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Lecture 2 Organizing and Displaying Data.pptx
Organizing and Displaying
Data
Shakir Rahman
BScN, MScN, MSc Applied Psychology, PhD Nursing (Candidate)
University of Minnesota USA.
Principal & Assistant Professor
Ayub International College of Nursing & AHS Peshawar
Visiting Faculty
Swabi College of Nursing & Health Sciences Swabi
Nowshera College of Nursing & Health Sciences Nowshera
Objectives
Bythe endof this sessionthe learnerswill beableto:
• Apply two methods (frequency distribution and graphs) for
organizing,summarizingandpresentingthedata
• Construct the frequency table for individual and grouped
data
• Explore the different graphical representation appropriate
for the particular variablescales
Presentation of Data
Statisticaldata including (qualitative & quantitative)aregenerally
presentedby:
• Tables
 Frequencytable
• 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 datain a
meaningfulway.
• Eachindividual value(in caseof smaller range)andeach class
interval (in caseof larger range) is referred to as a ‘class’.
• The number of data values contained in a specificclass is the
‘frequency’.
Example 1
Suppose we are interested in studying the number of children in
the families of a community. The following data has been
collected based on a random sample of n=30 families.
2,2,5,3,0,1,3,2,3,4,1,3,4,5,7,3,2,4,1,0,5,8,6,5,4,2,4,4,7,6
Example 1
• Suppose we are interested in studying the number of
children in the families of a community. The following data
has been collected based on a random sample of n=30
families.
2, 2,5,3,0,1,3,2,3,4,1,3,4,5,7,3,2,4,1,0,5,8,6,5,4,2,4,4,7,6
Step #1
• Arrangedata in ascendingorder
0,0,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,6,6,7,7,8
• Smalerrangeof data--- Individual data values canbe
used for making the frequency table
Step # 2
X = Number of children f = Frequency
0 2
1 3
2 5
3 5
4 6
5 4
6 2
7 2
8 1
Construct a Frequency Table
Step # 3
5 out of 30 families had 2children
4 out of 30 families had 5children
Interpretation
X=# of children f = Frequency
0 2
1 3
2 5
3 5
4 6
5 4
6 2
7 2
8 1
Example 2
• Now suppose we need to construct a similar frequency table for the
age of patients with heart related problemsin a clinic.The following
data has been collected based on random sample of n=30 patients who
went to the emergency room of the clinic for heart relatedproblems.
Following isthe data set:
42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56,58,66,54,
56,52,40,55,71,69
Example 2
• Now supposewe need to construct a similar frequency table for the
ageof patients with heart related problems in a clinic. The following
data has been collected basedon random sample of n=30 patients who
went to the emergencyroomof the clinicfor heart relatedproblems.
Followingisthe dataset:
42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56,
58,66,54,56,52,40,55,71,69
Step #1
• Arrange data in ascendingorder
32,36,38,40,40,42,43,45,47,51,51,52,52,53,53,54,55,56,56,58,
59,61,62,63,64,66,67,68,69,71
Step # 1
• Range of data increases---Data willhave to be grouped into
classesfor making the frequency table.
• Find range of the data
Range = Max value – Min Smallest value
71 – 32 = 39
• Decide number of classes (depends on number of
observations). Ranges between 5-15
• Calculate class width
Class width = Range_____
Number of classes
= 39/8 = 4.8 = 5
Step # 2
Age ( in years) Class
Limits
f = Frequency
32-36 2
37-41 3
42-46 3
47-51 3
52-56 8
57-61 3
62-66 4
67-71 4
Total 30
Construct a Frequency Table
Interpretation
Age ( in years)
Class Limits
f = Frequency
32-36 2
37-41 3
42-46 3
47-51 3
52-56 8
57-61 3
62-66 4
67-71 4
Total 30
Interpretation: 4 patients are falling between the ages of 62-66 years
Step # 3
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.
Relative Frequency = Frequency x100
Total observations
Relative
frequency
X= Number of children f = Frequency CF = Relative Frequency
0 2 2/30=0.067*100 =6.7%
1 3 3/30=0.100*100= 10%
2 5 5/30=0.167*100=16.7%
3 5 5/30=0.167*100=16.7%
4 6 6/30=0.200*100=20%
5 4 4/30=0.133*100=13.3%
6 2 2/30=0.067*100=6.7%
7 2 2/30=0.067*100=6.7%
8 1 1/30=0.033*100=3.3%
Interpretation??
