Busn210ch02

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Slides by

JOHNLOUCKSSt. Edward’sUniversity

2 Slide

Chapter 2, Part AChapter 2, Part ADescriptive Statistics:Descriptive Statistics:

Tabular and Graphical PresentationsTabular and Graphical Presentations Summarizing Categorical DataSummarizing Categorical Data Summarizing Quantitative DataSummarizing Quantitative Data

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Summarizing Categorical DataSummarizing Categorical Data

Frequency DistributionFrequency Distribution Relative Frequency Distribution Relative Frequency Distribution Percent Frequency Percent Frequency

DistributionDistribution Bar ChartBar Chart Pie ChartPie Chart CrosstabulatioCrosstabulatio

nn

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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 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.

Frequency DistributionFrequency Distribution

5 Slide

Guests staying at Marada Inn were asked to rate theGuests staying at Marada Inn were asked to rate thequality of their accommodations as being quality of their accommodations as being excellentexcellent,,above averageabove average, , averageaverage, , below averagebelow average, or , or poorpoor. The. Theratings provided by a sample of 20 guests are: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


Example: Marada InnExample: Marada Inn

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PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent

22 33 55 99 11

TotalTotal 20 20

RatingRating FrequencyFrequency


7 Slide

Using Excel’s COUNTIF FunctionUsing Excel’s COUNTIF Functionto Construct a Frequency Distributionto Construct a Frequency Distribution

Excel Formula Excel Formula WorksheetWorksheet

Note: Rows 9-21 are not shown.Note: Rows 9-21 are not shown.

A B C D1 Quality Rating Quality Rating Frequency2 Above Average Poor =COUNTIF($A$2:$A$21,C2)3 Below Average Below Average =COUNTIF($A$2:$A$21,C3)4 Above Average Average =COUNTIF($A$2:$A$21,C4)5 Average Above Average =COUNTIF($A$2:$A$21,C5)6 Average Excellent =COUNTIF($A$2:$A$21,C6)7 Above Average Total =SUM(D2:D6)8 Above Average

8 Slide

Excel Value Excel Value WorksheetWorksheet

Using Excel’s COUNTIF FunctionUsing Excel’s COUNTIF Functionto Construct a Frequency Distributionto Construct a Frequency Distribution


A B C D1 Quality Rating Quality Rating Frequency2 Above Average Poor 23 Below Average Below Average 34 Above Average Average 55 Average Above Average 96 Average Excellent 17 Above Average Total 208 Above Average

9 Slide

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.

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

10 Slide

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.

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.

11 Slide

Relative Frequency andRelative Frequency andPercent Frequency DistributionsPercent Frequency Distributions

PoorPoorBelow AverageBelow AverageAverageAverageAbove AverageAbove AverageExcellentExcellent

.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


12 Slide

Excel Formula Excel Formula WorksheetWorksheet

Note: Columns A-B and rows 9-21 and are not shown.Note: Columns A-B and rows 9-21 and are not shown.

Using Excel to Construct Relative Using Excel to Construct Relative Frequency and Percent Frequency Frequency and Percent Frequency

DistributionsDistributions C D E F

1 Quality Rating FrequencyRelative

FrequencyPercent

Frequency2 Poor =COUNTIF($A$2:$A$21,C2) =D2/$D$7 =E2*1003 Below Average =COUNTIF($A$2:$A$21,C3) =D3/$D$7 =E3*1004 Average =COUNTIF($A$2:$A$21,C4) =D4/$D$7 =E4*1005 Above Average =COUNTIF($A$2:$A$21,C5) =D5/$D$7 =E5*1006 Excellent =COUNTIF($A$2:$A$21,C6) =D6/$D$7 =E6*1007 Total =SUM(D2:D6) =SUM(E2:E6) =SUM(F2:F6)8

13 Slide

Excel Value Excel Value WorksheetWorksheet

Using Excel to Construct Relative Using Excel to Construct Relative Frequency and Percent Frequency Frequency and Percent Frequency

DistributionsDistributions C D E F

1 Quality Rating FrequencyRelative

FrequencyPercent

Frequency2 Poor 2 0.10 103 Below Average 3 0.15 154 Average 5 0.25 255 Above Average 9 0.45 456 Excellent 1 0.05 57 Total 20 1.00 1008

Note: Columns A-B and rows 9-21 and are not shown.Note: Columns A-B and rows 9-21 and are not shown.

14 Slide

Bar Chart (In Excel this is called a Column Bar Chart (In Excel this is called a Column Chart)Chart)

A A bar chartbar chart 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.

