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# Chapter 3: Prsentation of Data

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### Chapter 3: Prsentation of Data

1. 1. PRESENTATION OF DATA Textual, Tabular, Graphical
2. 2. A. TEXTUAL PRESENTATION OF DATA data 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
3. 3. B. TABULAR PRESENTATION OF DATA The Frequency Distribution Table this is a table which shows data arranged into different classes and the number of cases which fall into each class
4. 4. B. TABULAR PRESENTATION OF DATA Ungrouped Frequency Distribution means there is only one category per row used if the range of the set of data is not so wide, for instance 10 or less
5. 5. UNGROUPED FREQUENCY DISTRIBUTION Year Level Number of Students (f) Freshman 350 Sophomore 300 Junior 250 Senior 200 N = 1, 100 Table 3.0 Distribution of Students in ABS High School According to Year Level Source: ABS High School Registrar RowClassifier Table number Table Title Column Header Source Note
6. 6. FOR EXAMPLE: Construct a grouped and an ungrouped frequency distribution tables for the age of 50 service crews at Jollimee Restaurant 18 19 19 25 20 21 18 22 18 19 25 18 21 24 25 22 18 23 24 19 18 21 23 20 24 23 19 21 23 20 20 21 22 24 23 25 21 20 22 20 19 19 18 21 21 19 24 21 21 21
7. 7. FOR EXAMPLE: The Ungrouped Frequency Distribution Table for the Age of 50 Service Crews at Jollimee Age Frequency Percentage Frequency 18 7 0.1400 19 8 0.1600 20 6 0.1200 21 11 0.2200 22 4 0.0800 23 5 0.1000 24 5 0.1000 25 4 0.0800
8. 8. B. TABULAR PRESENTATION OF DATA Grouped Frequency Distribution means there are several categories in one row used if the range of the set of data is so wide, for instance 11 and above
9. 9. FOR EXAMPLE: The Grouped Frequency Distribution Table for the Age of 50 Service Crews at Jollimee Age Frequency Percentage Frequency 18 - 19 15 0.3000 20 - 21 17 0.3400 22- 23 9 0.1800 24 - 25 9 0.1800 N = 50 classintervals lower limits LL upper limits UL Class width (i) = UL – LL + 1
10. 10. B. TABULAR PRESENTATION OF DATA Simple Frequency Distribution Table consists only of class interval and frequency
11. 11. FOR EXAMPLE: Construct an ungrouped frequency distribution tables for the test scores of 50 students in Statistics 43 35 40 9 25 30 18 17 50 12 35 46 10 36 33 37 41 21 20 31 42 27 28 31 28 19 18 13 28 16 26 13 4 48 40 48 40 39 32 32 34 29 30 20 26 15 14 10 38 35
12. 12. FOR EXAMPLE: A Simple Grouped Frequency Distribution for the Test Scores of 50 Students in Statistics Class Interval(c. i) Tally Frequency (f) 4 - 9 II 2 10 - 15 IIII - II 7 16 – 21 IIII - III 8 22 – 27 IIII 4 28 – 33 IIII – IIII – I 11 34 – 39 IIII – III 8 40 – 45 IIII – I 6 46 – 51 IIII 4 N = 50
13. 13. B. TABULAR PRESENTATION OF DATA Complete Frequency Distribution Table has class mark or midpoint (X), class boundaries (c.b), relative frequency or percentage frequency and the less than cumulative and the greater than cumulative frequencies.
