chapter 2 (summarizing data)_student
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Chapter 2
Summarizing data
Summarizing Qualitative Data
Summarizing Quantitative Data
Part A
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Why summarizing data?
Survey,investigation
Rawdata
Disadvantage?
How to extract some information from
these data?
- arranging
- putting them intoorder
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I. Summarizing Qualitative Data
Frequency Distribution
Relative Frequency Distribution
Percent Frequency Distribution Bar Graph
Pie Chart
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A frequency distribution is
The objective is
Frequency Distribution
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Example: Marada Inn
Guests staying at Marada Inn wereasked to rate the quality of their
accommodations as being excellent,
above average, average, below average, or
poor. The ratings provided by a sample of 20 guests are:
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Example: Marada Inn
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average
Above Average
Below Average
Poor
Excellent
Above Average
Average
Above Average
Above Average
Below Average
Poor
Above Average
Average
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Why Use Frequency Distributions?
A frequency distribution is a way tosummarize data
The distribution condenses the raw datainto a more useful form...
and allows for a quick visual interpretationof the data
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The relative frequency of a class is
A relative frequency distribution is
Relative Frequency Distribution
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Relative Frequency Distribution
Ratings Frequency Relative frequency
Poor
Below Average
Average
Above AverageExcellent
Total
2
3
5
91
20
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Bar Graph
A graphical device for depicting qualitative data.
On one axis (usually the horizontal axis), we specifythe label or the name of each of the class.
On the other axis (usually the vertical axis), we specifythe frequency, relative frequency of each class
A bar of fixed width is drawn above each class
label, we extend the height appropriately. The bars are separated to emphasize the fact that each
class is a separate category.
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Insights Gained from the Preceding Pie Chart
Example: Marada Inn
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1. Simple frequency distribution
Simple frequencydistribution consists of alist of data values, eachshowing the number of
items having that value(the frequency).
Data values Frequency
0 10
1 12
2 9
3 8
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Frequency distribution table
Number of childrenin family
Number of workers
0
1
2
3
4
5
6
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2. Grouped frequency distributions
Used when the data set contains a large numberof data values.
A grouped frequency distribution summaries
data into groups of values, each showing thenumber of items having values in the group.
Each group of data value called class
Used for both continuous data and discrete data
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Example: Hudson Auto Repair
The manager of Hudson Auto
would like to have a better
understanding of the cost
of parts used in the engine
tune-ups performed in theshop. She examines 50
customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the next
slide.
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Example
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Dot Plot
Tune-up Parts Cost
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Hi
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Histogram
Tune-up Parts Cost
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Cumulative Frequency Distribution
Part costs ($) Frequency Cumulativefrequency
Relativecumulativefrequency
Hudson Auto Repair
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Chapter 2
Summarizing data
Exploratory Data Analysis
Crosstabulation and Scatter Diagrams
Part B
x
y
E l t D t A l i
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Exploratory Data Analysis
The techniques of exploratory data analysis consist of
simple arithmetic and easy-to-draw pictures that canbe used to summarize data quickly.
One such technique is the stem-and-leaf display.
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Stem-and-Leaf Display
E l H d A t R i
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Example: Hudson Auto Repair
The manager of Hudson Auto
would like to have a better
understanding of the cost
of parts used in the engine
tune-ups performed in the
shop. She examines 50
customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed on the next
slide.
E l H d A t R i
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Example: Hudson Auto Repair
Sample 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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St etched Stem and Leaf Displa
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Stretched Stem-and-Leaf Display
St d L f Di l
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Stem-and-Leaf Display
Leaf Units
Where the leaf unit is not shown, it is assumedto equal 1.
Leaf units may be 100, 10, 1, 0.1, and so on.
In the preceding example, the leaf unit was 1.
A single digit is used to define each leaf.
Example: Leaf Unit 0 1
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Example: Leaf Unit = 0.1
If we have data with values such as8.6 11.7 9.4 9.1 10.2 11.0 8.8
a stem-and-leaf display of these data will be
Example: Leaf Unit 10
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Example: Leaf Unit = 10
If we have data with values such as
1806 1717 1974 1791 1682 1910 1838
a stem-and-leaf display of these data will be
Crosstabulations and Scatter
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Crosstabulations and ScatterDiagrams
Crosstabulation and a scatter diagram are twomethods for summarizing the data for two (or more)variables simultaneously.
Often a manager is interested in tabular andgraphical methods that will help understand the
relationship between two variables.
So far we have focused on methods that are usedto summarize the data for one variable at a time.
Crosstabulation
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Crosstabulation
Crosstabulation can be used when:
A crosstabulation is
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Cross-tabulation
Example: Finger Lakes Homes
The number of Finger Lakes homes sold for each
style and price for the past two years is shownbelow
Crosstabulation
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Crosstabulation
Insights Gained from Preceding
Crosstabulation
Crosstabulation
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PriceRange Colonial Log Split A-Frame Total
< $99,000
> $99,000
18 6 19 12 55
45
30 20 35 15Total 100
12 14 16 3
Home Style
Crosstabulation
Frequency distributionfor the price variable
Frequency distributionfor the home style variable
Cross-tabulation: Row or Column
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Percentages
Converting the entries in the table into row
percentages or column percentages canprovide additional insight about therelationship between the two variables.
Crosstabulation: Row Percentages
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Crosstabulation: Row Percentages
C t b l ti C l P t
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Crosstabulation: Column Percentages
Scatter Diagram and Trendline
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The general pattern of the plotted points suggests theoverall relationship between the variables.
One variable is shown on the horizontal axis and theother variable is shown on the vertical axis.
A scatter diagram is a graphical presentation of the
relationship between two quantitative variables.
Scatter Diagram and Trendline
A trendline is an approximation of the relationship.
Scatter Diagram
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Scatter Diagram
A Positive Relationship
x
y
Scatter Diagram
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Scatter Diagram
A Negative Relationship
x
y
Scatter Diagram
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Scatter Diagram
No Apparent Relationship
x
y
Example: Panthers Football Team
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Example: Panthers Football Team
Scatter Diagram
The Panthers football team is interestedin investigating the relationship, if any,
between interceptions made and points scored.
1
3
21
3
14
24
1817
30
x= Number ofInterceptions
y= Number ofPoints Scored
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Scatter Diagram
Example: Panthers Football Team
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Insights Gained from the Preceding Scatter Diagram
Example: Panthers Football Team
Tabular and Graphical Procedures
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Tabular and Graphical Procedures
Qualitative Data Quantitative Data
TabularMethods
TabularMethods
GraphicalMethods
GraphicalMethods
FrequencyDistribution
Rel. Freq. Dist.Crosstabulation
Bar GraphPie Chart
FrequencyDistribution
Rel. Freq. Dist.Cum. Freq. Dist.
Cum. Rel. Freq.DistributionStem-and-Leaf
DisplayCrosstabulation
Dot PlotHistogramOgiveScatter
Diagram
Data
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