chapter 2 (summarizing data)_st
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Chapter 2Chap
ter 2
Summarizing dataSummarizing data
Summarizing Qualitative DataSummarizing Qualitative Data
Summarizing Quantitative DataSummarizing Quantitative Data
Part A
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Why summarizing data?Why summarizing data?
Raw dataRaw data
Disadvantage?Disadvantage?
How to extract information from the data?How to extract information from the data?
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Example: hours worked in one week by employeesExample: hours worked in one week by employees
in a companys production departmentin a companys production department
46.346.3 45.145.1 45.645.6 45.645.6 46.146.1 45.045.0 43.543.5 39.239.2 39.239.2 39.139.1
39.239.2
42.342.3
39.639.6
39.539.5
38.938.9
44.444.4
43.443.4
43.243.2
43.843.8
39.139.1
44.244.2 43.543.5 42.042.0 43.143.1 42.442.4 42.442.4 42.842.8 42.942.9 43.143.1 39.839.8
41.341.3 40.040.0 39.639.6 39.739.7 42.142.1 39.839.8 44.344.3 46.246.2 41.341.3 40.840.8
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Example: arrayed dataExample: arrayed data
38.938.9 39.139.1 39.139.1 39.239.2 39.239.2 39.239.2 39.539.5 39.639.6 39.639.6 39.739.7
39.839.8 39.839.8 40.040.0 40.840.8 41.341.3 41.341.3 42.042.0 42.142.1 42.342.3 42.442.4
42.442.4 42.842.8 42.942.9 43.143.1 43.143.1 43.243.2 43.443.4 43.543.5 43.543.5 43.843.8
44.244.2 44.344.3 44.444.4 45.045.0 45.145.1 45.645.6 45.645.6 46.146.1 46.246.2 46.346.3
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I. Summarizing Qualitative DataI. Summarizing Qualitative Data
Frequency DistributionFrequency Distribution
Relative Frequency DistributionRelative Frequency Distribution
Percent Frequency DistributionPercent Frequency Distribution Bar GraphBar Graph
Pie ChartPie Chart
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AAfrequency distribution?freq
uency distribution?AAfrequency distribution?freq
uency distribution?
Objective?Objective?Objective?Objective?
Frequency Distributionrequency Distribution
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Example: Marada InnExample: Marada Inn
Guests staying at Marada Inn wereGuests staying at Marada Inn wereasked to rate the quality of theirasked to rate the quality of their
accommodations as beingaccommodations as being exce l l en tx ce l l en t ,,above a ve r agebove a ve r age ,, ave rageve r age ,, be l ow ave ragee l ow ave rage , or, orpoo roo r . The ratings provided by a sample of 20 guests are:. The ratings provided by a sample of 20 guests are:
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Example: Marada InnExample: Marada Inn
Below AverageBelow Average
Above AverageAbove Average
Above AverageAbove Average
AverageAverage
Above AverageAbove Average
AverageAverage
Above AverageAbove Average
AverageAverage
Above AverageAbove Average
Below AverageBelow Average
PoorPoor
ExcellentExcellent
Above AverageAbove Average
AverageAverage
Above AverageAbove Average
Above AverageAbove Average
Below AverageBelow Average
PoorPoor
Above AverageAbove Average
AverageAverage
AverageAverage
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Frequency DistributionFrequency Distribution
PoorPoor
Below AverageBelow Average
AverageAverage
Above AverageAbove Average
ExcellentExcellent
22
33
55
99
11
TotalTotal 2020
RatingRating FrequencyFrequency
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TheThe relative frequencyrelative frequency of a class?of a class?TheThe relative frequencyrelative frequency of a class?of a class?
AArelative frequency distribution?relative frequency distribution?AArelative frequency distribution?relative frequency distribution?
Relative Frequency DistributionRelative Frequency Distribution
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Percent Frequency DistributionPercent Frequency Distribution
TheThe percent frequencypercent frequency of a class?of a class?TheThe percent frequencypercent frequency of a class?of a class?
AApercent frequency distribution?percent frequency distribution?AApercent frequency distribution?percent frequency distribution?
