2 organizing and graphing data
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Probability & StatisticsProbability & StatisticsProbability & StatisticsProbability & Statistics
Organizing & Graphing DataOrganizing & Graphing Data
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Introduction
When data is collected it needs to be organized insome way so that the pattern of the results canbe seen.
For example, below is an unordered list of theheights of the girls in a first year class, measuredin cm.141, 150, 144, 145, 150, 148, 136, 134, 144, 155,147, 151, 154
We could rearrange it from smallest to highest
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Stem-and-Leaf Diagram
A simple way to see distribution details in a dataset
METHOD: Separate the sorted data series
into leading digits (the stem) and
the trailing digits (theleaves)
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Graphing Data
Goals for effective data presentation:
Present data to display essential information
Communicate complex ideas clearly and accurately
Avoid distortion that might convey the wrong
message
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Types of Data
Data
Categorical Numerical
Discrete Continuous
Examples:
Marital Status Are you registered to
vote? Eye Color
(Defined categories or
groups)
Examples:
Number of Children Defects per hour
(Counted items)
Examples:
Weight Voltage
(Measured characteristics)
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GraphicalPresentation of Data
Data in raw form are usually not easyto use for decision making
Some type oforganizationis needed
Table
Graph The type of graph to use depends on
the variable being summarized
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GraphicalPresentation of Data
Techniques reviewed in this chapter:
Categorical
Variables
Numerical
Variables
Frequency distribution Bar chart Pie chart Pareto diagram
Line chart Frequency distribution Histogram and ogive Stem-and-leaf display Scatter plot
(continued)
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The FrequencyDistribution Table
Example: Hospital Patients by Unit
Hospital Unit Number of Patients
Cardiac Care 1,052
Emergency 2,245
Intensive Care 340Maternity 552
Surgery 4,630(Variables are
categorical)
Summarize data by category
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Bar and Pie
Charts Bar charts and Pie charts are
often used for qualitative(category) data
Height of bar or size of pie sliceshows the frequency orpercentage for each category
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Bar Chart Example
Hospital Patients by Un
0
1000
2000
3000
4000
5000
Card
iac
Care
ergen
cy
ntensive
Care
atern
ity
Surgery
Nu
mberof
patientsperyear
Hospital NumberUnit of Patients
Cardiac Care 1,052
Emergency 2,245
Intensive Care 340
Maternity 552
Surgery 4,630
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Hospital Patients by Un
Emergenc
25%
Maternit6%
Surger53%
Cardiac Car
12%
Intensive Car
4%
Pie Chart Example
(Percentages
are rounded to
the nearest
percent)
Hospital Number % ofUnit of Patients Total
Cardiac Care 1,052 11.93
Emergency 2,245 25.46
Intensive Care 340 3.86
Maternity 552 6.26
Surgery 4,630 52.50
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Pareto Diagram
Used to portray categorical data
A bar chart, where categories are shown in
descending order of frequency
A cumulative polygon is often shown in the
same graph
Used to separate the vital few from the
trivial many
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Example: 400 defective items areexamined for cause of defect:
Source of
Manufacturing Error
Number of
defectsBad Weld 34
Poor Alignment 223
Missing Part 25
Paint Flaw 78Electrical Short 19
Cracked case 21
Total 400
Pareto Diagram Example
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Step 1: Sort by defect cause, in descending order
Step 2: Determine % in each category
Source of
Manufacturing
Error
Number of defects % of Total
Defects
Poor Alignment 223 55.75
Paint Flaw 78 19.50
Bad Weld 34 8.50
Missing Part 25 6.25Cracked case 21 5.25
Electrical Short 19 4.75
Total 400 100%
Pareto Diagram Example
(continued)
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Pareto Diagram Example
cumulative%
(linegraph)
%
ofde
fectsineach
category
(bargra
ph)
Pareto Diagram: Cause of M anufactur in
0 %
1 0%
2 0%
3 0%
4 0%
5 0%
6 0%
P o o r Alig n m e n t P a in t F la w B ad W e ld M is s in g Pa rt C ra c ke d ca s e E le c tr ic a l S h or t
0 %
1 0%
2 0%
3 0%
4 0%
5 0%
6 0%
7 0%
8 0%
9 0%
100%
Step 3: Show results graphically(continued)
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Graphs for Time-Series
Data A line chart (time-series plot) is used toshow the values of a variable over time
Time is measured on the horizontal axis
The variable of interest is measured onthe vertical axis
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Line Chart ExampleMagazine Subscriptions by Ye
0
50
100
150
200
250
300
350
1
990
1
991
1
992
1
993
1
994
1
995
1
996
1
997
1
998
1
999
2
000
2
001
2
002
2
003
2
004
2
005
2
006
Thousandsofsubscribers
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Frequency Histogram
One of the more commonly usedpictorials in statistics is the
frequency histogram, which in someways similar to a bar chart and tellshow many items are in each numericalcategory.
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Example of Frequency
Histogram
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Example of Frequency
Histogram
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Frequency Polygon
In this chart, the frequency of each class
is indicated by points or dots drawn at themidpoints of each class interval.
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Example of Frequency Polygon
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Cumulative Frequency or Ogive
An ogive (a cumulative line graph) is bestused when you want to display the total atany given time.
The relative slopes from point to point willindicate greater or lesser increases; forexample, a steeper slope means a greater
increase than a more gradual slope.
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Example of Cumulative Frequencyor Ogive
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