15 Slide

Poor BelowAverage

Average AboveAverage

Excellent

Freq

uenc

y

Rating

Bar Chart (In Excel this is called a Column Bar Chart (In Excel this is called a Column Chart)Chart)

123456789

10 Marada Inn Quality RatingsMarada Inn Quality Ratings

16 Slide

Using Excel’s Chart ToolsUsing Excel’s Chart Toolsto Construct a Bar Chartto Construct a Bar Chart

Step 1.Step 1. Select cells C1:D6 Select cells C1:D6Step 2.Step 2. Click the Click the InsertInsert tab on the Ribbon tab on the Ribbon

Step 4.Step 4. When the list of column chart subtypes appears: When the list of column chart subtypes appears: Go to the Go to the 2-D Column2-D Column section section

Click Click Clustered ColumnClustered Column (the leftmost chart) (the leftmost chart)Step 5.Step 5. In the In the Chart LayoutsChart Layouts group, click the group, click the MoreMore button button (the downward pointing (the downward pointing arrowarrow with a line over it) with a line over it) to display all the optionsto display all the options

… … continuedcontinued

Step 3.Step 3. In the In the ChartsCharts group, click group, click ColumnColumn

17 Slide

Step 6.Step 6. Choose Choose Layout 9Layout 9



Step 7.Step 7. Click the Click the Chart TitleChart Title and replace it with and replace it with Marada Inn Quality RatingsMarada Inn Quality RatingsStep 8.Step 8. Click the Click the Horizontal Axis (Category) Horizontal Axis (Category)

TitleTitle and and replace it with replace it with Quality RatingQuality RatingStep 9.Step 9. Click the Click the Vertical Axis (Value) TitleVertical Axis (Value) Title

andand replace it with replace it with FrequencyFrequencyStep 10.Step 10. Right click the Right click the Series 1 Legend EntrySeries 1 Legend Entry

and chooseand choose DeleteDelete from the list of options that from the list of options that

appearappear

18 Slide

Step 11.Step 11. Right click the vertical axis and choose Right click the vertical axis and choose Format AxisFormat Axis from the options that from the options that

appearappear


Step 12.Step 12. When the Format Axis dialog box When the Format Axis dialog box appears:appears:

Go to the Go to the Axis OptionsAxis Options section section Select Select FixedFixed for for Major UnitMajor Unit and and

enter 2.0 inenter 2.0 in the corresponding boxthe corresponding box Click CloseClick Close

19 Slide


C D E9101112131415161718192021

Marada Inn Quality Ratings

0

2

4

6

8

10

Poor BelowAverage

Average AboveAverage

Excellent

Quality Rating

Freq

uenc

y

20 Slide

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 frequencies; then use the relative frequencies to subdivide the circle into sectors that correspond toto subdivide the circle into sectors that correspond to the relative frequency for each class.the relative frequency for each class. Since there are 360 degrees in a circle, a class with aSince there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90relative frequency of .25 would consume .25(360) = 90 degrees of the circle.degrees of the circle.

21 Slide

BelowAverage 15%

Average 25%

AboveAverage 45%

Poor10%

Excellent 5%

Marada InnMarada Inn Quality Quality RatingsRatings

Pie ChartPie Chart

22 Slide

Insights Gained from the Preceding Pie ChartInsights Gained from the Preceding Pie Chart


• 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.

23 Slide

Excel’s chart tools can be used to develop a pie chart forExcel’s chart tools can be used to develop a pie chart forthe Marada quality rating data in much the same way wethe Marada quality rating data in much the same way wedeveloped the bar chart.developed the bar chart.

Using Excel’s Chart ToolsUsing Excel’s Chart Toolsto Construct a Pie Chartto Construct a Pie Chart

The major difference is that in step 3 we would chooseThe major difference is that in step 3 we would choosePiePie in the Charts group. in the Charts group.

24 Slide

Using Excel’s Chart ToolsUsing Excel’s Chart Toolsto Construct a Pie Chartto Construct a Pie Chart

C D E91011121314151617181920

Marada Inn Quality Ratings

Excellent5%

Average25%

Poor10%

Above Average

45%

Below Average

15%

25 Slide

Excel’s PivotTable ReportExcel’s PivotTable Reportand PivotChart Reportand PivotChart Report

You have now seen how Excel’s COUNTIF function canYou have now seen how Excel’s COUNTIF function canbe used to develop a frequency distribution and Excel’sbe used to develop a frequency distribution and Excel’sChart Tools can be used to create bar and pie charts.Chart Tools can be used to create bar and pie charts.But there is a more powerful set of Excel tools that canBut there is a more powerful set of Excel tools that canbe used for categorical data:be used for categorical data:

• PivotTable report PivotTable report • PivotChart reportPivotChart report

26 Slide

Summarizing Quantitative DataSummarizing Quantitative Data

Frequency DistributionFrequency Distribution Relative Frequency andRelative Frequency and Percent Frequency Percent Frequency

DistributionsDistributions Dot PlotDot Plot HistogramHistogram Cumulative DistributionsCumulative Distributions OgiveOgive Stem-Leaf DisplayStem-Leaf Display CrosstabulationCrosstabulation Scatter DiagramScatter Diagram

27 Slide

The manager of Hudson Auto would like to The manager of Hudson Auto would like to gain again a

better understanding of the cost of parts used in better understanding of the cost of parts used in thethe

engine tune-ups performed in the shop. She engine tune-ups performed in the shop. She examinesexamines

50 customer invoices for tune-ups. The costs of 50 customer invoices for tune-ups. The costs of parts,parts,

rounded to the nearest dollar, are listed on the rounded to the nearest dollar, are listed on the nextnext

slide.slide.

