presentation of data
DESCRIPTION
Presentation of Data. Prepared by: Ms. Bernabeth Jo T. Tendero. Textual Presentation. 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 - PowerPoint PPT PresentationTRANSCRIPT
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Presentation of Data
Prepared by:
Ms. Bernabeth Jo T. Tendero
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Textual Presentation
• 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
(Basilia Ebora Blay)
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Textual Presentation
Disadvantage:• Readers sometimes get bored
(Basilia Ebora Blay)
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Tabular Presentation
• Very effective and efficient means of organizing and summarizing data
• A lot of information can be seen in one table
• Makes comparison of figures quick under each category
(Luis A. Tattao)
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Parts of a Tables
Block(Age Bracket)
Fat Content of Diet
Extremely Low Fairly Low Moderately Low
15 – 24 0.73 0.67 0.15
25 – 35 0.86 0.75 0.21
36 – 44 0.94 0.81 0.26
45 – 54 1.40 1.32 0.75
55 – 64 1.62 1.41 0.78
Table 6. Fat Content of Diet by Age Bracket
Table Number Table Heading
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Parts of the Table• Table heading – includes the table number
and the title
• Body – main part of the table containing the figures being presented
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Parts of a Tables
Block(Age Bracket)
Fat Content of Diet
Extremely Low Fairly Low Moderately Low
15 – 24 0.73 0.67 0.15
25 – 35 0.86 0.75 0.21
36 – 44 0.94 0.81 0.26
45 – 54 1.40 1.32 0.75
55 – 64 1.62 1.41 0.78
Table 6. Fat Content of Diet by Age Bracket
Table Number Table Heading
Stubs and Classes
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Parts of the Table• Table heading – includes the table number
and the title
• Body – main part of the table containing the figures being presented
• Stubs or classes – the categories describing the data, usually found at the left-hand side of the table
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Parts of a Tables
Block(Age Bracket)
Fat Content of Diet
Extremely Low Fairly Low Moderately Low
15 – 24 0.73 0.67 0.15
25 – 35 0.86 0.75 0.21
36 – 44 0.94 0.81 0.26
45 – 54 1.40 1.32 0.75
55 – 64 1.62 1.41 0.78
Table 6. Fat Content of Diet by Age Bracket
Table Number Table Heading
Stubs and ClassesCaption
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Parts of the Table• Table heading – includes the table number and the
title• Body – main part of the table containing the figures
being presented• Stubs or classes – the categories describing the
data, usually found at the left-hand side of the table• Caption – designations of the information
contained in columns, usually found at the top of the column. (Luis A. Tattao)
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Frequency Distribution Table
• A summary table in which data are arranged into conveniently established, numerically ordered class grouping or categories
• A tabular presentation of data grouped into classes together with the number of observations in each class
(Luis A. Tattao)
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Steps in Constructing a Frequency Distribution Table
1. Determine the Range, R:
Range = Highest Value – Lowest Value
2. Determine the approximate number of class intervals , k
k = 1 + 3.3 log N
N = population or the total
number of observation
3. Obtain the class width , C
k
RangeC
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Steps in Constructing a Frequency Distribution Table
4. For Class Intervals (CI)
Use the lowest score as the lower limit (LL) of the first interval , add (C-1) to it to obtain the upper limit (UL) of the first interval
LL = LL of the previous interval + C
UL = LL + (C-1)
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Example
Age of Patients in Hospital X, June 200425 28 27 30 32 25 31 26 29 6
31 20 21 32 18 50 53 60 50 54
45 40 37 25 20 27 32 24 29 30
25 24 10 12 15 28
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Solution:
1. Determine the Range, R:
R = 60 - 6
= 54
2. k = 1 + 3.3 log N
= 1 + 3.3 log 36
= 6.1358
6
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Solution3. Obtain the class width , C
= 9
4. Class Intervals
6 is the LL of the 1st interval
UL = 6 + (9-1)
= 14 of the 1st interval
6
54C
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Solution
2nd interval
LL = 6 + 9
= 15
UL = 15 + 8
= 23
Compute for the other intervals
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years) Tally Marks Frequency
60 – 68 I 1
51 – 59 II 2
42 – 50 III 3
33 – 41 II 2
24 – 32 IIIII – IIIII – IIIII – IIIII 20
15 – 23 IIIII 5
6 – 14 III 3
N = 36
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Assignment• Construct the frequency distribution table
for the student’s scores in a statistics quiz5 6 4 5 4 5 2 3 8 8
6 7 8 7 7 7 6 6 6 9
2 5 6 3 9 5 5 5 5 6
6 7 6 7 6 7 6 8 3 3
4 5 5 5 4 4 4 9 9 9
2 2 2 4 4 3 4 3 4 3
9 5 5 4 8 6 9 2 7 7
3 3 5 8 8 9 2
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Answer to Assignment
1. Determine the Range, R:
R = 9 – 2
= 7
2. k = 1 + 3.3 log N
= 1 + 3.3 log 77
= 7.2254
7
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Solution3. Obtain the class width , C
= 1
4. Class Intervals
Since there is only the class width is only 1 that means the frequency distribution table is ungrouped.