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Relative Frequency andRelative Frequency and
Percent Frequency DistributionsPercent Frequency Distributions
PoorPoorBelow AverageBelow Average
AverageAverage
Above AverageAbove Average
ExcellentExcellent
.10.10
.15.15
.25.25
.45.45
.05.05TotalTotal 1.001.00
10101515
2525
4545
55100100
RelativeRelative
FrequencyFrequency
PercentPercent
FrequencyFrequencyRatingRating
.10(100) =.10(100) =
1010
1/20 = .051/20 = .05
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Bar GraphBar Graph
AAbar graphbar graph: graphical device: graphical device
On horizontal axis (usually): labels of the classes.On horizontal axis (usually): labels of the classes.
On vertical axis (usually): scaleOn vertical axis (usually): scale(frequency, relative frequency, percent frequency)(frequency, relative frequency, percent frequency)
Using fixed-width barUsing fixed-width bar
Bars are separatedBars are separated
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PoorPoor BelowAverage
BelowAverage
AverageAverage AboveAverage
AboveAverage
ExcellentExcellent
Frequency
Frequency
Ratingating
Bar GraphBar Graph
11
22
33
44
5566
77
88
991010
Marada Inn Quality RatingsMarada Inn Quality Ratings
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Pie ChartPie Chart
TheThe pie chartpie chart: commonly used graphical device: commonly used graphical device
s First draw aFirst draw a circlecircle; then subdivide the; then subdivide the
circle into sectors/partscircle into sectors/parts
s A relative frequency of .25 wouldA relative frequency of .25 would
consume ? degrees of the circle.consume ? degrees of the circle.
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BelowAverage
15%
BelowAverage
15%
Average
25%
Average
25%
AboveAverage
45%
AboveAverage
45%
Poor10%
Poor10%
Excellent5%
Excellent5%
Marada InnMarada InnQuality RatingsQuality RatingsMarada InnMarada InnQuality RatingsQuality Ratings
Pie ChartPie Chart
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s Insights Gained from the Preceding Pie Chart?Insights Gained from the Preceding Pie Chart?
Example: Marada InnExample: Marada Inn
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II. Summarizing Quantitative DataII. Summarizing Quantitative Data
Frequency DistributionFrequency Distribution Relative Frequency and Percent FrequencyRelative Frequency and Percent Frequency
DistributionsDistributions
Dot PlotDot Plot
HistogramHistogram
Cumulative DistributionsCumulative Distributions
OgiveOgive
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1. Simple frequency distribution1. Simple frequency distribution
Simple frequency distributionSimple frequency distribution
Applicable to?Applicable to?
Not suitable for?Not suitable for?
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ExampleExample
The following data record the number ofThe following data record the number ofchildren in the families of the 47 workers in achildren in the families of the 47 workers in a
company:company:
11 11 33 22 00 22 00 11 22 22 11 33
55 22 44 00 00 22 44 11 11 22 22 00
33 00 00 22 11 33 66 00 22 11 00 33
22 22 22 11 00 00 11 11 33 11 44
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Constructing a simple frequencyConstructing a simple frequency
distribution using a tally chartdistribution using a tally chart
Data valueData value Tally marksTally marks TotalTotal
0
12
3
45
6
||||||||||||||||||||||
||||||||||||||||||||||||||||||||||||||||||||||||||
||||||||||||||
||||||||
||
1111
12121313
66
3311
11
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Frequency distribution tableFrequency distribution table
Number of childrenNumber of children
in familyin familyNumber of workersNumber of workers
00 1111
11 1212
22 1313
33 66
44 33
55 11
66 11
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Disadvantage of simple frequencyDisadvantage of simple frequency
distribution?distribution?
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2. Grouped frequency distributions2. Grouped frequency distributions
A large number of values.A large number of values.
A grouped frequency distribution?A grouped frequency distribution?
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Example: Hudson Auto RepairExample: Hudson Auto Repair
The manager of Hudson AutoThe manager of Hudson Auto
would like to have a betterwould like to have a better
understanding of the costunderstanding of the cost
of parts used in the engineof parts used in the engine
tune-ups performed in thetune-ups performed in theshop. She examines 50shop. She examines 50
customer invoices for tune-ups. The costs of parts,customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the nextrounded to the nearest dollar, are listed on the next
slide.slide.
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Example: Hudson Auto RepairExample: Hudson Auto Repair
s Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
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Grouped Frequency DistributionGrouped Frequency Distribution
Guidelines for Selecting Number of ClassesGuidelines for Selecting Number of Classes
Use between 5 and 20 classes.Use between 5 and 20 classes.
Data sets with a larger number of elementsData sets with a larger number of elements
usually require a larger number of classes.usually require a larger number of classes.
