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© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 11 11 SlideSlide
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Slides Prepared bySlides Prepared by
Juei-Chao ChenJuei-Chao ChenFu Jen Catholic UniversityFu Jen Catholic University
Slides Prepared bySlides Prepared by
Juei-Chao ChenJuei-Chao ChenFu Jen Catholic UniversityFu Jen Catholic University
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 22 22 SlideSlide
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Chapter 2Chapter 2STATISTICS STATISTICS in in PRACTICEPRACTICE
• The Colgate-Palmolive Company uses statistics in its quality assurance program for home laundry detergent products.• One concern is customer satisfaction with the quantity of detergent in a carton. To control the problem of heavy detergent powder, limits are placed on the acceptable range of powder density. • Statistical samples are taken and the density of each powder sample is measured.• Data summaries are then provided for operating personnel so that corrective action can be taken if necessary to keep the density within the desired quality.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 33 33 SlideSlide
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Chapter 2Chapter 2Descriptive Statistics:Descriptive Statistics:
Tabular and Graphical PresentationsTabular and Graphical Presentations
2.1 Summarizing Qualitative Data
2.2 Summarizing Quantitative Data
2.3 Exploratory Data Analysis:
The Stem-and- Leaf Display
2.4 Crosstabulations and Scatter Diagrams
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 44 44 SlideSlide
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Chapter 2Chapter 2Descriptive Statistics:Descriptive Statistics:
Tabular and Graphical PresentationsTabular and Graphical PresentationsPart APart A
• Summarizing Qualitative Data
• Summarizing Quantitative Data
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 55 55 SlideSlide
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2.1 Summarizing Qualitative Data2.1 Summarizing Qualitative Data
• Frequency Distribution
• Relative Frequency Distributions
• Percent Frequency Distributions
• Bar Graphs
• Pie Charts
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 66 66 SlideSlide
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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 nonoverlapping classes.in each of several nonoverlapping 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 nonoverlapping classes.in each of several nonoverlapping 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
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 77 77 SlideSlide
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Frequency DistributionFrequency Distribution• Example: Data from a sample of 50 Soft Drink
Purchases
• Frequency Distribution Soft Drink FrequencyCoke Classic 19Diet Coke 8Dr. Pepper 5Pepsi-Cola 13Sprite 5 Total 50
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Example: Marada InnExample: 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:
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
AverageAverage
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Frequency DistributionFrequency Distribution
PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent
22 33 55 99 11
TotalTotal 20 20
RatingRating FrequencyFrequency
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The The relative frequencyrelative frequency of a class is the fraction or of a class is the fraction or proportion of the total number of data itemsproportion 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 or of a class is the fraction or proportion of the total number of data itemsproportion of the total number of data items belonging to the class.belonging to the class.
Relative FrequencyRelative Frequency
Frequency of the classRelative frequency of a class= n
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1111 1111 SlideSlide
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Relative Frequency DistributionsRelative Frequency Distributions
• A A relative frequency distributionrelative frequency distribution is a tabular summary is a tabular summary of a set of data showing the relative frequency for each of a set of data showing the relative frequency for each class.class.
• A A relative frequency distributionrelative frequency distribution is a tabular summary is a tabular summary of a set of data showing the relative frequency for each of a set of data showing the relative frequency for each class.class.
Example: Relative and Percent Frequency Distribution of Soft Drink Purchases
Soft Drink Relative FrequencyCoke Classic .38Diet Coke .16Dr. Pepper .10Pepsi-Cola .26Sprite .10 Total 1.00
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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.
Example: Percent Frequency Distribution of Soft Drink Purchases
Soft Drink Percent FrequencyCoke Classic 38Diet Coke 16Dr. Pepper 10Pepsi-Cola 26Sprite 10 Total 100
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1313 1313 SlideSlide
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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
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1414 1414 SlideSlide
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Bar GraphBar Graph• A bar graph is a graphical device for depicting qualitative data.
• On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.
• A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis).
• Using a bar of fixed width drawn above each class label, we extend the height appropriately.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1515 1515 SlideSlide
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Bar GraphBar Graph• Example: Bar Graph of Soft Drink Purchases
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1616 1616 SlideSlide
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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
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1717 1717 SlideSlide
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Pie ChartPie Chart
• The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data.
• 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.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1818 1818 SlideSlide
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Pie ChartPie Chart
• Example: Pie Chart of Soft Drink Purchases
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1919 1919 SlideSlide
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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
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2020 2020 SlideSlide
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• Insights Gained from the Preceding Pie Chart
Example: Marada InnExample: Marada Inn
• One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might please the manager.