7
7C
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Table 1. Frequency Distribution of the students’ scores in a quiz
in StatisticsScores Frequency
9 8
8 7
7 9
6 12
5 14
4 11
3 9
2 7
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Class Mark (x)
• Midpoint of a class interval
• Example:
60 – 68 2
LLULx
2
6860 x
64x
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Class Boundaries• A.k.a. exact limits
• Obtained by subtracting 0.5 from the LL and adding 0.5 to UL
• Example: 60 – 68
• 60 – 0.5 = 59.5
• 68 + 0.5 = 68.5
• Class Boundary: 59.5 – 68.5
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years) Tally Marks Frequency
60 – 68 I 1
51 – 59 II 2
42 – 50 III 3
33 – 41 II 2
24 – 32 IIIII – IIIII – IIIII – IIIII 20
15 – 23 IIIII 5
6 – 14 III 3
N = 36
Calculate the class mark and the class boundaries of this FDT
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Table 1. Ages of Patients in Hospital X, June 2004Age (in years) Frequency Class Mark Class
Boundary
60 – 68 1 64 59.5 – 68.5
51 – 59 2 55 50.5 – 59.5
42 – 50 3 46 41.5 – 50.5
33 – 41 2 37 32.5 – 41.5
24 – 32 20 28 23.5 – 32.5
15 – 23 5 19 14.5 – 23.5
6 – 14 3 10 5.5 – 14.5
N = 36
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Relative frequency (rf)
• Percentage of frequency
• Written in decimal form
N
frequencyrf
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years) Frequency
60 – 68 1
51 – 59 2
42 – 50 3
33 – 41 2
24 – 32 20
15 – 23 5
6 – 14 3
N = 36
36
1rf 0278.0
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years)
Frequency Class Mark Class Boundary
Relative Frequency
60 – 68 1 64 59.5 – 68.5 0.0278
51 – 59 2 55 50.5 – 59.5 0.0556
42 – 50 3 46 41.5 – 50.5 0.0833
33 – 41 2 37 32.5 – 41.5 0.0556
24 – 32 20 28 23.5 – 32.5 0.5556
15 – 23 5 19 14.5 – 23.5 0.1389
6 – 14 3 10 5.5 – 14.5 0.0833
N = 36
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Less than Cumulative frequency (<cf)
• Obtained by cumulating frequency from top to bottom
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years)
Frequency Class Mark Class Boundary
Relative Frequency
60 – 68 1 64 59.5 – 68.5 0.0278
51 – 59 2 55 50.5 – 59.5 0.0556
42 – 50 3 46 41.5 – 50.5 0.0833
33 – 41 2 37 32.5 – 41.5 0.0556
24 – 32 20 28 23.5 – 32.5 0.5556
15 – 23 5 19 14.5 – 23.5 0.1389
6 – 14 3 10 5.5 – 14.5 0.0833
N = 36
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years)
Frequency Class Mark Class Boundary
Relative Frequency
Less than cumulative frequency
(<cf)
60 – 68 1 64 59.5 – 68.5 0.0278 1
51 – 59 2 55 50.5 – 59.5 0.0556 3
42 – 50 3 46 41.5 – 50.5 0.0833 6
33 – 41 2 37 32.5 – 41.5 0.0556 8
24 – 32 20 28 23.5 – 32.5 0.5556 28
15 – 23 5 19 14.5 – 23.5 0.1389 33
6 – 14 3 10 5.5 – 14.5 0.0833 36
N = 36
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More than cumulative frequency (>cf)
• Obtained by cumulating the frequency from bottom to top
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Table 1. Ages of Patients in Hospital X, June 2004
Age (in years)
Frequency Class Mark
Class Boundary
Relative Frequency
Less than cumulative frequency
(<cf)
More than comulative frequency
(>cf)
60 – 68 1 64 59.5 – 68.5 0.0278 1 36
51 – 59 2 55 50.5 – 59.5 0.0556 3 35
42 – 50 3 46 41.5 – 50.5 0.0833 6 32
33 – 41 2 37 32.5 – 41.5 0.0556 8 30
24 – 32 20 28 23.5 – 32.5 0.5556 28 10
15 – 23 5 19 14.5 – 23.5 0.1389 33 5
6 – 14 3 10 5.5 – 14.5 0.0833 36 2
N = 36
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Practice
Weights (in lbs.) of First Year High School Students in XYZ School
105 107 120 94 107 105
95 115 106 85 105 117
103 86 96 94 96 99
100 115 115 99 107 85
86 87 86 85 95 89
96 85 117 86 95 116
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R = 120 – 35 = 35
k = 1 + 3.3 log 36 = 6.14 = 6
C = 35/6 = 5.8 = 6
Weight (in lbs.)