Example: Hudson Auto RepairExample: Hudson Auto Repair


28 Slide

Sample of Parts Cost($) for 50 Tune-Sample of Parts Cost($) for 50 Tune-upsups91 78 93 57 75 52 99 80 97 62

71 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



29 Slide


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 classes.Smaller data sets usually require fewer classes.

30 Slide


Guidelines for Selecting Width of ClassesGuidelines for Selecting Width of Classes

Largest Data Value Smallest Data ValueNumber of Classes

•Use classes of equal width.Use classes of equal width.•Approximate Class Width =Approximate Class Width =

31 Slide


If we choose six classes: If we choose six classes:

50-5950-59

60-69 60-69 70-7970-79 80-8980-89 90-9990-99

100-109100-109

22 1313 1616 77 77 55Total 50Total 50

Parts Cost ($)Parts Cost ($) FrequencyFrequency

Approximate Class Width = (109 - 52)/6 = 9.5 Approximate Class Width = (109 - 52)/6 = 9.5 1010


32 Slide

Using Excel’s PivotTable ReportUsing Excel’s PivotTable Reportto Construct a Frequency Distributionto Construct a Frequency Distribution

Step 1Step 1 Click the Click the InsertInsert tab on the Ribbon tab on the RibbonStep 2Step 2 In the In the TablesTables group, click the icon above the group, click the icon above the word PivotTableword PivotTableStep 3Step 3 When the When the Create PivotTableCreate PivotTable dialog box appears: dialog box appears: Choose Choose Select a table or rangeSelect a table or range Enter A1:A51 in the Enter A1:A51 in the Table/RangeTable/Range box box ChooseChoose Existing Worksheet Existing Worksheet as the locationas the location for the PivotTablefor the PivotTable Enter C1 in the Enter C1 in the LocationLocation box box Click Click OKOK


33 Slide

Step 5Step 5 Click on Click on Sum of Parts CostSum of Parts Cost in the in the ValuesValues area areaStep 6Step 6 Click Click Value Field SettingsValue Field Settings from the list of options from the list of options that appearthat appearStep 7Step 7 When the Value Field Settings dialog box appears: When the Value Field Settings dialog box appears: Under Under Summarize value field bySummarize value field by, choose , choose CountCount Click Click OKOK

Step 4Step 4 In the PivotTable Field List, go to Choose Fields In the PivotTable Field List, go to Choose Fields to add to report:to add to report: Drag the Drag the Parts CostParts Cost field to the field to the Row LabelsRow Labels area area Drag the Drag the Parts CostParts Cost field to the field to the ValuesValues area area


34 Slide

Step 2Step 2 Choose Choose GroupGroup from the list of options that appears from the list of options that appearsStep 3Step 3 When the Grouping dialog box appears: When the Grouping dialog box appears: Enter 50 in the Enter 50 in the Starting atStarting at box box Enter 109 in the Enter 109 in the Ending atEnding at box box Enter 10 in the Enter 10 in the ByBy box box Click Click OKOK

Step 1Step 1 Right click any cell in the PivotTable report Right click any cell in the PivotTable report containing a parts cost. containing a parts cost.


To construct the frequency distribution, we must groupTo construct the frequency distribution, we must groupthe rows containing parts costs.the rows containing parts costs.

35 Slide

Excel Value Worksheet Excel Value Worksheet


A B C D1 Parts Cost Parts Cost Count of Parts Cost2 91 50-59 23 71 60-69 134 104 70-79 165 85 80-89 76 62 90-99 77 78 100-109 58 69 50Grand Total


36 Slide


50-5950-59

60-69 60-69 70-7970-79 80-8980-89 90-9990-99

100-109100-109

PartsPartsCost ($)Cost ($)

.04.04 .26.26 .32.32 .14.14 .14.14 .10.10

Total 1.00 Total 1.00

RelativeRelativeFrequencyFrequency

44 2626 3232 1414 1414 1010

100 100

PercentPercent FrequencyFrequency

2/502/50 .04(10.04(100)0)


37 Slide

• Only 4% of the parts costs are in the $50-59 class.Only 4% of the parts costs are in the $50-59 class.

• The greatest percentage (32% or almost one-third)The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class.of the parts costs are in the $70-79 class.

• 30% of the parts costs are under $70.30% of the parts costs are under $70.

• 10% of the parts costs are $100 or more.10% of the parts costs are $100 or more.

Insights Gained from the % Frequency Insights Gained from the % Frequency Distribution:Distribution:



38 Slide

Dot PlotDot Plot

One of the simplest graphical summaries of One of the simplest graphical summaries of data is a data is a dot plotdot plot..

A horizontal axis shows the range of data A horizontal axis shows the range of data values.values. Then each data value is represented by a dot Then each data value is represented by a dot placed above the axis.placed above the axis.

39 Slide

Dot PlotDot Plot

5050 6060 7070 8080 9090 100100 110110Cost ($)

Tune-up Parts CostTune-up Parts Cost


40 Slide

HistogramHistogram

Another common graphical presentation ofAnother common graphical presentation of quantitative data is a quantitative data is a histogramhistogram.. The variable of interest is placed on the horizontalThe variable of interest is placed on the horizontal axis.axis. A rectangle is drawn above each class interval withA rectangle is drawn above each class interval with its height corresponding to the interval’s its height corresponding to the interval’s frequencyfrequency,, relative frequencyrelative frequency, or , or percent frequencypercent frequency.. Unlike a bar graph, a histogram has Unlike a bar graph, a histogram has no naturalno natural separation between rectanglesseparation between rectangles of adjacent classes. of adjacent classes.