• For each customer who gave an “excellent” rating, there were two customers who gave a “poor” rating (looking at the top of the pie). This should displease the manager.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2121 2121 SlideSlide
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2.2 Summarizing Quantitative Data2.2 Summarizing Quantitative Data
• Frequency Distribution• Relative Frequency and Percent Frequency
Distributions• Dot Plot• Histogram• Cumulative Distributions• Ogive
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2222 2222 SlideSlide
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Frequency DistributionFrequency Distribution• The three steps necessary to define the classes for a frequency distribution with quantitative data are:
1. Determine the number of nonoverlapping classes. we recommend using between 5 and 20 classes. 2. Determine the width of each class.
3. Determine the class limits.
Largest data value –Smallest data valueApproximate class width= Number of classes
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2323 2323 SlideSlide
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Frequency DistributionFrequency Distribution
• Guidelines for Selecting Number of Classes
• Use between 5 and 20 classes.
• Data sets with a larger number of elements usually require a larger number of classes.
• Smaller data sets usually require fewer classes
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2424 2424 SlideSlide
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Frequency DistributionFrequency Distribution
• Guidelines for Selecting Width of Classes
Use classes of equal width.
Approximate Class Width =
Largest data value –Smallest data value
Number of classes
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2525 2525 SlideSlide
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Frequency DistributionFrequency Distribution• Example: These data show the time in days
required to complete year-end audits for a sample of 20 clients of Sanderson and Clifford, a small public accounting firm with the data rounded to the nearest day.
YEAR-END AUDITTIMES (IN DAYS)12 14 19 18 15 15 18 1720 27 22 2322 21 33 2814 18 16 13
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2626 2626 SlideSlide
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Frequency DistributionFrequency Distribution• Example:
1. Number of classes = 5
2. provides an approximate class width of
(33 — 12)/5= 4.2.
3. We therefore decided to round up and use a class
width of five days in the frequency distribution.
4. FREQUENCY
DISTRIBUTION
FOR THE
AUDIT TIMES DATA
Audit Time Frequency (days) 10-14 4 15-19 8 20-24 5 25-29 2 30-34 1 Total 20
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2727 2727 SlideSlide
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Example: Hudson Auto RepairExample: 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.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2828 2828 SlideSlide
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Example: Hudson Auto RepairExample: Hudson Auto Repair
• Sample of Parts Cost for 50 Tune-ups
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
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
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2929 2929 SlideSlide
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Frequency DistributionFrequency Distribution
For Hudson Auto Repair, if we choose six classes:
50-59
60-69 70-79 80-89 90-99
100-109
22 1313 1616 77 77 55
Total 50Total 50
Parts Cost ($)Parts Cost ($) Frequency
Approximate Class Width = (109 - 52)/6 = 9.5 10
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3030 3030 SlideSlide
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Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions
50-59
60-69 70-79 80-89 90-99
100-109
PartsCost ($)
.04 .26 .32 .14 .14 .10
Total 1.00
RelativeRelativeFrequencyFrequency
44 2626
3232
1414
1414
1010
100 100
Percent Frequency
2/502/50 .04(10.04(100)0)
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3131 3131 SlideSlide
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• Only 4% of the parts costs are in the $50-59 class.
• The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class.
• 30% of the parts costs are under $70.
• 10% of the parts costs are $100 or more.
• Insights Gained from the Percent Frequency Distribution
Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3232 3232 SlideSlide
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Dot PlotDot Plot
• One of the simplest graphical summaries of data is a dot plot.
• A horizontal axis shows the range of data values.
• Then each data value is represented by a dot placed above the axis.
• Example: Dot Plot for The Audit Time Data
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3333 3333 SlideSlide
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50 60 70 80 90 100 11050 60 70 80 90 100 110
Cost ($)Cost ($)
Dot PlotDot Plot
Tune-up Parts CostTune-up Parts Cost
. . . ..... .......... .. . .. . . ... . .. . . . . ..... .......... .. . .. . . ... . .. .
. . . .. . . . . .. . . . . .. .. .. .. . . . .. .. .. .. . .
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3434 3434 SlideSlide
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HistogramHistogram
• Another common graphical presentation of quantitative data is a histogram.
• The variable of interest is placed on the horizontal axis.
• A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, relative frequency, or percent frequency.
• Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3535 3535 SlideSlide
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HistogramHistogram
• Example: Histogram for The Audit Time Data
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3636 3636 SlideSlide
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HistogramHistogram
22
44
66
88
1010
1212
1414
1616
1818
PartsCost ($) PartsCost ($)
Fre
qu
ency
Fre
qu
ency
50-59 60-69 70-79 80-89 90-99 100-11050-59 60-69 70-79 80-89 90-99 100-110
Tune-up Parts Cost
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3737 3737 SlideSlide
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• Histogram provides information about the shape.
