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PRESENTATION AND
ORGANIZATION OF DATA
METHODS OF PRESENTING DATA
TABULAR FORM
PARAGRAPH OR TEXTUAL FORM
GRAPHICAL FORM
TABULAR FORM
Data are organize into rows and columns
Statistical table is used to describe the data
Numerical facts are presented in more concise and systematic manner.
PARTS OF STATISTICAL TABLE
TABLE HEAD( TABLE NUMBER AND TABLE TITLE)
BOX HEAD
BODY
FOOTNOTE AND SOURCE (OPTIONAL)
PARAGRAPH /TEXTUAL FORM
Uses sentences or paragraph to describe the data
Combines text and numerical facts
Used if there are only few numerical data and to emphasize on some figures.
GRAPHICAL FORM
Graphs and charts are used to illustrate the data
Graph is a pictorial or geometric representation of data
Presenting more clearly, more creatively in attractive and colorful figures.
PARTS OF STATISTICAL CHARTS
TITLE
COORDINATE AXES
LABELS
LEGEND
SCALE
GRIDLINES
SOURCE(OPTIONAL)
Tabular PRESENTATION
of DATATable 4
Distribution of Students in ABC College According to Year Level
Year Level
Number of Students
First year 300 Second year 250 Third year 285 Fourth year 215
N = 1050 Source: ABC College Registrar
Table number & title
TYPES OF STATISTICAL CHART
• LINE GRAPH• BAR GRAPH• PIE CHART• PICTOGRAPH• STATISTICAL MAP• SCATTER DIAGRAM
BAR GRAPH
A bar graph is used to show relationships between groups.
The two items being compared do not need to affect each other. It's a fast way to show big differences.
Bar Graph is a graph that is useful for comparing the amounts for one set of data.
BAR GRAPH
Base: Class IntervalHeight: Frequency
(c.i) f10 - 14 315 - 19 620 - 24 1225 - 29 730 - 34 435 - 39 3
12
02468
10
10 t
o 14
20 t
o 24
30 t
o 34
There are gaps between bars. This is appropriate to use for discrete variables!
Take Note !!
Bar Chart
Base: Class MarkHeight: Frequency (c.i) f X
10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37
0
2
4
6
8
10
12
12 17 22 27 32 37
There is no gap between bars. This is appropriate to use for continuous variables!
Take Note !!
Histogram
line graph
Line Graph is a graph that is useful for showing how data changes over time.
A line graph is used to show continuing data; how one thing is affected by another.
It's clear to see how things are going by the rises and falls a line graph shows.
LINE GRAPH
PIE CHART
• A PIE CHART is used to show how a part of something relates to the whole.
• This kind of graph is needed to show percentages effectively.
PIE GRAPH
Pie Chart
(c.i) f10 - 14 315 - 19 620 - 24 1225 - 29 730 - 34 435 - 39 3
9%
17%
34%
20%
11%9%
PICTOGRAPH
Pictograph is a graph that uses pictures or symbols to show data.
A pictograph uses an icon to represent a quantity of data values in order to decrease the size of the graph.
PICTOGRAPH
STATISTICAL MAPA statistical map chart displays data by
shading sections of a map, and must include a key.
STATISTICAL MAP
ORGANIZING QUANTITATIVE DATA
• ARRAY – arrangement of data in ascending or descending order
• FREQUENCY DISTRIBUTION- tabular arrangement of data by classes or categories with corresponding frequencies
• STEM AND LEAF PLOT- a representation of a distribution where the individual scores are preserved. Here, the leftmost digit will become the stem and the right digit become the leaf.
Tabular PRESENTATION
of DATA
It is a table which shows the data arranged into different classes and the number of cases which
fall into each class is tallied.
Table 3.0The Ungrouped Frequency Distribution TableFor the Age of 50 Service Crews at Jollimee
Age Frequency Percentage Frequency
18 7 0.14
19 8 0.16
20 6 0.12
21 11 0.22
22 4 0.08
23 5 0.10
24 5 0.10
25 4 0.08
N = 50
Table 3.1The Grouped Frequency Distribution TableFor the Age of 50 Service Crews at Jollimee
Age Frequency Percentage Frequency
18-19 15 0.30
20-21 17 0.34
22-23 9 0.18
24-25 9 0.18
N = 50
Tabular PRESENTATION
of DATA Table 3.2 The Grouped Frequency Distribution for the
Test Scores of 50 Students in Statistics
Class Interval ( c. i )
Tally Frequency ( f )
Class Mark (X)
Class Boundary
3 - 8 9 - 14
15 - 20 21 - 26 27 - 32 33 - 38 39 - 44 45 - 50
I IIII – II IIII – III IIII IIII – IIII - I IIII – III IIII – II IIII
1 7 8 4
11 8 7 4
5.5 11.5 17.5 23.5 29.5 35.5 41.5 47.5
2.5 - 8.5 8.5 – 14.5 14.5 – 20.5 20.5 – 26.5 26.5 – 32.5 32.5 – 38.5 38.5 – 44.5 44.5 – 50.5
N = 50
Tabular PRESENTATION
of DATA
Class Interval(c.i)3 - 89 - 14
15 - 2021 - 2627 - 3233 - 3839 - 4445 - 50
The first column in a frequency distributiontable is the class interval (c.i). The first
column in (c.i) is the lower limit (LL), whilethe second column is the upper limit (UL). There are eight classes in this table, which
starts from 3 - 8 and ends to 45 - 50.
