Download - Chapter 3: Prsentation of Data
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PRESENTATION OF DATATextual, Tabular, Graphical
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A. TEXTUAL PRESENTATION OF DATAdata presented in paragraph or in sentences
includes: enumeration of important characteristicsemphasizing the most significant featureshighlighting the most striking attributes of the set of data
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B. TABULAR PRESENTATION OF DATA
The Frequency Distribution Tablethis is a table which shows data arranged into different classes and the number of cases which fall into each class
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B. TABULAR PRESENTATION OF DATA
Ungrouped Frequency Distributionmeans 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
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UNGROUPED FREQUENCY DISTRIBUTION
Year Level Number of Students (f)
Freshman 350
Sophomore 300
Junior 250
Senior 200
N = 1, 100
Table 3.0Distribution of Students in ABS High
SchoolAccording to Year Level
Source: ABS High School Registrar
Row
C
lass
ifier
Table number
Table Title
Column Header
Source Note
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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 1925 18 21 24 25 22 18 23 24 1918 21 23 20 24 23 19 21 23 2020 21 22 24 23 25 21 20 22 2019 19 18 21 21 19 24 21 21 21
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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
N = 50
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B. TABULAR PRESENTATION OF DATA
Grouped Frequency Distributionmeans there are several categories in one row
used if the range of the set of data is so wide, for instance 11 and above
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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
class
in
terv
als
lower limits LL
upper limits UL Class width (i) = UL – LL + 1
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B. TABULAR PRESENTATION OF DATA
Simple Frequency Distribution Tableconsists only of class interval and frequency
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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 1235 46 10 36 33 37 41 21 20 3142 27 28 31 28 19 18 13 28 1626 13 4 48 40 48 40 39 32 3234 29 30 20 26 15 14 10 38 35
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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
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B. TABULAR PRESENTATION OF DATA
Complete Frequency Distribution Tablehas 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.
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COMPLETE FREQUENCY DISTRIBUTION TABLE
The Range (R)The difference between the highest and the lowest score
R = Hs - Ls
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COMPLETE FREQUENCY DISTRIBUTION TABLE
The Class Interval (c.i)A grouping or category defined by a lower limit an upper limit
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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 0.5If the unit is 0.1; half a unit is 0.05
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COMPLETE FREQUENCY DISTRIBUTION TABLE
The class mark or Midpoint (x)Average of the upper and lower limits that is
X = UL + LL
2
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COMPLETE FREQUENCY DISTRIBUTION TABLE
The class size (i)the difference between the upper class boundary and the lower class boundary of a class interval
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COMPLETE FREQUENCY DISTRIBUTION TABLE
The relative frequency (rf)Is obtained by dividing the frequency of each class by N
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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
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STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
1. Determine the Range.
R = Highest score – Lowest score
= 90 – 51
= 39
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FOR EXAMPLE:
the test scores of 50 students in Statistics
51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83
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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)
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FOR EXAMPLE:
the test scores of 50 students in Statistics
51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83
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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)
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FOR EXAMPLE:
the test scores of 50 students in Statistics
51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83
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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.
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STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
5. Write the obtained frequency from each class interval by counting the tallied form.
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STEPS IN CONSTRUCTING A FREQUENCY DISTRIBUTION
6. Determine the class mark of each class interval
X = lower limit + upper limit
2
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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.
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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.
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FOR EXAMPLE:
the test scores of 50 students in Statistics
51 65 68 87 76 56 69 75 89 8061 66 73 86 79 70 71 54 87 7868 74 66 88 77 67 73 64 90 7772 52 67 86 79 74 59 70 89 8555 63 74 82 84 57 68 72 81 83
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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
76-8071-75
66-70
61-65
56-60
86-90
IIII
IIII-IIIIII - IIII
IIII-IIII
IIII
III
IIII-III
5
79
10
4
3
8
83
7873
68
63
58
88
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FOR EXAMPLE:
the test scores of 50 students in Statistics
43 35 40 9 25 30 18 17 50 1235 46 10 36 33 37 41 21 20 3142 27 28 31 28 19 18 13 28 1626 13 4 48 40 48 40 39 32 3234 29 30 20 26 15 14 10 38 35
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COMPLETE FREQUENCY DISTRIBUTION TABLEClass 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
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B. TABULAR PRESENTATION OF DATA
The Contingency Tableshows the data enumerated by cell
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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
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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
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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
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BAR CHART
10 to 14
20 to 24
30 to 34
0 2 4 6 8 10 12
The Bar Chart for the Number of Stamps Collected by 35 StudentsSeries 2 Series 1
Base: Class IntervalHeight: Frequency
c.if
10-14320-241230-344
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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
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HISTOGRAM
12 17 22 27 32 370
2
4
6
8
10
12
The Histogram for the Ages of 35 Aerobics Students
Base: Class Mark Height: Frequency
c.i fX
10-1431220-24122230-34432
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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
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FREQUENCY POLYGON
10 15 20 25 30 35 40
3
12
4
The Frequency Polygon for the Ages of 35 Aerobics Students
Axis Title
Axis
Tit
le
Base: Class Mark Height: Frequency
c.ifX
10-14312
20-241222
30-34432
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FREQUENCY POLYGON
0 5 10 15 20 25 30 35 40
3
12
4
9.514.5
19.524.5
29.534.5
39.5
The Less than Ogive for the Ages of 35 Aerobics Students
Axis Title
Base: Lower Class Boundary Height: <cf
<Ogivec.b
<cf-9.5
09.5-14.5 314.5-19.5 919.5-24.5 2124.5-29.5 2829.5-34.5 3234.5-39.5 35
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FREQUENCY POLYGON
35 32 28 21 9 3
39.5
34.5
29.5
24.5
19.5
14.5
The Greater than for the Ages of 35 Aerobics StudentsAxis Title
Base: Lower Class Boundary Height: >cf
>Ogivec.b
>cf-9.5
09.5-14.5 314.5-19.5 919.5-24.5 2124.5-29.5 2829.5-34.5 3234.5-39.5 35
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THE GRAPHS
4. Pie Chart:@ a circle graph showing the
proportion of each class through the relative or percentage frequency
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PIE CHART
0.08
0.31
0.1
Base: Class IntervalHeight: Frequency
c.ifX
10-14312
20-241222
30-34432
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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.