Introduction. Data presentation
Frequency distribution. Distribution center indicators. RMS. Covariance. Effects of
diversification. Choice of the weighing method.
More: https://ek.biem.sumdu.edu.ua/
Lecture 2 Organizing and Displaying Data.pptxshakirRahman10
Objectives:
Apply two methods (frequency distribution and graphs) for organizing, summarizing and presenting the data
Construct the frequency table for individual and grouped data
Explore the different graphical representation appropriate for the particular variable scales
Presentation of Data:
Statistical data including (qualitative & quantitative) are generally presented by:
Tables
Frequency table
Graphs
Histogram
Frequency Polygon
Bar Graph
Pie Chart
Frequency Table:
A frequency distribution is the organization of raw data in table form, using classes and frequencies.
It is a method to organize, summarize and present the data in a meaningful way.
Each individual value (in case of smaller range) and each class interval (in case of larger range) is referred to as a ‘class’.
The number of data values contained in a specific class is the ‘frequency’.
Relative Frequency:
Represents the relative percentage to total cases of any class interval. It is obtained by dividing the number of cases in each class interval by the total number of cases and multiplying by 100.
Cumulative Frequency:
Cumulative frequencies are used to show how many data values are accumulated up to and including a specific class.
Cumulative Relative Frequency:
Gives the proportion of individuals having a measurement less than or equal to the upper boundary of the class interval.
Class Boundaries:
Class boundaries are used to separate the classes so that there are no gaps in the frequency distribution.
Mostly used in case of continuous data.
Graphical Presentation of the Data:
Another way of summarizing data is by use of graphs.
Gives a nice overview of the essential features of the dataset.
Should be self explanatory, with a descriptive title, labeled axes and indication of the units of observation.
Histogram:
The Histogram is a graph that displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.
It is used to summarize continuous data.
It consists of horizontal axis which depicts the class interval and a vertical axis which depicts the frequency (or relative frequency) of observations.
Frequency Polygon:
Another commonly used type of graph used to display continuous data only.
Superior to histogram (can compare two frequency distribution)
Formed by joining the midpoints of histogram column tops
Bar Charts:
Convenient graphical device that is used for displaying nominal or ordinal data (example gender, ethnicity, treatment category) and discrete variables.
Pie Chart:
A pie chart is a way of summarizing a set of qualitative data.
This type of chart is a circle divided into a series of segments.
Each segment represents a particular category. The area of each segment is the same proportion of a circle as the category is of the total data set.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Contenu connexe
Similaire à 20- Tabular & Graphical Presentation of data(UG2017-18).ppt
Introduction. Data presentation
Frequency distribution. Distribution center indicators. RMS. Covariance. Effects of
diversification. Choice of the weighing method.
More: https://ek.biem.sumdu.edu.ua/
Lecture 2 Organizing and Displaying Data.pptxshakirRahman10
Objectives:
Apply two methods (frequency distribution and graphs) for organizing, summarizing and presenting the data
Construct the frequency table for individual and grouped data
Explore the different graphical representation appropriate for the particular variable scales
Presentation of Data:
Statistical data including (qualitative & quantitative) are generally presented by:
Tables
Frequency table
Graphs
Histogram
Frequency Polygon
Bar Graph
Pie Chart
Frequency Table:
A frequency distribution is the organization of raw data in table form, using classes and frequencies.
It is a method to organize, summarize and present the data in a meaningful way.
Each individual value (in case of smaller range) and each class interval (in case of larger range) is referred to as a ‘class’.
The number of data values contained in a specific class is the ‘frequency’.
Relative Frequency:
Represents the relative percentage to total cases of any class interval. It is obtained by dividing the number of cases in each class interval by the total number of cases and multiplying by 100.
Cumulative Frequency:
Cumulative frequencies are used to show how many data values are accumulated up to and including a specific class.
Cumulative Relative Frequency:
Gives the proportion of individuals having a measurement less than or equal to the upper boundary of the class interval.
Class Boundaries:
Class boundaries are used to separate the classes so that there are no gaps in the frequency distribution.
Mostly used in case of continuous data.
Graphical Presentation of the Data:
Another way of summarizing data is by use of graphs.