Frequency Class Mark
Class Boundary
Relative Frequency
Less than cumulative frequency
(<cf)
More than comulative frequency
(>cf)
85 – 90 10 87.5 84.5 – 90.5 27.78 10 36
91 – 96 8 93.5 90.5 – 96.5 22.22 18 26
97 – 102 3 99.5 96.5 – 102.5 8.33 21 18
103 – 108 8 105.5 102.5 – 108.5 22.22 29 15
109 – 114 0 111.5 108.5 – 114.5 0 29 7
115 – 120 7 117.5 114.5 – 120.5 19.44 36 7
N = 36
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Contingency Table
• Has two or more frequencies shown
• Use to record and analyzed the relationship between 2 or more variables
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Example
Table 3.5. The Contingency Table for the Opinion of Viewers on the New Program
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
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Graphical Presentation
• Data are presented in a form of graph or a diagram
• A graph is a geometrical presentation of data
• A graph must have a figure number and a title. If data came from another source, a source note should be incuded.
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Advantages of a Graph
• Helps to visualize certain properties and characteristics of the data at one glance (Tattao)
• Helps facilitate comparison and interpretation without going through the numerical data (Blay)
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TYPES OF GRAPH
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Bar Graph
• Comparing numbers by means of rectangles of uniform widths but of lengths proportional to the numbers being represented (Tattao)
• Can be simple or compound
• Can be vertical or horizontal
• Used both for qualitative and quantitative data
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Simple and Vertical
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Horizontal and Compound
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Line graph
• Shows trends and increases and decreases in data sets
• Obtained by plotting the frequency of the category above the point of the horizontal axis representing that category, and then joining the points with a straight line
• Also used for both qualitative and quantitative data
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From Table to Graph
Temperatures In NY City
Day Temperature
1 43° F
2 53° F
3 50° F
4 57° F
5 59° F
6 67° F
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From Table to GraphValue of Sarah’s Car
Year Value
2001 $24,000
2002 $22,500
2003 $19,700
2004 $17,500
2005 $14,500
2006 $10,000
2007 $ 5,800
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From Table to Graph
Sam’s Weight
Month Weight in kg
January 49
February 54
March 61
April 69
May 73
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Pie Chart
• Useful when presenting the sizes of components that make up a certain whole entity
• A circle subdivided into slices that represents various categories
• Each slice is proportional to the percentages corresponding to that category
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Constructing Pie Chart
Table 3.12. Monthly Expenses of a Filipino Family with Four Children.
Monthly Expenses Amount in Pesos
Food P 9,000
Transportation P 2,000
Miscellaneous P 3,000
Total P 14,000
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Constructing Pie Chart
1. Obtain the percentage for each category.
Example:
Monthly Expenses Amount in Pesos Percentage (%)
Food P 9,000 64.3
Transportation P 2,000 14.3
Miscellaneous P 3,000 21.4
Total P 14,000 100
%100000,14
000,9%
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Constructing Pie Chart2. Convert percentage into degrees using this
conversion factor:
Example:
Monthly Expenses
Amount in Pesos
Percentage (%)
Degrees
Food P 9,000 64.3 231.5
Transportation P 2,000 14.3 51.5
Miscellaneous P 3,000 21.4 77.0
Total P 14,000 100 360
percent 1
degrees 3.6
degrees 231.5degrees 48.231%3.64percent 1
degrees 3.6%3.64
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Constructing Pie Chart3. Use protractor to measure the degrees
needed to make each slices
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Pictograph
• Makes use of symbols
• Used to compare few discrete data usually of one kind
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Example of Pictograph
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Example of Pictograph
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Example of Pictograph
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Statistical Map
• Shows the graphical location
• may contain different symbols on the map
• Legend tells what symbols represent
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Statistical Map
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Histogram• Representation of frequency distribution table• Rectangles has widths that represent class
intervals and areas are proportional to frequencies• Constructed by marking off true class boundaries
along horizontal axis and erecting over each class interval a rectangle whose height equals the frequency of that class
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Example of Histogram
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Table 1. Ages of Patients in Hospital X, June 2004Age (in years) Frequency Class Mark Class
Boundary
60 – 68 1 64 59.5 – 68.5
51 – 59 2 55 50.5 – 59.5
42 – 50 3 46 41.5 – 50.5
33 – 41 2 37 32.5 – 41.5
24 – 32 20 28 23.5 – 32.5
15 – 23 5 19 14.5 – 23.5
6 – 14 3 10 5.5 – 14.5
N = 36
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Frequency Polygon
• Line graph associated with Frequency Distribution Table
• Obtained by plotting the Class Mark vs. the Frequency of that class. Points are joined with straight lines.
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Example of Frequency Polygon
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Ogive
• Graphical presentation of the cumulative frequency of an FDT
• Constructed by plotting lower class boundary of each class vs. the cumulative frequency of the corresponding class. Points are joined with straight lines
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Example of Ogive