Smaller data sets usually require fewer classesSmaller data sets usually require fewer classes
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Grouped Frequency DistributionGrouped Frequency Distribution
Guidelines for Selecting Width of ClassesGuidelines for Selecting Width of Classes
Use classes of equal width.Use classes of equal width.
Approximate Class WidthApproximate Class Width
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Frequency DistributionFrequency Distribution
For Hudson Auto Repair, if we choose sixFor Hudson Auto Repair, if we choose six
classes:classes:
50-5950-5960-6960-69
70-7970-79
80-8980-89
90-9990-99100-109100-109
Parts Cost ($)Parts Cost ($) FrequencyFrequency
Approximate Class Width = (109 - 52)/6 = 9.5 ~ 10Approximate Class Width = (109 - 52)/6 = 9.5 ~ 10
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Relative Frequency andRelative Frequency and
Percent Frequency DistributionsPercent Frequency Distributions
50-5950-59
60-6960-69
70-7970-79
80-8980-89
90-9990-99100-109100-109
PartsParts
Cost ($)Cost ($)
.04.04
.26.26
.32.32
.14.14
.14.14
.10.10
Total 1.00Total 1.00
RelativeRelative
FrequencyFrequency
44
2626
3232
1414
14141010
100100
PercentPercent
FrequencyFrequency
2/502/50 ..
04(10004(100
))
R l i F dR l ti F d
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s Insights Gained from the Percent FrequencyInsights Gained from the Percent Frequency
DistributionDistribution
Relative Frequency andRelative Frequency and
Percent Frequency DistributionsPercent Frequency Distributions
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Definitions associated with frequencyDefinitions associated with frequency
distribution classesdistribution classes
Class limits:Class limits:
Class boundaries:Class boundaries:
Note: upper boundary of one class will coincidesNote: upper boundary of one class will coincideswith the lower boundary of the next classwith the lower boundary of the next class
Sometimes limits and boundaries will coincideSometimes limits and boundaries will coincidee.g. 12 and up to 13, 13 and up to 14, 14 and upe.g. 12 and up to 13, 13 and up to 14, 14 and upto 15to 15
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Definitions associated with frequencyDefinitions associated with frequency
distribution classesdistribution classes
Class widths (class lengths):Class widths (class lengths):
Class mid-points:Class mid-points:
D Pl
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Dot PlotDot Plot
One of the simplest graphicalOne of the simplest graphicalsummaries of data is asummaries of data is a dot plotdot plot..
A horizontal axis shows the range ofA horizontal axis shows the range of
data values.data values. Then each data value is represented byThen each data value is represented by
a dot placed above the axis.a dot placed above the axis.
D Pl
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5050 6060 7070 8080 9090 100100 1101105050 6060 7070 8080 9090 100100 110110
Cost ($)Cost ($)
Dot PlotDot Plot
Tune-up Parts CostTune-up Parts Cost
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HistogramHistogram
Common graphical presentation of quantitativeCommon graphical presentation of quantitative
datadata
Horizontal axis: values of classesHorizontal axis: values of classes
A rectangle is drawn above each class intervalA rectangle is drawn above each class interval
Unlike a bar graph, a histogram has no gap betweenUnlike a bar graph, a histogram has no gap between
rectanglerectangle
Hi t
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HistogramHistogram
22
44
66
88
1010
1212
1414
1616
1818
Parts
Cost ($)
Parts
Cost ($)
Freque
ncy
Freque
ncy
5059 6069 7079 8089 9099 100-1105059 6069 7079 8089 9099 100-110
Tune-up Parts CostTune-up Parts Cost
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Cumulative frequency distributionCumulative frequency distributionCumulative frequency distributionCumulative frequency distribution
Cumulative relative frequency distributionCumulative relative frequency distributionCumulative relative frequency distributionCumulative relative frequency distribution
Cumulative DistributionsCumulative Distributions
Cumulative percent frequency distributionCumulative percent frequency distributionCumulative percent frequency distributionCumulative percent frequency distribution
C l i Di ib iC l ti Di t ib ti
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Cumulative DistributionsCumulative Distributions Hudson Auto RepairHudson Auto Repair
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OgiveOgive
s A graph of a cumulative distribution.A graph of a cumulative distribution.
s Horizontal axis: data valuesHorizontal axis: data values
s Vertical axisVertical axis
- cumulative frequencies, orcumulative frequencies, or
- cumulative relative frequencies, orcumulative relative frequencies, or- cumulative percent frequenciescumulative percent frequencies
s The frequency of each class: plotted as a point.The frequency of each class: plotted as a point.
s The plotted points connected by straight lines.The plotted points connected by straight lines.