14. 14. COMPLETE FREQUENCY DISTRIBUTION TABLE The Range (R) The difference between the highest and the lowest score R = Hs - Ls
15. 15. COMPLETE FREQUENCY DISTRIBUTION TABLE The Class Interval (c.i) A grouping or category defined by a lower limit an upper limit
16. 16. COMPLETE FREQUENCY DISTRIBUTION TABLE The class boundaries (c.b) It is half a unit below the LL and half a unit above the UL If the unit is one; a half unit is 0.5 If the unit is 0.1; half a unit is 0.05
17. 17. COMPLETE FREQUENCY DISTRIBUTION TABLE The class mark or Midpoint (x) Average of the upper and lower limits that is X = UL + LL 2
18. 18. COMPLETE FREQUENCY DISTRIBUTION TABLE The class size (i) the difference between the upper class boundary and the lower class boundary of a class interval
19. 19. COMPLETE FREQUENCY DISTRIBUTION TABLE The relative frequency (rf) Is obtained by dividing the frequency of each class by N
20. 20. COMPLETE FREQUENCY DISTRIBUTION TABLE The less than cumulative frequency (<cf) and the greater than cumulative frequency (>cf) are obtained by cumulating the frequency (f) from top to bottom and bottom to top respectively
21. 21. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 1. Determine the Range. R = Highest score – Lowest score = 90 – 51 = 39
22. 22. FOR EXAMPLE: the test scores of 50 students in Statistics 51 65 68 87 76 56 69 75 89 80 61 66 73 86 79 70 71 54 87 78 68 74 66 88 77 67 73 64 90 77 72 52 67 86 79 74 59 70 89 85 55 63 74 82 84 57 68 72 81 83
23. 23. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 2. Determine the desired class interval. The ideal number is somewhere between 5 and 15. c.i = 8 (researcher’s choice)
24. 24. FOR EXAMPLE: the test scores of 50 students in Statistics 51 65 68 87 76 56 69 75 89 80 61 66 73 86 79 70 71 54 87 78 68 74 66 88 77 67 73 64 90 77 72 52 67 86 79 74 59 70 89 85 55 63 74 82 84 57 68 72 81 83
25. 25. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 3. Determine the approximate size or class width of class interval. i = Range/ Class Interval = 39/8 = 4.875 = 5 (rounded to whole number)
26. 26. FOR EXAMPLE: the test scores of 50 students in Statistics 51 65 68 87 76 56 69 75 89 80 61 66 73 86 79 70 71 54 87 78 68 74 66 88 77 67 73 64 90 77 72 52 67 86 79 74 59 70 89 85 55 63 74 82 84 57 68 72 81 83
27. 27. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 4. Construct a frequency table by making the class intervals starting with the lowest value in the lower limit of the first class interval then add the computed class size to obtain the lower limit of the next class interval.
28. 28. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 5. Write the obtained frequency from each class interval by counting the tallied form.
29. 29. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 6. Determine the class mark of each class interval X = lower limit + upper limit 2
30. 30. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 7. Determine the class boundaries or class limits by subtracting 0.5 from every lower limit and adding 0.5 from every upper limit.
31. 31. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION 7. Determine the class boundaries or class limits by subtracting 0.5 from every lower limit and adding 0.5 from every upper limit.
32. 32. FOR EXAMPLE: the test scores of 50 students in Statistics 51 65 68 87 76 56 69 75 89 80 61 66 73 86 79 70 71 54 87 78 68 74 66 88 77 67 73 64 90 77 72 52 67 86 79 74 59 70 89 85 55 63 74 82 84 57 68 72 81 83
33. 33. FOR EXAMPLE: the test scores of 50 students in Statistics Class Interval Tally Frequency Class Mark 51-55 IIII 4 53 N = 50 81-85 76-80 71-75 66-70 61-65 56-60 86-90 IIII IIII-II IIII - IIII IIII-IIII IIII III IIII-III 5 7 9 10 4 3 8 83 78 73 68 63 58 88