41 Slide

HistogramHistogram

2468

1012141618

PartsCost ($)

Freq

uenc

y

5059 6069 7079 8089 9099 100-110

Tune-up Parts CostTune-up Parts Cost Example: Hudson Auto RepairExample: Hudson Auto Repair

42 Slide

Using Excel’s Chart ToolsUsing Excel’s Chart Toolsto Construct a Histogramto Construct a Histogram

Step 1.Step 1. Select cells C2:D7 Select cells C2:D7Step 2.Step 2. Click the Click the Insert Insert tab on the Ribbontab on the Ribbon

Step 4.Step 4. When the list of column chart subtypes appears: When the list of column chart subtypes appears: Go to the Go to the 2-D Column2-D Column section section

Click Click Clustered ColumnClustered Column (the leftmost chart) (the leftmost chart)


Step 3.Step 3. In the In the Charts Charts group, click group, click ColumnColumn

Step 5.Step 5. In the In the Chart LayoutsChart Layouts group, click the group, click the MoreMore button (the downward pointing button (the downward pointing arrowarrow with with a line over it) to display all the optionsa line over it) to display all the options

43 Slide


Step 6.Step 6. Choose Choose Layout 8Layout 8Step 7.Step 7. Select the Select the Chart TitleChart Title and replace it with and replace it with Tune-up Parts CostTune-up Parts Cost

Step 9.Step 9. Select the Select the Vertical (Value) Axis TitleVertical (Value) Axis Title and replace and replace it with it with FrequencyFrequency

Step 8.Step 8. Select the Select the Horizontal (Category) Axis TitleHorizontal (Category) Axis Title and and replace it withreplace it with Parts Cost ($) Parts Cost ($)

44 Slide


C D E101112131415161718192021222324

Tune-up Parts Cost

0

5

10

15

20

50-59 60-69 70-79 80-89 90-99 100-109

Parts Cost ($)

Freq

uenc

y

45 Slide

SymmetricSymmetric

HistogramHistogram

Rela

tive

Freq

uenc

y

.05

.10

.15

.20

.25

.30

.35

0

• Left tail is the mirror image of the right tailLeft tail is the mirror image of the right tail• Examples: heights and weights of peopleExamples: heights and weights of people

46 Slide

HistogramHistogram

Moderately Skewed LeftModerately Skewed Left

Rela

tive

Freq

uenc

y

.05

.10

.15

.20

.25

.30

.35

0

• A longer tail to the leftA longer tail to the left• Example: exam scoresExample: exam scores

47 Slide

Moderately Right SkewedModerately Right Skewed

HistogramHistogram

Rela

tive

Freq

uenc

y

.05

.10

.15

.20

.25

.30

.35

0

• A Longer tail to the rightA Longer tail to the right• Example: housing valuesExample: housing values

48 Slide

HistogramHistogram

Highly Skewed RightHighly Skewed RightRe

lativ

e Fr

eque

ncy

.05

.10

.15

.20

.25

.30

.35

0

• A very long tail to the rightA very long tail to the right• Example: executive salariesExample: executive salaries

49 Slide

Cumulative frequency distributionCumulative frequency distribution shows the shows the numbernumber of items with values less than or equal to the of items with values less than or equal to the upper limit of each class..upper limit of each class..

Cumulative relative frequency distributionCumulative relative frequency distribution – shows – shows the the proportionproportion of items with values less than or 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 the percentagepercentage of items with values less than or of items with values less than or equal to the upper limit of each class.equal to the upper limit of each class.

50 Slide

Cumulative DistributionsCumulative Distributions

Hudson Auto RepairHudson Auto Repair

<< 59 59

<< 69 69 << 79 79 << 89 89 << 99 99

<< 109 109

Cost ($)Cost ($) CumulativeCumulativeFrequencyFrequency

CumulativeCumulativeRelativeRelative

FrequencyFrequencyCumulativeCumulative

PercentPercent FrequencyFrequency

22 1515 3131 3838 4545

50 50

.04.04 .30.30 .62.62 .76.76 .90.90

1.00 1.00

44 3030 6262 7676 9090

100 100

2 + 2 + 1313 15/5015/50 .30(10.30(10

0)0)

51 Slide

OgiveOgive

An An ogiveogive is a graph of a cumulative is a graph of a cumulative distribution.distribution. The data values are shown on the horizontal The data values are shown on the horizontal axis.axis. Shown on the vertical axis are the:Shown on the vertical axis are the:• cumulative frequencies, orcumulative frequencies, or• cumulative relative frequencies, orcumulative relative frequencies, or• cumulative percent frequenciescumulative percent frequencies

The frequency (one of the above) of each class The frequency (one of the above) of each class is plotted as a point.is plotted as a point.

The plotted points are connected by straight The plotted points are connected by straight lines.lines.