Ogive withOgive with
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PartsParts
Cost ($)Cost ($) PartsParts
Cost ($)Cost ($)
2020
4040
6060
8080
100100
CumulativePercentFrequency
CumulativePercentFrequency
CumulativePercentFrequency
CumulativePercentFrequency
50 60 70 80 90 100 11050 60 70 80 90 100 11050 60 70 80 90 100 11050 60 70 80 90 100 110
(89.0,(89.0,
76)76)
Ogive withOgive with
Cumulative Percent FrequenciesCumulative Percent Frequencies
Tune-up Parts CostTune-up Parts CostTune-up Parts CostTune-up Parts Cost
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Chapter 2Chapter 2
Summarizing dataSummarizing data
Exploratory Data AnalysisExploratory Data Analysis
Cross-tabulation and Scatter DiagramsCross-tabulation and Scatter Diagrams
Part B
xx
yy
E l t D t A l iE l t D t A l i
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Exploratory Data AnalysisExploratory Data Analysis
The techniques ofThe techniques ofexploratory data analysisexploratory data analysis consist ofconsist of
simple arithmetic and easy-to-draw pictures that cansimple arithmetic and easy-to-draw pictures that canbe used to summarize data quickly.be used to summarize data quickly.
One such technique is theOne such technique is the stem-and-leaf displaystem-and-leaf display..
St d L f Di lSt d L f Di l
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Stem-and-Leaf DisplayStem-and-Leaf Display
Each digit on a stem is aEach digit on a stem is a leafleaf..
Each line in the display is referred to as aEach line in the display is referred to as a stemstem..
To the right of the vertical line we record the lastTo the right of the vertical line we record the last
digit for each item in rank order.digit for each item in rank order.
The first digits of each data item are arranged to theThe first digits of each data item are arranged to the
left of a vertical line.left of a vertical line.
It isIt is similar to a histogramsimilar to a histogram on its side, but it has theon its side, but it has the
advantage of showing the actual data values.advantage of showing the actual data values.
A stem-and-leaf display shows both theA stem-and-leaf display shows both the rank orderrank order
andand shape of the distributionshape of the distribution of the data.of the data.
E l d R iE l H d A t R i
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Example: Hudson Auto RepairExample: Hudson Auto Repair
The manager of Hudson AutoThe manager of Hudson Auto
would like to have a betterwould like to have a better
understanding of the costunderstanding of the cost
of parts used in the engineof parts used in the engine
tune-ups performed in thetune-ups performed in the
shop. She examines 50shop. She examines 50
customer invoices for tune-ups. The costs of parts,customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the nextrounded to the nearest dollar, are listed on the next
slide.slide.
E l H d A R iE l H d A t R i
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Example: Hudson Auto RepairExample: Hudson Auto Repair
s Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73
St d L f Di lSt d L f Di l
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Stem-and-Leaf DisplayStem-and-Leaf Display
56789
100
2 72 72 2 2 2 5 6 7 8 8 8 9 9 92 2 2 2 5 6 7 8 8 8 9 9 9
1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 91 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9
0 0 2 3 5 8 90 0 2 3 5 8 9
1 3 7 7 7 8 91 3 7 7 7 8 9
1 4 5 5 91 4 5 5 9
a stema stem
a leafa leaf
St t h d St d L f Di lStretched Stem and Leaf Display
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Stretched Stem-and-Leaf DisplayStretched Stem-and-Leaf Display
Whenever a stem value is stated twice, the first valueWhenever a stem value is stated twice, the first value
corresponds to leaf values of 0 - 4, and the secondcorresponds to leaf values of 0 - 4, and the second
value corresponds to leaf values of 5 - 9.value corresponds to leaf values of 5 - 9.
If we believe the original stem-and-leaf display hasIf we believe the original stem-and-leaf display has
condensed the data too much, we cancondensed the data too much, we can stretch thestretch thedisplaydisplay by using two stems for each leading digit(s).by using two stems for each leading digit(s).