6.7% of the families had 2 children
3.3% families had 8 children
Relative Frequency
Cumulative Frequency
Cumulative frequencies are used to show how many data values
are accumulated up to and including a specific class.
X= # of
children
f = Frequency
Rf= Relative Frequency
cf = Cumulative
frequency
0 2 2/30=0.067*100 =6.7% 2
1 3 3/30=0.100*100= 10% 5
2 5 5/30=0.167*100=16.7% 10
3 5 5/30=0.167*100=16.7% 15
4 6 6/30=0.200*100=20% 21
5 4 4/30=0.133*100=13.3% 25
6 2 2/30=0.067*100=6.7% 27
7 2 2/30=0.067*100=6.7% 29
8 1 1/30=0.033*100=3.3% 30
Cumulative Frequency
X=# of
children
Frequ
ency
Relative frequency Cumulative frequency
0 2 2/30=0.067*100 =6.7% 2
1 3 3/30=0.100*100= 10% 5
2 5 5/30=0.167*100=16.7% 10
3 5 5/30=0.167*100=16.7% 15
4 6 6/30=0.200*100=20% 21
5 4 4/30=0.133*100=13.3% 25
6 2 2/30=0.067*100=6.7% 27
7 2 2/30=0.067*100=6.7% 29
8 1 1/30=0.033*100=3.3% 30
Interpretation
10 families had 2 or less than 2 children
21 families had less than 5 children
25 families had 1 or more than 1 children
Cumulative Relative Frequency
• Gives the proportion of individuals having a
measurement less than or equal to the upper boundary
of the class interval.
Relative cumulative Frequency=Cumulative Frequency x100
Total observation
Cumulative Frequency &Relative
Cumulative Frequency
X= # of
children
frequency Relative
frequency
Cumulative
frequency
crf =
Cumulative
relative
frequency
0 2 2/30=0.067*100=6.7% 2 2/30=0.067*100=6.7%
1 3 3/30=0.100*100= 10% 5 5/30=0.167*100=16.7%
2 5 5/30=0.167*100=16.7% 10 10/30=0.333*100=33.3%
3 5 5/30=0.167*100=16.7% 15 15/30=0.500*100=50.0%
4 6 6/30=0.200*100=20% 21 21/30=0.700*100=70%
5 4 4/30=0.133*100=13.3% 25 25/30=0.833*100=83.3%
6 2 2/30=0.067*100=6.7% 27 27/30=0.90*100=90%
7 2 2/30=0.067*100=6.7% 29 29/30=0.967*100=96.7%
8 1 1/30=0.033*100=3.3% 30 30/30=1.00*100=100%
Interpretation?
33.3% families had 2 or less than 2 children
70% families had less than 5 children
83.3% families had more than 1 children
Example 2
• Now suppose we need to construct a similar frequency
table for the age of patients with heart related problems
in a clinic. The following data has been collected based
on random sample of n=30 patients who went to the
emergencyroom of the clinic for heart relatedproblems.
Following isthe dataset:
42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56,
58,66,54,56,52,40,55,71,69
Frequency Table
Age ( in years)
Class Limits
Frequency Relative frequency
32-36 2 2/30=0.067*100=6.7%
37-41 3 3/30=0.100*100=10%
42-46 3 3/30=0.100*100=10%
47-51 3 3/30=0.100*100=10%
52-56 8 8/30=0.267*100=26.7%
57-61 3 3/30=0.100*100=10%
62-66 4 4/30=0.134*100=13.4%
67-71 4 4/30=0.134*100=13.4%
Total 30 100%
Interpretation: 26.7% of the patients are between 52-56 years of age
Frequency Table
Age ( in years)
Class Limits
Frequency Relative frequency Cumulative
frequency
Cumulative relative
frequency
32-36 2 2/30=0.067*100=6.7% 2 2/30=0.067*100=6.7%
37-41 3 3/30=0.100*100=10% 5 5/30=0.167*100=16.7%
42-46 3 3/30=0.100*100=10% 8 8/30=0.267*100=26.7%
47-51 3 3/30=0.100*100=10% 11 11/30=0.367*100=36.7%
52-56 8 8/30=0.267*100=26.7% 19 19/30=0.633*100=63.3%
57-61 3 3/30=0.100*100=10% 22 22/30=0.733*100=73.3%
62-66 4 4/30=0.134*100=13.4% 26 26/30=0.867*100=86.7%
67-71 4 4/30=0.134*100=13.4% 30 30/30=1.00*100=100%
Total 30 100%
Interpretation
• 11patients arebetween the agesof 32to51
• 86.7%patients arebelow 67yearsof age
• 63.3%patients are lessthan 57yearsof age
• 83.3%patients aremore than 41yearsold
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 wayof summarizing data isby useofgraphs.
