descriptive statistics: tabular and graphical presentations
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Descriptive Statistics: Tabular and Graphical Presentations. Chapter 2 BA 201 – Spring 2011. Summarizing Data Using Tabular and Graphical Presentations. Categorical Data. Quantitative Data. Frequency, Relative Frequency, and Percent Frequency Distributions Dot Plot Histogram - PowerPoint PPT PresentationTRANSCRIPT
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Descriptive Statistics:Tabular and Graphical Presentations
Chapter 2BA 201 – Spring 2011
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Summarizing Data Using Tabular and Graphical Presentations
Categorical Data Frequency, Relative
Frequency, and Percent Frequency Distributions
Bar Chart Pie Chart Cross Tabulations
Quantitative Data Frequency, Relative
Frequency, and Percent Frequency Distributions
Dot Plot Histogram Cumulative
Distributions Ogive Cross Tabulations Stem-and-Leaf Scatter Diagrams
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Frequency Distribution
A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several non-overlapping classes.
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Frequency Distribution Categorical Data
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
Marada Inn Ratings – customer ratings
Count ratings in each category
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Frequency DistributionCategorical Data
PoorBelow AverageAverageAbove AverageExcellent
2 3 5 9 1
Total 20
Rating Frequency
Count for class
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Frequency DistributionQuantitative Data
Hudson Auto Repair – cost of parts in tune-up
91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73
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Frequency DistributionQuantitative Data
1. Determine the number of non-overlapping classes.• 5 to 20 classes based on quantity of data.
2. Determine the width of each class.• Equal width.• =(largest value – smallest value)/# of
classes3. Determine the class limits.
• Each item in one class only.
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Frequency Distribution
Using six classes. Largest = 109, Smallest = 52.
50-59
60-69 70-79 80-89 90-99
100-109
2 13 16 7 7 5Total 50
Parts Cost ($) Frequency
Approximate Class Width = (109 - 52)/6 = 9.5 10
Hudson Auto Repair
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Relative Frequency Distribution
A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.
The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.
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Percent Frequency Distribution
A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.
The percent frequency of a class is the relative frequency multiplied by 100.
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Relative Frequency andPercent Frequency Distributions
PoorBelow AverageAverageAbove AverageExcellent
.10 .15 .25 .45 .05 1.00
10 15 25 45 5 100
RelativeFrequency
PercentFrequencyRating
.10(100) = 10
1/20 = .05Total
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Bar Chart
A bar chart is a graphical device for depicting qualitative data.• Horizontal axis – labels for classes.• Vertical axis – frequency scale.
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Poor BelowAverage
Average AboveAverage
Excellent
Freq
uenc
y
Rating
Bar Chart
123456789
10 Marada Inn Quality Ratings
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Pareto Diagram
Bar Chart Bars arranged in descending order from left to
right.
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Freq
uenc
y
Rating123456789
10 Marada Inn Quality Ratings
PoorBelowAverage
Average AboveAverage
Excellent
Pareto Diagram
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Pie Chart First draw a circle; then use the relative
frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class.
Since there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90 degrees of the circle.
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BelowAverage 15%
Average 25%
AboveAverage 45%
Poor10%
Excellent 5%
Marada Inn Quality Ratings
Pie Chart
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Frequency Distribution Practice
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Dot Plot
A horizontal axis shows the range of data values.
Each data value represented by a dot above the axis.
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Dot Plot
50 60 70 80 90 100 110Cost ($)
Tune-up Parts CostHudson Auto Repair
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Histogram
Variable of interest is on the horizontal axis. A rectangle is drawn above each class interval
with its height corresponding to the interval’s frequency, relative frequency, or percent frequency.
No separation between classes.
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Histogram
2468
1012141618
PartsCost ($)
Freq
uenc
y
50-59 60-69 70-79 80-89 90-99 100-110
Tune-up Parts Cost
Hudson Auto Repair
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Skewness
Symmetric
Skewed Left Skewed Right
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Histogram Practice
b. Start the first class at zero.
