf 3456734567 Completion times

15. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

16. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7171 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

17. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 731731 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

18. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 3 1 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

19. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 3 1 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

20. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 3 1 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

21. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 3 1 8 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

22. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 3 1 8 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

23. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 3 1 8 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

24. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 3 7 1 8 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

25. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 3 7 1 8 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

26. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 3 7 4 1 8 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

27. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 3 7 4 1 8 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

28. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 3 7 4 1 8 3 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

29. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 3 7 4 1 8 3 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

30. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 3 7 4 1 8 3 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

31. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

32. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 3 7 4 8 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

33. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 5 3 7 4 8 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

34. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 5 4 3 7 4 8 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median, quartiles and inter-quartile range Completion times

35. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 5 4 3 3 7 4 8 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

36. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 5 4 3 3 7 4 8 1 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

37. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 7 3 6 6 8 8 1 9 2 5 4 3 5 3 7 4 8 1 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

38. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 3 7 4 8 1 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

39. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 3 7 4 8 1 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

40. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 4 8 1 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

41. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 4 8 1 2 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

42. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 3 7 4 8 1 2 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

43. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times

44. Example - drawing a stem and leaf Answer (a):- (1) key: 4|7 means 47 (2) put values into preliminary diagram: 3456734567 8 7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7 3 7 4 8 1 2 1 8 3 5 2 Question:- 29 students were set a simple task. Their completion times to the nearest second were: 47 61 53 43 46 46 68 48 72 57 48 54 41 63 49 42 58 65 45 44 43 51 45 38 46 44 52 43 47 (a) set these data into a stem and leaf diagram (b) find the median Completion times Don’t forget the key

45. Tabulation A table is a systematic arrangement of statistical data in columns and rows Rows are horizontal arrangements while columns are vertical arrangements The purpose of a table is to simplify the presentation and to facilitate comparison.

46. Essential parts of a table Title of the table Source notes Foot note

47. Types of tables Simple (one way) tables Only one xtics is shown Cross tabulation More than one xtics are included in the table Allows you to compare two subgroups of information

48. Examples Simple tableCross tabulation Table 2. Percentage of employees at management by gender Table 1. Percentage of employees at management

49. Exercise In a certain test 50 students sat for the exam. 30 of them were males students, twenty of them failed the exam, 10 female passed the exam. Present the above information in a table form.

50. Data presentation

51. Ways of presenting data. They include Pictograms Graphs

52. Pictogram Data is represented using a self-explanatory pictorial symbol. Are attractive and easy to remember but are limited when dealing with large quantities.

54. Graphs Graphical presentation Qualitative data presentation Quantitative data presentation  Line graphs  Dot plots  Histogram  Frequency polygon Ogive Bar graphs Pie charts

55. Bar Graphs The height of the bar represents the number of items in that category. The bars can be vertical or horizontal. The width of the bars and the gap between one bar and another should be uniform throughout.

56. Types of bar graphs Simple bar graphs Subdivided bar graphs Multiple bar graphs Percentage bar graphs Deviation bars

57. Simple bar graph

58. Multiple bar graphs

59. Stacked (Subdivided) bar graphs

60. Pie Chart Used to show proportions of different categories of classes. they are appropriate for displaying frequencies of nominal variables (data are neither measured nor ordered but subjects are merely allocated to distinct categories: for example, a record of students' course choices) and displaying “shares such as ” how parties divide up popular votes, electoral votes e.t.c. Using different colors for each slice can help the reader quickly grasp the information in the chart

61. Example

62. But pie charts are not helpful if there are many unordered categories – Just show the quantities in tabular form

63. Line graph A line graph is used to illustrate change over time. Line graphs need: - Title - Labeled X and Y axes - Equal Intervals Data displayed by points connected into lines

65. Histogram Displays data by using continuous vertical bars. The scale along the horizontal axis is continuous. The width of the bars is equal to the class interval.

66. Note: the distinction between a bar graph and a histogram is that a bar graph is one dimensional only the height matters while a histogram is two dimensional, both height and width of the bars matter

67. A frequency polygon Can be constructed by joining the midpoints of the top of the bars in a histogram

68. Cumulative frequency curve (Ogive) Represents the cumulative frequencies for the classes in a frequency distribution