34. 34. FOR EXAMPLE: the test scores of 50 students in Statistics 43 35 40 9 25 30 18 17 50 12 35 46 10 36 33 37 41 21 20 31 42 27 28 31 28 19 18 13 28 16 26 13 4 48 40 48 40 39 32 32 34 29 30 20 26 15 14 10 38 35
35. 35. COMPLETE FREQUENCY DISTRIBUTION TABLE Class Interval (c.i) Frequency (f) Class Mark (X) Class Boundary (c.b) Relative Frequency (rf) Less than Cumulative Frequency (<cf) Greater than Cumulative Frequency (>cf) 4 - 9 2 6.5 3.5 – 9.5 .0400 2 50 10 - 15 7 12.5 9.5 – 15.5 .1400 9 46 16 – 21 8 18.5 15.5 – 21.5 .1600 17 40 22 – 27 4 24.5 21.5 – 27.5 .0800 21 32 28 – 33 11 30.5 27.5 – 33.5 .2200 32 21 34 – 39 8 36.5 33.5 – 39.5 .1600 40 17 40 – 45 6 42.5 39.5 – 45.5 .1200 46 9 46 – 51 4 48.5 45.5 – 51.5 .0800 50 2 N = 50
36. 36. B. TABULAR PRESENTATION OF DATA The Contingency Table shows the data enumerated by cell
37. 37. EXAMPLE: CHOICE/ SAMPLE MEN WOMEN CHILDREN TOTAL Like the program 50 56 45 151 Indifferent 23 16 12 51 Do not like the program 43 55 40 138 Total 116 127 97 340 The Contingency Table for the Opinion of Viewers on the New TV Program
38. 38. C. GRAPHICAL PRESENTATION OF DATA A graph add life and beauty to one’s work, but more than this, it helps facilitate comparison and interpretation without going through the numerical data
39. 39. THE GRAPHS 1. Bar Chart: @ a graph represented by either vertical or horizontal rectangles whose bases represent the class intervals and whose heights represent the frequencies. @ it is used for discrete variables
40. 40. BAR CHART 0 2 4 6 8 10 12 10 to 14 20 to 24 30 to 34 The Bar Chart for the Number of Stamps Collected by 35 StudentsSeries 2 Series 1 Base: Class Interval Height: Frequency c.i f 10-14 3 20-24 12 30-34 4
41. 41. THE GRAPHS 2. Histogram: @ a graph represented by vertical or horizontal rectangles whose bases are the class marks and whose heights are the frequencies. @ it is used for continuous variables
42. 42. HISTOGRAM 0 5 10 15 12 17 22 27 32 37 The Histogram for the Ages of 35 Aerobics Students Base: Class Mark Height: Frequency c.i f X 10-14 3 12 20-24 12 22 30-34 4 32
43. 43. THE GRAPHS 3. Frequency Polygon: @ this is a line version of the histogram @ it is a line whose bases are the class marks and whose heights are the frequencies @ it is used for continuous variables
44. 44. FREQUENCY POLYGON 3 12 4 0 5 10 15 20 25 30 35 40 AxisTitle Axis TitleThe Frequency Polygon for the Ages of 35 Aerobics Students Base: Class Mark Height: Frequency c.i f X 10-14 3 12 20-24 12
45. 45. FREQUENCY POLYGON 3 12 4 9.5 14.5 19.5 24.5 29.5 34.5 39.5 0 5 10 15 20 25 30 35 40 Axis TitleThe Less than Ogive for the Ages of 35 Aerobics Students Base: Lower Class Boundary Height: <cf <Ogive c.b <cf -9.5 0 9.5-14.5 3 14.5-19.5 9 19.5-24.5 21 24.5-29.5 28 29.5-34.5 32 34.5-39.5 35
46. 46. FREQUENCY POLYGON 39.5 34.5 29.5 24.5 19.5 14.5 0 0 0 35 32 28 21 9 3Axis Title The Greater than for the Ages of 35 Aerobics Students Base: Lower Class Boundary Height: >cf >Ogive c.b >cf -9.5 0 9.5-14.5 3 14.5-19.5 9 19.5-24.5 21 24.5-29.5 28 29.5-34.5 32 34.5-39.5 35
47. 47. THE GRAPHS 4. Pie Chart: @ a circle graph showing the proportion of each class through the relative or percentage frequency
48. 48. PIE CHART 8% 31% 10% Base: Class Interval Height: Frequency c.i f X 10-14 3 12 20-24 12
49. 49. THE GRAPHS 5. Pictograph: @ sometimes called pictogram @ uses small pictures or figures of objects called isotopes n making comparisons. Each picture represents a definite quantity.