• Givesanice overview of the essential features of the
dataset.
• Shouldbe self explanatory, with adescriptive title,labeled
axesand indication ofthe units ofobservation.
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 usedto summarizecontinuousdata.
• It consistsof horizontal axiswhich depicts the class interval and a
vertical axiswhich depicts the frequency (or relative frequency) of
observations.
Example: Distribution of the salaries of the
acme corporation
Frequency Polygon
• Another commonly used type of graph used to display
continuous dataonly.
• Superior to histogram (can compare two frequency
distribution)
• Formed by joining the midpoints of histogram column tops
Example: Distribution of salaries of
the Acme Corporation
Bar Charts
• Convenient graphical device that is used for displaying
nominal or ordinal data (example gender,ethnicity, treatment
category) and discretevariables.
Example 1.Number of police officers
in Pakistan, 1993to 2001
Example 2
Pie Chart
• A piechartis awayof summarizingaset of qualitativedata.
• Thistype of chart is acircle divided into aseriesofsegments.
• Each segment represents a particular category. The area of
each segment is the same proportion of a circle as the
category isof the totaldata set.
Example 1
• Favoritemoviesin aclass
Example 2.Music preferences in
young adults 14to 19
Example 3.Student and faculty
response to the poll 'Should SBSON
adopt student uniforms?'
Acknowledgments
Dr Tazeen Saeed Ali
RM, RM, BScN, MSc ( Epidemiology &
Biostatistics), Ph.D. (Medical Sciences),
Post Doctorate (Health Policy & Planning)
Associate Dean School of Nursing &
Midwifery
The Aga Khan University Karachi.
Kiran Ramzan Ali Lalani
BScN, (MSc Epidemiology & Biostatistics)
Aga Khan University Karachi
Lecture 2 Organizing and Displaying Data.pptx
Lecture 2 Organizing and Displaying Data.pptx

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Lecture 2 Organizing and Displaying Data.pptx

  • 2. Organizing and Displaying Data Shakir Rahman BScN, MScN, MSc Applied Psychology, PhD Nursing (Candidate) University of Minnesota USA. Principal & Assistant Professor Ayub International College of Nursing & AHS Peshawar Visiting Faculty Swabi College of Nursing & Health Sciences Swabi Nowshera College of Nursing & Health Sciences Nowshera
  • 3. Objectives Bythe endof this sessionthe learnerswill beableto: • Apply two methods (frequency distribution and graphs) for organizing,summarizingandpresentingthedata • Construct the frequency table for individual and grouped data • Explore the different graphical representation appropriate for the particular variablescales
  • 4. Presentation of Data Statisticaldata including (qualitative & quantitative)aregenerally presentedby: • Tables  Frequencytable • Graphs  Histogram  Frequency Polygon  Bar Graph  Pie Chart
  • 5. 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 datain a meaningfulway. • Eachindividual value(in caseof smaller range)andeach class interval (in caseof larger range) is referred to as a ‘class’. • The number of data values contained in a specificclass is the ‘frequency’.