52 Slide

• Because the class limits for the parts-cost Because the class limits for the parts-cost data are 50-59, 60-69, and so on, there data are 50-59, 60-69, and so on, there appear to be one-unit gaps from 59 to 60, appear to be one-unit gaps from 59 to 60, 69 to 70, and so on.69 to 70, and so on.

OgiveOgive

• These gaps are eliminated by plotting points These gaps are eliminated by plotting points halfway between the class limits.halfway between the class limits.

• Thus, 59.5 is used for the 50-59 class, 69.5 Thus, 59.5 is used for the 50-59 class, 69.5 is used for the 60-69 class, and so on.is used for the 60-69 class, and so on.

Hudson Auto RepairHudson Auto Repair

53 Slide

PartsPartsCost ($)Cost ($)

20

40

60

80

100

Cum

ulat

ive

Perc

ent F

requ

ency

Cum

ulat

ive

Perc

ent F

requ

ency

50 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 Cost Example: Hudson Auto RepairExample: Hudson Auto Repair

54 Slide

Using Excel’s PivotChart ReportUsing Excel’s PivotChart Report

You have now seen how Excel’s PivotTable report can beYou have now seen how Excel’s PivotTable report can beused to construct a frequency distribution for quantitativeused to construct a frequency distribution for quantitativedata and how Excel’s Chart tools can be used to constructdata and how Excel’s Chart tools can be used to constructthe corresponding histogram.the corresponding histogram.However, Excel’s PivotChart report can be used toHowever, Excel’s PivotChart report can be used todevelop a frequency distribution and a graphical displaydevelop a frequency distribution and a graphical displayat the same time.at the same time.

55 Slide


Step 1.Step 1. Click the Click the InsertInsert tab on the Ribbon tab on the RibbonStep 2.Step 2. In the In the Tables Tables group, click the word group, click the word PivotTablePivotTable

Step 4.Step 4. When the When the Create PivotTable with PivotChartCreate PivotTable with PivotChart dialog box appears:dialog box appears:

Choose Choose Select a table or rangeSelect a table or range Enter A1:A51 in the Enter A1:A51 in the Table/RangeTable/Range box box Choose Choose Existing Worksheet Existing Worksheet as the location foras the location for the PivotTable and PivotChartthe PivotTable and PivotChart Enter C1 in the Enter C1 in the LocationLocation box box Click Click OKOK … … continuedcontinued

Step 3.Step 3. Choose Choose PivotChart PivotChart from the options that appearfrom the options that appear

56 Slide


Step 5.Step 5. In the In the PivotTable Field ListPivotTable Field List, go to , go to Choose FieldsChoose Fields to add to reportto add to report Drag the Drag the Parts CostParts Cost field to the field to the Axis FieldsAxis Fields (Categories)(Categories) area area Drag the Drag the Parts CostParts Cost field to the field to the ValuesValues area areaStep 6.Step 6. Click Click Sum of Parts CostSum of Parts Cost in the in the ValuesValues area areaStep 7.Step 7. Click Click Value Field SettingsValue Field Settings from the list of options from the list of options that appearthat appearStep 8.Step 8. When the Value Field Settings dialog appears: When the Value Field Settings dialog appears: Under Under Summarize value field bySummarize value field by, choose , choose CountCount Click Click OKOK


57 Slide


Step 9.Step 9. Right click cell C2 n the PivotTable report or any Right click cell C2 n the PivotTable report or any other cell containing a parts costother cell containing a parts costStep 10. Step 10. Choose Choose GroupGroup from the list of options from the list of optionsStep 11.Step 11. When the Grouping dialog box appears: When the Grouping dialog box appears: Enter ___ in the Enter ___ in the Starting at Starting at boxbox Enter ___ in the Enter ___ in the Ending atEnding at box box Click Click OKOKStep 12.Step 12. Click inside the resulting PivotChart Click inside the resulting PivotChartStep 13.Step 13. Click the Click the DesignDesign tab on the Ribbon tab on the Ribbon


58 Slide


Step 14.Step 14. In the In the Chart LayoutsChart Layouts group, click the group, click the MoreMore button (the downward pointing arrow with abutton (the downward pointing arrow with a line over it) to display all the optionsline over it) to display all the optionsStep 15. Step 15. Choose Choose Layout 8Layout 8Step 16.Step 16. Select the Select the Chart TitleChart Title and replace it with and replace it with Tune-up Parts CostsTune-up Parts CostsStep 17.Step 17. Select the Select the Horizontal Axis (Category) TitleHorizontal Axis (Category) Title and and replace it with replace it with Parts Cost ($)Parts Cost ($)Step 18.Step 18. Select the Select the Vertical (Value) Axis TitleVertical (Value) Axis Title and replace and replace it with it with FrequencyFrequency

59 Slide

End of Chapter 2, Part AEnd of Chapter 2, Part A

60 Slide

Chapter 2, Part BChapter 2, Part BDescriptive Statistics:Descriptive Statistics:

Tabular and Graphical PresentationsTabular and Graphical Presentations

Crosstabulations and Scatter DiagramsCrosstabulations and Scatter Diagrams Exploratory Data Analysis: Stem-and-Leaf Exploratory Data Analysis: Stem-and-Leaf

DisplayDisplay

61 Slide

Exploratory Data AnalysisExploratory Data Analysis

The techniques of The techniques of exploratory data analysisexploratory data analysis consist of consist of simple arithmetic and easy-to-draw pictures that cansimple arithmetic and easy-to-draw pictures that can be used to summarize data quickly.be used to summarize data quickly. One such technique is the One such technique is the stem-and-leaf displaystem-and-leaf display..