Gives a nice overview of the essential features of the dataset.
Should be self explanatory, with a descriptive title, labeled axes and indication of the units of observation.
Histogram:
The Histogram is a graph that displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.
It is used to summarize continuous data.
It consists of horizontal axis which depicts the class interval and a vertical axis which depicts the frequency (or relative frequency) of observations.
Frequency Polygon:
Another commonly used type of graph used to display continuous data only.
Superior to histogram (can compare two frequency distribution)
Formed by joining the midpoints of histogram column tops
Bar Charts:
Convenient graphical device that is used for displaying nominal or ordinal data (example gender, ethnicity, treatment category) and discrete variables.
Pie Chart:
A pie chart is a way of summarizing a set of qualitative data.
This type of chart is a circle divided into a series of segments.
Each segment represents a particular category. The area of each segment is the same proportion of a circle as the category is of the total data set.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
2. Objectives of this session
• To know how to make frequency distributions and its
importance
• To know different terminology in frequency distribution
table
• To learn different graphs/diagrams for graphical
presentation of data.
2
5. Frequency Distributions
• Data distribution – pattern of variability.
• The center of a distribution
• The ranges
• The shapes
• Simple frequency distributions
• Grouped frequency distributions
5
6. Simple Frequency Distribution
• The number of times that score occurs
• Make a table with highest score at top and decreasing
for every possible whole number
• N (total number of scores) always equals the sum of the
frequency
• f = N
6
7. Categorical or Qualitative
Frequency Distributions
• What is a categorical frequency distribution?
A categorical frequency distribution represents data that
can be placed in specific categories, such as gender,
blood group, & hair color, etc.
8. Categorical or Qualitative
Frequency Distributions -- Example
Example: The blood types of 25 blood donors are
given below. Summarize the data using a frequency
distribution.
AB B A O B
O B O A O
B O B B B
A O AB AB O
A B AB O A
10. Quantitative Frequency
Distributions -- Ungrouped
• What is an ungrouped frequency distribution?
An ungrouped frequency distribution simply lists the
data values with the corresponding frequency counts
with which each value occurs.
11. Quantitative Frequency Distributions –
Ungrouped -- Example
• Example: The at-rest pulse rate for 16 athletes at a
meet were 57, 57, 56, 57, 58, 56, 54, 64, 53, 54, 54,
55, 57, 55, 60, and 58. Summarize the information
with an ungrouped frequency distribution.
13. Example of a simple frequency distribution (ungrouped)
• 5 7 8 1 5 9 3 4 2 2 3 4 9 7 1 4 5 6 8 9 4 3 5 2 1 (No. of children in 25
families)
f
• 9 3
• 8 2
• 7 2
• 6 1
• 5 4
• 4 4
• 3 3
• 2 3
• 1 3
f = 25 (No. of families)
14. Relative Frequency Distribution
• Proportion of the total N
• Divide the frequency of each score by N
• Rel. f = f/N
• Sum of relative frequencies should equal 1.0
• Gives us a frame of reference
14
17. Cumulative Frequency
Distributions
• cf = cumulative frequency: number of scores at or below
a particular score
• A score’s standing relative to other scores
• Count from lower scores and add the simple frequencies
for all scores below that score
17
20. Quantitative Frequency
Distributions -- Grouped
• What is a grouped frequency distribution? A grouped
frequency distribution is obtained by constructing
classes (or intervals) for the data, and then listing the
corresponding number of values (frequency counts) in
each interval.
