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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Introduction to StatisticsIntroduction to Statistics
Chapter 2
Descriptive Statistics
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Slides Prepared bySlides Prepared by
JOHN S. LOUCKSJOHN S. LOUCKSSt. Edward’s UniversitySt. Edward’s University
Slides Prepared bySlides Prepared by
JOHN S. LOUCKSJOHN S. LOUCKSSt. Edward’s UniversitySt. Edward’s University
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Chapter 2Chapter 2Descriptive Statistics:Descriptive Statistics:
Tabular and Graphical PresentationsTabular and Graphical PresentationsPart APart A
Summarizing Qualitative DataSummarizing Qualitative Data Summarizing Quantitative DataSummarizing Quantitative Data
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Summarizing Qualitative DataSummarizing Qualitative Data
Frequency DistributionFrequency Distribution Relative Frequency Distribution Relative Frequency Distribution Percent Frequency DistributionPercent Frequency Distribution Bar GraphBar Graph Pie ChartPie Chart
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.
A A frequency distributionfrequency distribution is a tabular summary of is a tabular summary of data showing the frequency (or number) of itemsdata showing the frequency (or number) of items in each of several non-overlapping classes.in each of several non-overlapping classes.
The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.
The objective is to The objective is to provide insightsprovide insights about the data about the data that cannot be quickly obtained by looking only atthat cannot be quickly obtained by looking only at the original data.the original data.
Frequency DistributionFrequency Distribution
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Example: Marada InnExample: Marada Inn
Guests staying at Marada Inn wereGuests staying at Marada Inn wereasked to rate the quality of their asked to rate the quality of their accommodations as being accommodations as being excellentexcellent,,above averageabove average, , averageaverage, , below averagebelow average, or, orpoorpoor. The ratings provided by a sample of 20 . The ratings provided by a sample of 20
guests are:guests are:
Below AverageBelow Average
Above AverageAbove Average
Above AverageAbove Average
AverageAverage
Above Average Above Average
AverageAverage
Above AverageAbove Average
Average Average
Above AverageAbove Average
Below AverageBelow Average
PoorPoor
Excellent Excellent
Above AverageAbove Average
AverageAverage
Above AverageAbove Average
Above AverageAbove Average
Below AverageBelow Average
PoorPoor
Above Average Above Average
AverageAverage
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Frequency DistributionFrequency Distribution
PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent
22 33 55 99 11
TotalTotal 20 20
RatingRating FrequencyFrequency
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
The The relative frequencyrelative frequency of a class is the fraction of a class is the fraction or proportion of the total number of data itemsor proportion of the total number of data items belonging to the class.belonging to the class.
The The relative frequencyrelative frequency of a class is the fraction of a class is the fraction or proportion of the total number of data itemsor proportion of the total number of data items belonging to the class.belonging to the class.
A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.
A A relative frequency distributionrelative frequency distribution is a tabular is a tabular summary of a set of data showing the relativesummary of a set of data showing the relative frequency for each class.frequency for each class.
Relative Frequency DistributionRelative Frequency Distribution
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Percent Frequency DistributionPercent Frequency Distribution
The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100. The The percent frequencypercent frequency of a class is the relative of a class is the relative frequency multiplied by 100.frequency multiplied by 100.
AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.
AA percent frequency distributionpercent frequency distribution is a tabular is a tabular summary of a set of data showing the percentsummary of a set of data showing the percent frequency for each class.frequency for each class.
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions
PoorPoor
Below AverageBelow Average
AverageAverage
Above AverageAbove Average
ExcellentExcellent
.10.10
.15.15
.25.25
.45.45
.05.05
TotalTotal 1.00 1.00
1010
1515
2525
4545
55
100100
RelativeRelativeFrequencyFrequency
PercentPercentFrequencyFrequencyRatingRating
.10(100) = .10(100) = 1010
1/20 1/20 = .05= .05
FrequencyFrequency 22
33
55
99
11
2020
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Bar GraphBar Graph
A A bar graphbar graph is a graphical device for depicting is a graphical device for depicting qualitative data.qualitative data. On one axis (usually the horizontal axis), we specifyOn one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.the labels that are used for each of the classes. A A frequencyfrequency, , relative frequencyrelative frequency, or , or percent frequencypercent frequency scale can be used for the other axis (usually thescale can be used for the other axis (usually the vertical axis).vertical axis). Using a Using a bar of fixed widthbar of fixed width drawn above each class drawn above each class label, we extend the height appropriately.label, we extend the height appropriately.