62 Slide

Stem-and-Leaf DisplayStem-and-Leaf Display

Each digit on a stem is a Each digit on a stem is a leafleaf.. Each line in the display is referred to as a Each 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 is It is similar to a histogramsimilar to a histogram on its side, but it has the on 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 the A stem-and-leaf display shows both the rank orderrank order and and shape of the distributionshape of the distribution of the data. of the data.

63 Slide


The manager of Hudson Auto would like to The manager of Hudson Auto would like to gain again a

better understanding of the cost of parts used in better understanding of the cost of parts used in thethe

engine tune-ups performed in the shop. She engine tune-ups performed in the shop. She examinesexamines

50 customer invoices for tune-ups. The costs of 50 customer invoices for tune-ups. The costs of parts,parts,

rounded to the nearest dollar, are listed on the rounded to the nearest dollar, are listed on the nextnext

slide.slide.

64 Slide

Sample of Parts Cost ($) for 50 Sample of Parts Cost ($) for 50 Tune-upsTune-ups91 78 93 57 75 52 99 80 97 62

71 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



65 Slide


5566778899

1010

2 72 7 2 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 stema leafa leaf


66 Slide

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 corresponds to leaf values of 0 4, and the second 4, and the second value corresponds to leaf values of 5 value corresponds to leaf values of 5 9. 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 can condensed the data too much, we can stretch thestretch the displaydisplay by using two stems for each leading digit(s). by using two stems for each leading digit(s).

67 Slide

Stretched Stem-and-Leaf DisplayStretched Stem-and-Leaf Display

5 5 95 5 91 41 47 7 7 8 97 7 7 8 91 31 35 8 95 8 90 0 2 30 0 2 35 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 45 6 7 8 8 8 9 9 95 6 7 8 8 8 9 9 92 2 2 22 2 2 2772255

556666777788889999

10101010


68 Slide


Leaf UnitsLeaf Units

• Where the leaf unit is not shown, it is assumedWhere the leaf unit is not shown, it is assumed to 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.

69 Slide

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 9910101111

Leaf Unit = 0.1Leaf Unit = 0.16 86 81 41 4220 70 7

8.6 8.6 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

70 Slide

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 = 10881 91 90 30 31 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 isrepresented as represented as

an 8.an 8.

71 Slide

Crosstabulations and Scatter DiagramsCrosstabulations and Scatter Diagrams

CrosstabulationCrosstabulation and a and a scatter diagramscatter diagram are two are two methods for summarizing the data for two variablesmethods for summarizing the data for two variables simultaneously.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 used to summarize the data for to summarize the data for one variable at a timeone variable at a time..

72 Slide

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.

Crosstabulation can be used when:Crosstabulation can be used when:• One variable is Qualitative and the other isOne variable is Qualitative and the other is Categorical,Categorical,• Both variables are Qualitative, orBoth variables are Qualitative, or• Both variables are Categorical.Both variables are Categorical.

A A crosstabulationcrosstabulation is a tabular summary of is a tabular summary of data fordata for two variables and helps to reveal the two variables and helps to reveal the relationship between the two variables.relationship between the two variables.

73 Slide

PricePriceRangeRange Colonial Log Split A-FrameColonial Log Split A-FrameTotalTotal

<< $99,000 $99,000> $99,000> $99,000

18 6 19 1218 6 19 12 55554545

3030 20 35 15 20 35 15TotalTotal 10010012 14 16 312 14 16 3

Home StyleHome Style


Example: Finger Lakes HomesExample: Finger Lakes Homes

quantitativquantitativee

variablevariablecategoricacategorica

ll variablevariable

The number of Finger Lakes homes sold for The number of Finger Lakes homes sold for eacheach

style and price for the past two years is shown style and price for the past two years is shown below. below.

74 Slide


Insights Gained from Preceding CrosstabulationInsights Gained from Preceding Crosstabulation

• Only three homes in the sample are an A-FrameOnly three homes in the sample are an A-Frame style and priced at more than $99,000.style and priced at more than $99,000.

• The greatest number of homes (19) in the sampleThe greatest number of homes (19) in the sample are a split-level style and priced at less than orare a split-level style and priced at less than or equal to $99,000.equal to $99,000.