21. 21
Patien
t No
Hb
(g/dl)
Patien
t No
Hb
(g/dl)
Patien
t No
Hb
(g/dl)
1 12.0 11 11.2 21 14.9
2 11.9 12 13.6 22 12.2
3 11.5 13 10.8 23 12.2
4 14.2 14 12.3 24 11.4
5 12.3 15 12.3 25 10.7
6 13.0 16 15.7 26 12.5
7 10.5 17 12.6 27 11.8
8 12.8 18 9.1 28 15.1
9 13.2 19 12.9 29 13.4
10 11.2 20 14.6 30 13.1
Tabulate the hemoglobin values of 30 adult
male patients listed below
22. Steps for making a table
Step1 Find Minimum (9.1) & Maximum (15.7)
Step 2 Calculate difference 15.7 – 9.1 = 6.6
Step 3 Decide the number and width of
the classes (7 c.l) 9.0 -9.9, 10.0-10.9,----
Step 4 Prepare dummy table –
Hb (g/dl), Tally mark, No. patients
22
24. 24
Hb (g/dl) No. of
patients
9.0 – 9.9
10.0 – 10.9
11.0 – 11.9
12.0 – 12.9
13.0 – 13.9
14.0 – 14.9
15.0 – 15.9
1
3
6
10
5
3
2
Total 30
Table Frequency distribution of 30 adult male
patients by Hb
25. 25
Table Frequency distribution of adult patients by
Hb and gender
Hb
(g/dl)
Gender Total
Male Female
<9.0
9.0 – 9.9
10.0 – 10.9
11.0 – 11.9
12.0 – 12.9
13.0 – 13.9
14.0 – 14.9
15.0 – 15.9
0
1
3
6
10
5
3
2
2
3
5
8
6
4
2
0
2
4
8
14
16
9
5
2
Total 30 30 60
26. 26
Elements of a Table
Ideal table should have
Number
Title
Column headings
Foot-notes
Number - Table number for identification in a report
Title, place - Describe the body of the table,
variables,
Time period (What, how classified, where and when)
Column - Variable name, No. , Percentages (%), etc.,
Heading
Foot-note(s) - to describe some column/row
headings, special cells, source, etc.,
27. DIAGRAMS/GRAPHS
Qualitative data (Nominal & Ordinal)
--- Bar charts (one or two groups)
--- Pie charts
Quantitative data (discrete & continuous)
--- Histogram
--- Frequency polygon (curve)
--- Stem-and –leaf plot
--- Box-and-whisker plot
--- Scatter diagram 27
34. Descriptive statistics report: Boxplot
34
- minimum score
- maximum score
- lower quartile
- upper quartile
- median
- mean
- The skew of the distribution
positive skew: mean > median & high-score whisker is
longer
negative skew: mean < median & low-score whisker is
longer
37. 37
10%
20%
70%
Mild
Moderate
Severe
The prevalence of different degree of Hypertension
in the population
Pie Chart
•Circular diagram – total -100%
•Divided into segments each
representing a category
•Decide adjacent category
•The amount for each category is
proportional to slice of the pie
38. Percent of people dying from
top 10 causes of death in the United States in 2001
Top 10 causes of death: pie chart
Each slice represents a piece of one whole. The size of a slice depends on what
percent of the whole this category represents.
39. Bar Graphs
39
9
12
20
16
12
8
20
0
5
10
15
20
25
Smo Alc Chol DM HTN No
Exer
F-H
Riskfactor
Number
The distribution of risk factor among cases with
Cardio vascular Diseases
Heights of the bar indicates
frequency
Frequency in the Y axis and
categories of variable in the X
axis
The bars should be of equal
width and no touching the
other bars
40. HIV cases enrolment in USA by gender
0
2
4
6
8
10
12
1986 1987 1988 1989 1990 1991 1992
Year
Enrollment
(hundred)
Men
Women
40
Bar chart
41. HIV cases Enrollment
in USA by gender
0
2
4
6
8
10
12
14
16
18
1986 1987 1988 1989 1990 1991 1992
Year
Enrollment
(Thousands)
Women
Men
41
Stocked bar
chart
43. General rules for designing graphs
• A graph should have a self-explanatory legend
• A graph should help reader to understand data
• Axis labeled, units of measurement indicated
• Scales important. Start with zero (otherwise // break)
• Avoid graphs with three-dimensional impression, it may
be misleading (reader visualize less easily
43
44. 44
Tabular and Graphical Procedures
Data
Qualitative Data Quantitative Data
Tabular
Methods
Tabular
Methods
Graphical
Methods
Graphical
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•% Freq. Dist.
•Cross-tabulation
•Bar Graph
•Pie Chart
•Frequency
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
•Cross tabulation
•Histogram
•Freq. curve
•Box plot
•Scatter
Diagram
•Stem-and-Leaf
Display