  • 6. Example 1 Suppose we are interested in studying the number of children in the families of a community. The following data has been collected based on a random sample of n=30 families. 2,2,5,3,0,1,3,2,3,4,1,3,4,5,7,3,2,4,1,0,5,8,6,5,4,2,4,4,7,6
  • 7. Example 1 • Suppose we are interested in studying the number of children in the families of a community. The following data has been collected based on a random sample of n=30 families. 2, 2,5,3,0,1,3,2,3,4,1,3,4,5,7,3,2,4,1,0,5,8,6,5,4,2,4,4,7,6
  • 8. Step #1 • Arrangedata in ascendingorder 0,0,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,6,6,7,7,8 • Smalerrangeof data--- Individual data values canbe used for making the frequency table
  • 9. Step # 2 X = Number of children f = Frequency 0 2 1 3 2 5 3 5 4 6 5 4 6 2 7 2 8 1 Construct a Frequency Table
  • 10. Step # 3 5 out of 30 families had 2children 4 out of 30 families had 5children Interpretation X=# of children f = Frequency 0 2 1 3 2 5 3 5 4 6 5 4 6 2 7 2 8 1
  • 11. Example 2 • Now suppose we need to construct a similar frequency table for the age of patients with heart related problemsin a clinic.The following data has been collected based on random sample of n=30 patients who went to the emergency room of the clinic for heart relatedproblems. Following isthe data set: 42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56,58,66,54, 56,52,40,55,71,69
  • 12. Example 2 • Now supposewe need to construct a similar frequency table for the ageof patients with heart related problems in a clinic. The following data has been collected basedon random sample of n=30 patients who went to the emergencyroomof the clinicfor heart relatedproblems. Followingisthe dataset: 42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56, 58,66,54,56,52,40,55,71,69
  • 13. Step #1 • Arrange data in ascendingorder 32,36,38,40,40,42,43,45,47,51,51,52,52,53,53,54,55,56,56,58, 59,61,62,63,64,66,67,68,69,71
  • 14. Step # 1 • Range of data increases---Data willhave to be grouped into classesfor making the frequency table. • Find range of the data Range = Max value – Min Smallest value 71 – 32 = 39 • Decide number of classes (depends on number of observations). Ranges between 5-15 • Calculate class width Class width = Range_____ Number of classes = 39/8 = 4.8 = 5
  • 15. Step # 2 Age ( in years) Class Limits f = Frequency 32-36 2 37-41 3 42-46 3 47-51 3 52-56 8 57-61 3 62-66 4 67-71 4 Total 30 Construct a Frequency Table
  • 16. Interpretation Age ( in years) Class Limits f = Frequency 32-36 2 37-41 3 42-46 3 47-51 3 52-56 8 57-61 3 62-66 4 67-71 4 Total 30 Interpretation: 4 patients are falling between the ages of 62-66 years Step # 3
  • 17. 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. Relative Frequency = Frequency x100 Total observations
  • 18. Relative frequency X= Number of children f = Frequency CF = Relative Frequency 0 2 2/30=0.067*100 =6.7% 1 3 3/30=0.100*100= 10% 2 5 5/30=0.167*100=16.7% 3 5 5/30=0.167*100=16.7% 4 6 6/30=0.200*100=20% 5 4 4/30=0.133*100=13.3% 6 2 2/30=0.067*100=6.7% 7 2 2/30=0.067*100=6.7% 8 1 1/30=0.033*100=3.3% Interpretation?? 6.7% of the families had 2 children 3.3% families had 8 children Relative Frequency
  • 19. Cumulative Frequency Cumulative frequencies are used to show how many data values are accumulated up to and including a specific class. X= # of children f = Frequency Rf= Relative Frequency cf = Cumulative frequency 0 2 2/30=0.067*100 =6.7% 2 1 3 3/30=0.100*100= 10% 5 2 5 5/30=0.167*100=16.7% 10 3 5 5/30=0.167*100=16.7% 15 4 6 6/30=0.200*100=20% 21 5 4 4/30=0.133*100=13.3% 25 6 2 2/30=0.067*100=6.7% 27 7 2 2/30=0.067*100=6.7% 29 8 1 1/30=0.033*100=3.3% 30
  • 20. Cumulative Frequency X=# of children Frequ ency Relative frequency Cumulative frequency 0 2 2/30=0.067*100 =6.7% 2 1 3 3/30=0.100*100= 10% 5 2 5 5/30=0.167*100=16.7% 10 3 5 5/30=0.167*100=16.7% 15 4 6 6/30=0.200*100=20% 21 5 4 4/30=0.133*100=13.3% 25 6 2 2/30=0.067*100=6.7% 27 7 2 2/30=0.067*100=6.7% 29 8 1 1/30=0.033*100=3.3% 30 Interpretation 10 families had 2 or less than 2 children 21 families had less than 5 children 25 families had 1 or more than 1 children
  • 21. Cumulative Relative Frequency • Gives the proportion of individuals having a measurement less than or equal to the upper boundary of the class interval. Relative cumulative Frequency=Cumulative Frequency x100 Total observation