75 Slide


<< $99,000 $99,000> $99,000> $99,000

18 6 19 1218 6 19 12 55554545

3030 20 35 15 20 35 15TotalTotal 10010012 14 16 312 14 16 3


CrosstabulationCrosstabulationFrequencyFrequencydistributiondistribution

for thefor theprice rangeprice range

variable variable

Frequency distribution Frequency distribution forfor

the home style the home style variablevariable


76 Slide

Using Excel’s PivotTable ReportUsing Excel’s PivotTable Reportto Create a Crosstabulationto Create a Crosstabulation

Excel Worksheet (showing partial Excel Worksheet (showing partial data)data)


A B C D E1 Home Price ($) Style 2 1 >99K Colonial 3 2 <=99K Log 4 3 >99K Log 5 4 <=99K A-Frame 6 5 <=99K Colonial 7 6 <=99K Split-Level 8 7 >99K A-Frame 9 8 >99K Colonial

77 Slide

Displaying the Initial PivotTable Field List andDisplaying the Initial PivotTable Field List and PivotTable ReportPivotTable Report


Step 1Step 1 Click the Click the InsertInsert tab on the Ribbon tab on the RibbonStep 2Step 2 In the In the TablesTables group, click the icon above the group, click the icon above the word PivotTableword PivotTableStep 3Step 3 When the When the Create PivotTable Create PivotTable dialog box appears:dialog box appears:

Choose Choose Select a Table or RangeSelect a Table or Range Enter A1:C101 in the Enter A1:C101 in the Table/RangeTable/Range box box Choose Choose New WorksheetNew Worksheet as the location for as the location for

the PivotTable Reportthe PivotTable Report Click Click OKOK

78 Slide

Setting Up the PivotTable Field ListSetting Up the PivotTable Field List


Step 1Step 1 In the In the PivotTable Field ListPivotTable Field List, go to , go to Choose FieldsChoose Fields to add to reportto add to report Drag the Drag the Price ($) Price ($) field to field to Row LabelsRow Labels area area Drag the Drag the StyleStyle field to field to Column LabelsColumn Labels area area Drag the Drag the HomeHome field to the field to the ValuesValues area area

Step 4Step 4 When the Value Field Settings dialog box appears: When the Value Field Settings dialog box appears: Under Under Summarize value field bySummarize value field by, choose , choose CountCount Choose Choose New WorksheetNew Worksheet as the location for as the location for

Click Click OKOK

Step 2Step 2 Click on Click on Sum of HomeSum of Home in the in the ValuesValues area areaStep 3Step 3 Click Click Value Field SettingsValue Field Settings from the list of options from the list of options

79 Slide

Value WorksheetValue Worksheet


A B C D E F G1 Count of Home Style 2 Price ($) Colonial Log Split-Level A-Frame Grand Total3 <=99K 18 6 19 12 554 >99K 12 14 16 3 455 Grand Total 30 20 35 15 1006

80 Slide

Crosstabulation: Row or Column Crosstabulation: Row or Column PercentagesPercentages

Converting the entries in the table into row Converting the entries in the table into row percentages or column percentages can percentages or column percentages can provide additional insight about the provide additional insight about the relationship between the two variables.relationship between the two variables.

81 Slide


<< $99,000 $99,000> $99,000> $99,000

32.73 10.91 34.55 21.8232.73 10.91 34.55 21.82100100100100

Note: row totals are actually 100.01 due to rounding.Note: row totals are actually 100.01 due to rounding.26.67 31.11 35.56 6.6726.67 31.11 35.56 6.67


(Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100(Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100

Crosstabulation: Row PercentagesCrosstabulation: Row Percentages


82 Slide

PricePriceRangeRange Colonial Log Split A-FrameColonial Log Split A-Frame

<< $99,000 $99,000> $99,000> $99,000

60.00 30.00 54.29 80.0060.00 30.00 54.29 80.0040.00 70.00 45.71 20.0040.00 70.00 45.71 20.00


100100 100 100 100 100 100 100TotalTotal

(Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100(Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100

Crosstabulation: Column PercentagesCrosstabulation: Column Percentages


83 Slide

Crosstabulation: Simpson’s ParadoxCrosstabulation: Simpson’s Paradox

Simpson’ ParadoxSimpson’ Paradox: In some cases the : In some cases the conclusionsconclusions based upon an aggregated crosstabulation based upon an aggregated crosstabulation can becan be completely reversed if we look at the completely reversed if we look at the unaggregatedunaggregated data. Before drawing conclusions about data. Before drawing conclusions about relationships between two variables (for relationships between two variables (for aggregated data), you must investigate whether aggregated data), you must investigate whether any hidden variables could affect the results.any hidden variables could affect the results.

We must be careful in drawing conclusions about theWe must be careful in drawing conclusions about the relationship between the two variables in therelationship between the two variables in the aggregated crosstabulation.aggregated crosstabulation.

Data in two or more crosstabulations are oftenData in two or more crosstabulations are often aggregated to produce a summary crosstabulation.aggregated to produce a summary crosstabulation.

84 Slide

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.

A A scatter diagramscatter diagram is a graphical presentation of the is a graphical presentation of the relationship between two relationship between two quantitativequantitative variables. variables.

Scatter Diagram and TrendlineScatter Diagram and Trendline

A A trendlinetrendline is an approximation of the relationship. is an approximation of the relationship.

85 Slide

Scatter DiagramScatter Diagram

A Positive RelationshipA Positive Relationship

xx

yy

86 Slide


A Negative RelationshipA Negative Relationship

xx

yy

87 Slide


No Apparent RelationshipNo Apparent Relationship

xx

yy

88 Slide

Example: Panthers Football TeamExample: Panthers Football Team

1133221133

14142424181817173030

xx = Number of = Number ofInterceptionsInterceptions

yy = Number of = Number of Points ScoredPoints Scored


The Panthers football team is interested inThe Panthers football team is interested ininvestigating the relationship, if any, betweeninvestigating the relationship, if any, betweeninterceptions made and points scored.interceptions made and points scored.