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Cumulative Distributions
Shows items with values less than or equal to upper limit of class:• Frequency – number of items.• Relative frequency – proportion of items.• Percent frequency – percentage of items.
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Cumulative Distributions
Hudson Auto Repair
< 59
< 69 < 79 < 89 < 99
< 109
Cost ($) CumulativeFrequency
CumulativeRelative
Frequency
CumulativePercent
Frequency 2 15 31 38 45
50
.04 .30 .62 .76 .90
1.00
4 30 62 76 90
100
2 + 13 15/50 .30(100
)
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Ogive
An ogive is a graph of a cumulative distribution.
Data values on horizontal axis. Cumulative measure on vertical axis. Frequency of each class plotted as a point. Straight lines connect points.
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PartsCost ($)
20
40
60
80
100
Cum
ulat
ive
Perc
ent F
requ
ency
50 60 70 80 90 100 110
Ogive with Cumulative Percent Frequencies
Tune-up Parts Cost
Hudson Auto Repair
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Stem-and-Leaf Display
Easy way to show shape of rank order and shape of the distribution.
Leaf = right most digit. Stem = left most digit(s).
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Stem-and-Leaf Display
56789
10
2 7 2 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 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9
a stema leaf
Hudson Auto Repair
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Example of Leaf Unit = 0.1
If we have data with values such as
8 91011
Leaf Unit = 0.16 81 420 7
8.6 11.7 9.4 9.1 10.2 11.0 8.8a stem-and-leaf display of these data will be
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Stretched Stem-and-Leaf Display
5 5 91 47 7 7 8 91 35 8 90 0 2 35 5 5 6 7 8 9 9 91 1 2 2 3 4 45 6 7 8 8 8 9 9 92 2 2 2725
566778899
1010
Hudson Auto Repair
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33 Slide
Stem and Leaf Practice
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Crosstabulation
A crosstabulation is a tabular summary for two variables.
Left and top margins define classes for variables.
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PriceRange Colonial Log Split A-FrameTotal
< $200,000> $200,000
18 6 19 12 5545
30 20 35 15Total 10012 14 16 3
Home Style
Crosstabulation
Finger Lakes HomesThe number of Finger Lakes homes sold for each style and price for the past two years is shown below.
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PriceRange Colonial Log Split A-FrameTotal
< $200,000> $200,000
18 6 19 12 5545
30 20 35 15Total 10012 14 16 3
Home Style
CrosstabulationFrequencydistribution
for theprice range
variable
Frequency distribution for
the home style variable
Finger Lakes Homes
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PriceRange Colonial Log Split A-FrameTotal
< $200,000> $200,000
32.73 10.91 34.55 21.82100100
Note: row totals are actually 100.01 due to rounding.26.67 31.11 35.56 6.67
Home Style
(Colonial and > $200K)/(All > $200K) x 100 = (12/45) x 100
Crosstabulation: Row Percentages
Finger Lakes Homes
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38 Slide
PriceRange Colonial Log Split A-Frame
< $200,000> $200,000
60.00 30.00 54.29 80.0040.00 70.00 45.71 20.00
Home Style
100 100 100 100Total
(Colonial and > $200K)/(All Colonial) x 100 = (12/30) x 100
Crosstabulation: Column Percentages
Finger Lakes Homes
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39 Slide
Cross Tabulation Practice
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Scatter Diagram and Trendline
A scatter diagram is a graphical presentation of the relationship between two quantitative variables.
A trendline provides an approximation of the relationship.
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Panthers Football Team
13213
1424181730
Number ofInterceptions
Number of Points Scored
Scatter Diagram
The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored.
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Scatter Diagram
Number of Interceptions
Num
ber o
f Poi
nts S
core
d
51015202530
0
35
1 2 30 4
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