The The bars are separatedbars are separated to emphasize the fact that each to emphasize the fact that each class is a separate category.class is a separate category.
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
PoorPoor BelowAverageBelow
AverageAverageAverage Above
Average Above
AverageExcellentExcellent
Fre
qu
en
cy
Fre
qu
en
cy
RatingRating
Bar GraphBar Graph
1122
33
44
55
66
77
88
991010
Marada Inn Quality RatingsMarada Inn Quality Ratings
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Pie ChartPie Chart
The The pie chartpie chart is a commonly used graphical device is a commonly used graphical device for presenting relative frequency distributions forfor presenting relative frequency distributions for qualitative data.qualitative data. First draw a First draw a circlecircle; then use the relative; then use the relative frequencies to subdivide the circlefrequencies to subdivide the circle into sectors that correspond to theinto sectors that correspond to the
relative frequency for each class.relative frequency for each class. Since there are 360 degrees in a circle, Since there are 360 degrees in a circle,
a class with a relative frequency of .25 woulda class with a relative frequency of .25 would
consume .25(360) = 90 degrees of the circle.consume .25(360) = 90 degrees of the circle.
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
BelowAverage 15%
BelowAverage 15%
Average 25%Average 25%
AboveAverage 45%
AboveAverage 45%
Poor10%Poor10%
Excellent 5%Excellent 5%
Marada InnMarada Inn Quality Quality RatingsRatings
Marada InnMarada Inn Quality Quality RatingsRatings
Pie ChartPie Chart
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
Insights Gained from the Preceding Pie Insights Gained from the Preceding Pie ChartChart
Example: Marada InnExample: Marada Inn
• One-half of the customers surveyed gave MaradaOne-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent”a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might(looking at the left side of the pie). This might please the manager.please the manager.
• For For eacheach customer who gave an “excellent” rating, customer who gave an “excellent” rating, there were there were twotwo customers who gave a “poor” customers who gave a “poor” rating (looking at the top of the pie). This shouldrating (looking at the top of the pie). This should displease the manager.displease the manager.
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
In Class Group ExerciseIn Class Group Exercise
NameName FrequencyFrequency
BrownBrown 77
DavisDavis 66
JohnsonJohnson 1010
JonesJones 77
SmithSmith 1212
WilliamsWilliams 88
5050
The Following are the The Following are the voices gained by each voices gained by each representative of one representative of one class in a school class in a school
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
5 a5 a
NameName FrequencyFrequencyRelative Relative
FrequencyFrequencyPercent Percent
FrequencyFrequency
BrownBrown 77 .14.14 14%14%
DavisDavis 66 .12.12 12%12%
JohnsonJohnson 1010 .20.20 20%20%
JonesJones 77 .14.14 14%14%
SmithSmith 1212 .24.24 24%24%
WilliamsWilliams 88 .16.16 16%16%
5050 1.001.00 100%100%
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© 2005 Thomson/South-Western© 2005 Thomson/South-Western
5 b5 b
0
2
4
6
8
10
12
14
Brown Davis Johnson Jones Smith Williams
Frequency
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5c5c
% Degrees
Brown 0.14 50.4
Davis 0.12 43.2
Johnson 0.20 72
Jones 0.14 50.4
Smith 0.24 86.4
Williams 0.16 57.6
1.00 360
Percentage
14%
12%
20%14%
24%
16%Brown
Davis
Johnson
Jones
Smith
Williams
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5 d5 d
Most common: Smith, Johnson and Williams Most common: Smith, Johnson and Williams