Prepared by: Ms. Andrilyn S. Alcantara

1. PRESENTATION OF DATA
Textual, Tabular, Graphical

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. 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. 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. 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. 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. 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. 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. 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. B. TABULAR PRESENTATION OF DATA
Simple Frequency Distribution Table
consists only of class interval and frequency

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. 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. 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. COMPLETE FREQUENCY DISTRIBUTION TABLE
The Range (R)
The difference between the highest and the lowest score
R = Hs - Ls

15. COMPLETE FREQUENCY DISTRIBUTION TABLE
The Class Interval (c.i)
A grouping or category defined by a lower limit an upper
limit

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. COMPLETE FREQUENCY DISTRIBUTION TABLE
The class mark or Midpoint (x)
Average of the upper and lower limits that is
X = UL + LL
2

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. COMPLETE FREQUENCY DISTRIBUTION TABLE
The relative frequency (rf)
Is obtained by dividing the frequency of each class by N

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. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
1. Determine the Range.
R = Highest score – Lowest score
= 90 – 51
= 39

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. 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. 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. 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. 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. 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. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
5. Write the obtained frequency from each class
interval by counting the tallied form.

29. STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
6. Determine the class mark of each class interval
X = lower limit + upper limit
2

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. 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. 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. 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. 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. 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. B. TABULAR PRESENTATION OF DATA
The Contingency Table
shows the data enumerated by cell

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. THE GRAPHS
4. Pie Chart:
@ a circle graph showing the proportion of each class
through the relative or percentage frequency

48. PIE CHART
8%
31%
10%
Base: Class Interval
Height: Frequency
c.i f X
10-14 3
12
20-24 12

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.