St t h d St d L f Di lStretched Stem and Leaf Display
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Stretched Stem-and-Leaf DisplayStretched Stem-and-Leaf Display
5 5 95 5 91 41 4
7 7 7 8 97 7 7 8 9
1 31 35 8 95 8 90 0 2 30 0 2 3
5 5 5 6 7 8 9 9 95 5 5 6 7 8 9 9 91 1 2 2 3 4 41 1 2 2 3 4 4
5 6 7 8 8 8 9 9 95 6 7 8 8 8 9 9 92 2 2 22 2 2 2772255
55
66
66
77
77
88
88
99
991010
1010
St d L f Di lStem and Leaf Display
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Stem-and-Leaf DisplayStem-and-Leaf Display
s Leaf UnitsLeaf Units
Where the leaf unit is not shown, it is assumedWhere the leaf unit is not shown, it is assumedto equal 1.to equal 1.
Leaf units may be 100, 10, 1, 0.1, and so on.Leaf units may be 100, 10, 1, 0.1, and so on.
In the preceding example, the leaf unit was 1.In the preceding example, the leaf unit was 1.
A single digit is used to define each leaf.A single digit is used to define each leaf.
Example: Leaf Unit 0 1Example: Leaf Unit 0 1
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Example: Leaf Unit = 0.1Example: Leaf Unit = 0.1
If we have data with values such asIf we have data with values such as
88
99
1010
1111
Leaf Unit = 0.1Leaf Unit = 0.16 86 8
1 41 4
22
0 70 7
8.68.6 11.711.7 9.49.4 9.19.1 10.210.2 11.011.0 8.88.8
a stem-and-leaf display of these data will bea stem-and-leaf display of these data will be
Example: Leaf Unit 10Example: Leaf Unit 10
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Example: Leaf Unit = 10Example: Leaf Unit = 10
If we have data with values such asIf we have data with values such as
1616
1717
1818
1919
Leaf Unit = 10Leaf Unit = 1088
1 91 9
0 30 3
1 71 7
18061806 17171717 19741974 17911791 16821682 19101910 18381838
a stem-and-leaf display of these data will bea stem-and-leaf display of these data will be
The 82 in 1682The 82 in 1682is rounded downis rounded down
to 80 and isto 80 and is
represented as an 8.represented as an 8.
Crosstabulations and ScatterCrosstabulations and Scatter
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Crosstabulations and ScatterCrosstabulations and Scatter
DiagramsDiagrams
Cross-tabulationCross-tabulation and aand a scatter diagramscatter diagram are twoare two
methods for summarizing the data for two (or more)methods for summarizing the data for two (or more)
variables simultaneously.variables simultaneously.
Often a manager is interested in tabular andOften a manager is interested in tabular and
graphical methods that will help understand thegraphical methods that will help understand the
relationship between two variablesrelationship between two variables..
Thus far we have focused on methods that are usedThus far we have focused on methods that are usedto summarize the data forto summarize the data for one variable at a timeone variable at a time..
CrosstabulationCrosstabulation
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CrosstabulationCrosstabulation
The left and top margin labels define the classes forThe left and top margin labels define the classes for
the two variables.the two variables.
s Cross-tabulation can be used when:Cross-tabulation can be used when: one variable is qualitative and the other isone variable is qualitative and the other is
quantitative,quantitative,
both variables are qualitative, orboth variables are qualitative, or both variables are quantitative.both variables are quantitative.
AAcross-tabulationcross-tabulation is a tabular summary of data foris a tabular summary of data for
two variables.two variables.
CrosstabulationCrosstabulation
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PricePrice
RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame TotalTotal
$99,000> $99,000
18 6 19 1218 6 19 12 5555
4545
3030 20 35 1520 35 15TotalTotal 10010012 14 16 312 14 16 3
Home StyleHome Style
CrosstabulationCrosstabulation
s Example: Finger Lakes HomesExample: Finger Lakes Homes
The number of Finger Lakes homes sold for eachThe number of Finger Lakes homes sold for eachstyle and price for the past two years is shown below.style and price for the past two years is shown below.