• Symmetric
• Left tail is the mirror image of the right tail
• Examples: heights and weights of people
HistogramHistogram
Rela
tive F
req
uen
cyR
ela
tive F
req
uen
cy
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3838 3838 SlideSlide
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HistogramHistogram
• Moderately Skewed Left• A longer tail to the left• Example: exam scores
Rel
ativ
e F
requ
ency
Rel
ativ
e F
requ
ency
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3939 3939 SlideSlide
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• Moderately Right Skewed• A Longer tail to the right• Example: housing values
HistogramHistogram
Rel
ativ
e F
requ
ency
Rel
ativ
e F
requ
ency
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4040 4040 SlideSlide
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HistogramHistogram
• Highly Skewed Right• A very long tail to the right• Example: executive salaries
Rel
ativ
e F
requ
ency
Rel
ativ
e F
requ
ency
.05.05
.10.10
.15.15
.20.20
.25.25
.30.30
.35.35
00
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Cumulative frequency distributionCumulative frequency distribution shows the shows the number of items with values less than or equal tonumber of items with values less than or equal to the upper limit of each class..the upper limit of each class..
Cumulative frequency distributionCumulative frequency distribution shows the shows the number of items with values less than or equal tonumber of items with values less than or equal to the upper limit of each class..the upper limit of each class..
Cumulative relative frequency distributionCumulative relative frequency distribution – shows – shows the proportion of items with values less than orthe proportion of items with values less than or equal to the upper limit of each class.equal to the upper limit of each class.
Cumulative relative frequency distributionCumulative relative frequency distribution – shows – shows the proportion of items with values less than orthe proportion of items with values less than or equal to the upper limit of each class.equal to the upper limit of each class.
Cumulative DistributionsCumulative Distributions
Cumulative percent frequency distributionCumulative percent frequency distribution – shows – shows the percentage of items with values less than orthe percentage of items with values less than or equal to the upper limit of each class.equal to the upper limit of each class.
Cumulative percent frequency distributionCumulative percent frequency distribution – shows – shows the percentage of items with values less than orthe percentage of items with values less than or equal to the upper limit of each class.equal to the upper limit of each class.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4242 4242 SlideSlide
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Cumulative DistributionsCumulative Distributions
• Example: Cumulative Frequency, Cumulative
Relative Frequency and Cumulative Percent
Frequency Distributions for the Audit Data.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4343 4343 SlideSlide
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Cumulative DistributionsCumulative Distributions
• Hudson Auto Repair
<< 59 59
<< 69 69
<< 79 79
<< 89 89
<< 99 99
<< 109 109
Cost ($)Cost ($) CumulativeCumulativeFrequencyFrequency
CumulativeCumulativeRelativeRelative
FrequencyFrequency
CumulativeCumulativePercentPercent
FrequencyFrequency
22 1515
3131
3838
4545
5050
.04.04
.30.30
.62.62
.76.76
.90.90
1.00 1.00
44 3030
6262
7676
9090
100100
2 + 2 + 1313
15/5015/50 .30(10.30(100)0)
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4444 4444 SlideSlide
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OgiveOgive
• An ogive is a graph of a cumulative distribution.
• The data values are shown on the horizontal axis.
• Shown on the vertical axis are the:
• cumulative frequencies, or
• cumulative relative frequencies, or
• cumulative percent frequencies
• The frequency (one of the above) of each class is plotted as a point.
• The plotted points are connected by straight lines.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4545 4545 SlideSlide
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• Because the class limits for the parts-cost data are 50-59, 60-69, and so on, there appear to be one-unit gaps from 59 to 60, 69 to 70, and so on.
OgiveOgive
• These gaps are eliminated by plotting points halfway between the class limits.
• Thus, 59.5 is used for the 50-59 class, 69.5 is used for the 60-69 class, and so on.
• Hudson Auto Repair
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4646 4646 SlideSlide
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OgiveOgive
• Example: Ogive for the Audit Time Data.
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4747 4747 SlideSlide
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PartsPartsCost ($)Cost ($) PartsPartsCost ($)Cost ($)
2020
4040
6060
8080
100100
Cu
mu
lati
ve P
erc
en
t Fr
eq
uen
cyC
um
ula
tive P
erc
en
t Fr
eq
uen
cyC
um
ula
tive P
erc
en
t Fr
eq
uen
cyC
um
ula
tive P
erc
en
t Fr
eq
uen
cy
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
(89.5, (89.5, 76)76)
Ogive withOgive with
Cumulative Percent Frequencies Cumulative Percent Frequencies Tune-up Parts CostTune-up Parts CostTune-up Parts CostTune-up Parts Cost
© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4848 4848 SlideSlide
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End of Chapter 2, Part AEnd of Chapter 2, Part A