89 Slide


yy

xx

Number of InterceptionsNumber of Interceptions

Num

ber o

f Poi

nts S

core

dNu

mbe

r of P

oint

s Sco

red

5510101515202025253030

00

3535

11 22 3300 44

90 Slide

Insights Gained from the Preceding Scatter Insights Gained from the Preceding Scatter DiagramDiagram

• The relationship is not perfect; all plotted points inThe relationship is not perfect; all plotted points in the scatter diagram are not on a straight line.the scatter diagram are not on a straight line.

• Higher points scored are associated with a higherHigher points scored are associated with a higher number of interceptions.number of interceptions.

• The scatter diagram indicates a positive relationshipThe scatter diagram indicates a positive relationship between the number of interceptions and thebetween the number of interceptions and the number of points scored.number of points scored.

Example: Panthers Football TeamExample: Panthers Football Team

91 Slide

Using Excel’s Chart Wizard to ConstructUsing Excel’s Chart Wizard to Constructa Scatter Diagram and Trendlinea Scatter Diagram and Trendline

Excel Worksheet (showing data)Excel Worksheet (showing data)A B C

1Number of

InterceptionsNumber of

Points Scored 2 1 14 3 3 24 4 2 18 5 1 17 6 3 30 7

92 Slide

Step 1Step 1 Select cells A2:B6 Select cells A2:B6Step 2Step 2 Click the Click the InsertInsert tab on the Excel Ribbon tab on the Excel RibbonStep 3Step 3 In the In the ChartsCharts group, click group, click ScatterScatter

Using Excel’s Chart Tools toUsing Excel’s Chart Tools toConstruct a Scatter Diagram and Construct a Scatter Diagram and

TrendlineTrendline

. . . continue. . . continue

Step 4Step 4 When the list of scatter diagram subtypes appears: When the list of scatter diagram subtypes appears: Click Click Scatter with only MarkersScatter with only MarkersStep 5Step 5 In the In the Chart LayoutChart Layout group, click group, click Layout 1Layout 1Step 6Step 6 Select the Select the Chart TitleChart Title and replace it with and replace it with ScatterScatter Diagram for the PanthersDiagram for the PanthersStep 7Step 7 Select the Select the Horizontal Axis (Value) TitleHorizontal Axis (Value) Title and and replace it with replace it with Number of InterceptionsNumber of Interceptions

93 Slide

Step 8Step 8 Select the Select the Vertical (Value) Axis TitleVertical (Value) Axis Title and replace and replace it with it with Number of Points ScoredNumber of Points ScoredStep 9Step 9 Right click Right click Series 1 Legend Entry Series 1 Legend Entry and click and click DeleteDelete

Step 10Step 10 Position the pointer over any data point in the Position the pointer over any data point in the scatter diagram and right-click to display optionsscatter diagram and right-click to display options


TrendlineTrendline

Step 11Step 11 Choose Choose Add TrendlineAdd TrendlineStep 12Step 12 When the When the Format TrendlineFormat Trendline dialog box appears: dialog box appears: Select Trendline OptionsSelect Trendline Options Choose Choose LinearLinear from from Trend/Regression TypeTrend/Regression Type list list Click Click CloseClose

- - - - - - - - - - - - - - - - To Add a Trendline - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - To Add a Trendline - - - - - - - - - - - - - - -

94 Slide

A B C 8 9

10 11 12 13 14 15 16 17 18 19 20

Scatter Diagram for the Panthers

0

5

10

15

20

25

30

35

0 1 2 3 4Number of Interceptions

Num

ber o

fPo

ints

Sco

red.


TrendlineTrendline

95 Slide

Tabular and Graphical MethodsTabular and Graphical Methods

Categorical DataCategorical Data Quantitative DataQuantitative Data

TabularTabularMethodsMethods

TabularTabularMethodsMethods

GraphicalGraphical MethodsMethods

GraphicalGraphical MethodsMethods

• FrequencyFrequency DistributionDistribution• Rel. Freq. Dist.Rel. Freq. Dist.• Percent Freq. Percent Freq. DistributionDistribution• CrosstabulationCrosstabulation

• Bar GraphBar Graph• Pie ChartPie Chart

• FrequencyFrequency DistributionDistribution• Rel. Freq. Dist.Rel. Freq. Dist.• % Freq. Dist.% Freq. Dist.• Cum. Freq. Dist.Cum. Freq. Dist.• Cum. Rel. Freq.Cum. Rel. Freq. DistributionDistribution• Cum. % Freq.Cum. % Freq. Distribution Distribution • CrosstabulationCrosstabulation

• Dot PlotDot Plot• HistogramHistogram• OgiveOgive• Stem-and-Stem-and- Leaf DisplayLeaf Display• ScatterScatter DiagramDiagram

DataData

96 Slide

End of Chapter 2, Part BEnd of Chapter 2, Part B

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