quantitativequantitativevariablevariable
qualitativequalitativevariablevariable
CrosstabulationCrosstabulation
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CrosstabulationCrosstabulation
Insights Gained from Preceding Cross-Insights Gained from Preceding Cross-
tabulationtabulation
CrosstabulationCrosstabulation
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PricePrice
RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame TotalTotal
$99,000> $99,000
18 6 19 1218 6 19 12 5555
4545
3030 20 35 1520 35 15TotalTotal 100100
12 14 16 312 14 16 3
Home StyleHome Style
CrosstabulationCrosstabulation
Frequency distributionFrequency distributionfor the price variablefor the price variable
Frequency distributionFrequency distributionfor the home style variablefor the home style variable
Cross tabulation: Row or Column PercentagesCross-tabulation: Row or Column Percentages
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Cross-tabulation: Row or Column PercentagesCross-tabulation: Row or Column Percentages
Converting the entries in the table into rowConverting the entries in the table into row
percentages or column percentages canpercentages or column percentages canprovide additional insight about theprovide additional insight about the
relationship between the two variables.relationship between the two variables.
b l
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PricePrice
RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame TotalTotal
$99,000> $99,000
Home StyleHome Style
Crosstabulation: Row PercentagesCrosstabulation: Row Percentages
C b l i C l
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PricePrice
RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame
$99,000> $99,000
Home StyleHome Style
TotalTotal
Crosstabulation: Column PercentagesCrosstabulation: Column Percentages
Scatter Diagram and TrendlineScatter Diagram and Trendline
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The general pattern of the plotted points suggests theThe general pattern of the plotted points suggests the
overall relationship between the variables.overall relationship between the variables.
One variable is shown on the horizontal axis and theOne variable is shown on the horizontal axis and the
other variable is shown on the vertical axis.other variable is shown on the vertical axis.
AAscatter diagramscatter diagram is a graphical presentation of theis a graphical presentation of the
relationship between tworelationship between two quantitativequantitative variables.variables.
Scatter Diagram and TrendlineScatter Diagram and Trendline
AAtrendlinetrendline is an approximation of the relationship.is an approximation of the relationship.
Scatter DiagramScatter Diagram
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Scatter DiagramScatter Diagram
A Positive RelationshipA Positive Relationship
x
y
Scatter DiagramScatter Diagram
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Scatter DiagramScatter Diagram
A Negative RelationshipA Negative Relationship
xx
yy
Scatter DiagramScatter Diagram
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Scatter DiagramScatter Diagram
No Apparent RelationshipNo Apparent Relationship
xx
yy
Example: Panthers Football TeamExample: Panthers Football Team
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Example: Panthers Football TeamExample: Panthers Football Team
Scatter DiagramScatter Diagram
The Panthers football team is interestedThe Panthers football team is interested
in investigating the relationship, if any,in investigating the relationship, if any,
between interceptions made and points scored.between interceptions made and points scored.
11
33
22
11
33
1414
2424
1818
1717
3030
xx= Number of= Number ofInterceptionsInterceptions
yy= Number of= Number ofPoints ScoredPoints Scored
Scatter DiagramScatter Diagram
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Scatter DiagramScatter Diagram
yy
xx
Number of InterceptionsNumber of Interceptions
Nu
mberofPointsScored
Nu
mberofPointsScored
55
1010
15152020
2525
3030
00
3535
11 22 3300 44
Example: Panthers Football TeamExample: Panthers Football Team
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s Insights Gained from the Preceding Scatter DiagramInsights Gained from the Preceding Scatter Diagram
Example: Panthers Football TeamExample: Panthers Football Team
Tabular and Graphical ProceduresTabular and Graphical Procedures
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Tabular and Graphical ProceduresTabular and Graphical Procedures
Qualitative DataQualitative DataQualitative DataQualitative Data Quantitative DataQuantitative DataQuantitative DataQuantitative Data
TabularTabular
MethodsMethodsTabularTabular
MethodsMethodsTabularTabular
MethodsMethodsTabularTabular
MethodsMethodsGraphicalGraphical
MethodsMethodsGraphicalGraphical
MethodsMethodsGraphicalGraphical
MethodsMethodsGraphicalGraphical
MethodsMethods
FrequencyFrequency
DistributionDistributionRel. Freq. Dist.Rel. Freq. Dist.Percent Freq.Percent Freq.
DistributionDistributionCrosstabulationCrosstabulation
Bar GraphBar GraphPie ChartPie Chart
FrequencyFrequency
DistributionDistributionRel. Freq. Dist.Rel. Freq. Dist.Cum. Freq. Dist.Cum. Freq. Dist.
Cum. Rel. Freq.Cum. Rel. Freq.DistributionDistributionStem-and-LeafStem-and-Leaf
DisplayDisplayCrosstabulationCrosstabulation
Dot PlotDot PlotHistogramHistogramOgiveOgiveScatterScatter
DiagramDiagram
DataDataDataData
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