The size of the class interval or the classWidth(c) is 6. It is obtained by getting
the difference between consecutiveupper or lower limits, or by
getting UL - LL + 1unit.Ex. 8 - 3 + 1 = 6
14 - 9 + 1 = 6, ...
TERMINOLOGIES ABOUT FREQUENCY DISTRIBUTION
CLASS INTERVALS
• refers to groups or categories• Example: 8 classes or groups
Class Interval(c.i)3 - 89 - 1415 - 2021 - 2627 - 3233 - 3839 - 4445 - 50
CLASS LIMITS
• Numbers used to name the classes• Example: 9-14 are class limits• Lower class limit is 9• Upper class limit is 14
Table 3.2 The Grouped Frequency Distribution for the
Test Scores of 50 Students in Statistics
Class Interval ( c. i )
Tally Frequency ( f )
Class Mark (X)
Class Boundary
3 - 8 9 - 14
15 - 20 21 - 26 27 - 32 33 - 38 39 - 44 45 - 50
I IIII – II IIII – III IIII IIII – IIII - I IIII – III IIII – II IIII
1 7 8 4
11 8 7 4
5.5 11.5 17.5 23.5 29.5 35.5 41.5 47.5
2.5 - 8.5 8.5 – 14.5 14.5 – 20.5 20.5 – 26.5 26.5 – 32.5 32.5 – 38.5 38.5 – 44.5 44.5 – 50.5
N = 50
CLASS MARK/CLASS MIDPOINT• Xi = (lcli + ucli)/2 where i refers to class number• Grades number class mark
of student• 29-38 3 33.5• 39-48 1 43.5• 49-58 4 53.5• 59-68 10 63.5• 69-78 15 73.5• 79-88 12 83.5• 89-98 5 93.5• TOTAL 50
CLASS BOUNDARIES
• True class limits• Grades class boundaries• 29-38 28.5-38.5• 39-48 38.5-48.5• 49-58 48.5-58.5• 59-68 58.5-68.5• 69-78 68.5-78.5• 79-88 78.5-88.5• 89-98 88.5-98.5• how ? ( 88+89)/2 and (98+99)/2
CLASS WIDTH /CLASS SIZE ( C)
• Difference between 2 consecutive lcl, ucl, lcb, ucb, classmarks
• c= 43.5 –33.5 = 10 using consecutive class marks• c= 38.5 –28.5 = 10 using consecutive ucb• c= 49 –39= 10 using consecutive lcl
number of student
CONSTRUCTION OF FREQUENCY DISTRIBUTION
1. Find the range, R: highest value – lowest value
2. Solve for the number of classes, k
Sturges’ formula k= 1 +3.332 log N
3. Find class size, c
c= R/k
4. Tally
DISTRIBUTIONS DERIVED FROM FREQUENCY DISTRIBUTION
• Relative Frequency Distribution• Cumulative Frequency Distribution
GRAPHICAL REPRESENATATION OF FREQUENCY DISTRIBUTION
• Frequency Histogram- a bar graph to present frequency distribution
• Frequency Polygon- line graph to present frequency distribution
• Ogive- a line graph to present cumulative frequency distribution
FREQUENCY HISTOGRAM• x-axis, classes y-axis, frequency
Base: Class MarkHeight: Frequency (c.i) f X
10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37
0
2
4
6
8
10
12
12 17 22 27 32 37
There is no gap between bars. This is appropriate to use for continuous variables!
Take Note !!
Histogram
FREQUENCY POLYGON
• x-axis, class marks y-axis, frequency
Frequency Polygon
Base: Class MarkHeight: Frequency
(c.i) f X 10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37
0
2
4
6
8
10
12
14
7 12 17 22 27 32 37 42
This is appropriateto use for
continuous variables!
Take Note !!Additional “X” areadded on both ends in orderto close the polygon.
OGIVE
• LINE GRAPH TO PRESENT THE CUMULATIVE FREQUENCY DISTRIBUTION
• x-axis, class boundaries• y-axis, cumulative frequency
< Ogive Base: Upper Class Boundary Height: < cf
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
0
5
10
15
20
25
30
35
40
9.5 14.5 19.5 24.5 29.5 34.5 39.5
< Ogive
There is additionalUpper c.b. “9.5” with<cf equal to 0.
Take Note !!
> Ogive Base: Lower Class Boundary Height: > cf
c.b. >cf 9.5-14.5 3514.5-19.5 3219.5-24.5 2624.5-29.5 1429.5-34.5 734.5-39.5 339.5- 0
>cf & Lower c.b. 0
5
10
15
20
25
30
35
40
9.5 14.5 19.5 24.5 29.5 34.5 39.5
> Ogive
There is additionalLower c.b. “39.5” with>cf equal to 0.
Take Note !!
Ogives Base: Class IntervalHeight: Cumulative Frequency
0
5
10
15
20
25
30
35
40
9.5 14.5 19.5 24.5 29.5 34.5 39.5
<cf & Upper c.b.>cf & Lower c.b.
< Ogive
> Ogive
c.b. <cf >cf 9.5-14.5 3 3514.5-19.5 9 3219.5-24.5 21 2624.5-29.5 28 1429.5-34.5 32 734.5-39.5 35 3
The Contingency TableThis is a table which shows the data
enumerated by cell.
Table 3.5The Contingency Table for the Opinion of Viewers
on the New TV Program
34097127116Total
138405543Do not like the program
51121623Indifferent
151455650Like the program
TotalChildrenWomenMenChoice/Sample