  • 22. Cumulative Frequency &Relative Cumulative Frequency X= # of children frequency Relative frequency Cumulative frequency crf = Cumulative relative frequency 0 2 2/30=0.067*100=6.7% 2 2/30=0.067*100=6.7% 1 3 3/30=0.100*100= 10% 5 5/30=0.167*100=16.7% 2 5 5/30=0.167*100=16.7% 10 10/30=0.333*100=33.3% 3 5 5/30=0.167*100=16.7% 15 15/30=0.500*100=50.0% 4 6 6/30=0.200*100=20% 21 21/30=0.700*100=70% 5 4 4/30=0.133*100=13.3% 25 25/30=0.833*100=83.3% 6 2 2/30=0.067*100=6.7% 27 27/30=0.90*100=90% 7 2 2/30=0.067*100=6.7% 29 29/30=0.967*100=96.7% 8 1 1/30=0.033*100=3.3% 30 30/30=1.00*100=100% Interpretation? 33.3% families had 2 or less than 2 children 70% families had less than 5 children 83.3% families had more than 1 children
  • 23. Example 2 • Now suppose we need to construct a similar frequency table for the age of patients with heart related problems in a clinic. The following data has been collected based on random sample of n=30 patients who went to the emergencyroom of the clinic for heart relatedproblems. Following isthe dataset: 42,38,51,53,40,68,62,36,32,45,51,67,53,59,47,63,52,64,61,43,56, 58,66,54,56,52,40,55,71,69
  • 24. Frequency Table Age ( in years) Class Limits Frequency Relative frequency 32-36 2 2/30=0.067*100=6.7% 37-41 3 3/30=0.100*100=10% 42-46 3 3/30=0.100*100=10% 47-51 3 3/30=0.100*100=10% 52-56 8 8/30=0.267*100=26.7% 57-61 3 3/30=0.100*100=10% 62-66 4 4/30=0.134*100=13.4% 67-71 4 4/30=0.134*100=13.4% Total 30 100% Interpretation: 26.7% of the patients are between 52-56 years of age
  • 25. Frequency Table Age ( in years) Class Limits Frequency Relative frequency Cumulative frequency Cumulative relative frequency 32-36 2 2/30=0.067*100=6.7% 2 2/30=0.067*100=6.7% 37-41 3 3/30=0.100*100=10% 5 5/30=0.167*100=16.7% 42-46 3 3/30=0.100*100=10% 8 8/30=0.267*100=26.7% 47-51 3 3/30=0.100*100=10% 11 11/30=0.367*100=36.7% 52-56 8 8/30=0.267*100=26.7% 19 19/30=0.633*100=63.3% 57-61 3 3/30=0.100*100=10% 22 22/30=0.733*100=73.3% 62-66 4 4/30=0.134*100=13.4% 26 26/30=0.867*100=86.7% 67-71 4 4/30=0.134*100=13.4% 30 30/30=1.00*100=100% Total 30 100%
  • 26. Interpretation • 11patients arebetween the agesof 32to51 • 86.7%patients arebelow 67yearsof age • 63.3%patients are lessthan 57yearsof age • 83.3%patients aremore than 41yearsold
  • 27. 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.
  • 28. Graphical Presentation of the Data • Another wayof summarizing data isby useofgraphs. • Givesanice overview of the essential features of the dataset. • Shouldbe self explanatory, with adescriptive title,labeled axesand indication ofthe units ofobservation.
  • 29. 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 usedto summarizecontinuousdata. • It consistsof horizontal axiswhich depicts the class interval and a vertical axiswhich depicts the frequency (or relative frequency) of observations.
  • 30. Example: Distribution of the salaries of the acme corporation
  • 31. Frequency Polygon • Another commonly used type of graph used to display continuous dataonly. • Superior to histogram (can compare two frequency distribution) • Formed by joining the midpoints of histogram column tops
  • 32. Example: Distribution of salaries of the Acme Corporation
  • 33. Bar Charts • Convenient graphical device that is used for displaying nominal or ordinal data (example gender,ethnicity, treatment category) and discretevariables.
  • 34. Example 1.Number of police officers in Pakistan, 1993to 2001
  • 36. Pie Chart • A piechartis awayof summarizingaset of qualitativedata. • Thistype of chart is acircle divided into aseriesofsegments. • Each segment represents a particular category. The area of each segment is the same proportion of a circle as the category isof the totaldata set.
  • 38. Example 2.Music preferences in young adults 14to 19
  • 39. Example 3.Student and faculty response to the poll 'Should SBSON adopt student uniforms?'
  • 40. Acknowledgments Dr Tazeen Saeed Ali RM, RM, BScN, MSc ( Epidemiology & Biostatistics), Ph.D. (Medical Sciences), Post Doctorate (Health Policy & Planning) Associate Dean School of Nursing & Midwifery The Aga Khan University Karachi. Kiran Ramzan Ali Lalani BScN, (MSc Epidemiology & Biostatistics) Aga Khan University Karachi