chapter 2 (summarizing data)_st

8/3/2019 Chapter 2 (Summarizing Data)_st

1/68

Chapter 2Chap

ter 2

Summarizing dataSummarizing data

Summarizing Qualitative DataSummarizing Qualitative Data

Summarizing Quantitative DataSummarizing Quantitative Data

Part A


2/68

Why summarizing data?Why summarizing data?

Raw dataRaw data

Disadvantage?Disadvantage?

How to extract information from the data?How to extract information from the data?


3/68

Example: hours worked in one week by employeesExample: hours worked in one week by employees

in a companys production departmentin a companys production department

46.346.3 45.145.1 45.645.6 45.645.6 46.146.1 45.045.0 43.543.5 39.239.2 39.239.2 39.139.1

39.239.2

42.342.3

39.639.6

39.539.5

38.938.9

44.444.4

43.443.4

43.243.2

43.843.8

39.139.1

44.244.2 43.543.5 42.042.0 43.143.1 42.442.4 42.442.4 42.842.8 42.942.9 43.143.1 39.839.8

41.341.3 40.040.0 39.639.6 39.739.7 42.142.1 39.839.8 44.344.3 46.246.2 41.341.3 40.840.8


4/68

Example: arrayed dataExample: arrayed data

38.938.9 39.139.1 39.139.1 39.239.2 39.239.2 39.239.2 39.539.5 39.639.6 39.639.6 39.739.7

39.839.8 39.839.8 40.040.0 40.840.8 41.341.3 41.341.3 42.042.0 42.142.1 42.342.3 42.442.4

42.442.4 42.842.8 42.942.9 43.143.1 43.143.1 43.243.2 43.443.4 43.543.5 43.543.5 43.843.8

44.244.2 44.344.3 44.444.4 45.045.0 45.145.1 45.645.6 45.645.6 46.146.1 46.246.2 46.346.3


5/68

I. Summarizing Qualitative DataI. Summarizing Qualitative Data

Frequency DistributionFrequency Distribution

Relative Frequency DistributionRelative Frequency Distribution

Percent Frequency DistributionPercent Frequency Distribution Bar GraphBar Graph

Pie ChartPie Chart


6/68

AAfrequency distribution?freq

uency distribution?AAfrequency distribution?freq

uency distribution?

Objective?Objective?Objective?Objective?

Frequency Distributionrequency Distribution


7/68

Example: Marada InnExample: Marada Inn

Guests staying at Marada Inn wereGuests staying at Marada Inn wereasked to rate the quality of theirasked to rate the quality of their

accommodations as beingaccommodations as being exce l l en tx ce l l en t ,,above a ve r agebove a ve r age ,, ave rageve r age ,, be l ow ave ragee l ow ave rage , or, orpoo roo r . The ratings provided by a sample of 20 guests are:. The ratings provided by a sample of 20 guests are:


8/68


Below AverageBelow Average

Above AverageAbove Average


AverageAverage


AverageAverage


AverageAverage



PoorPoor

ExcellentExcellent


AverageAverage




PoorPoor


AverageAverage

AverageAverage


9/68


PoorPoor


AverageAverage


ExcellentExcellent

22

33

55

99

11

TotalTotal 2020

RatingRating FrequencyFrequency


10/68

TheThe relative frequencyrelative frequency of a class?of a class?TheThe relative frequencyrelative frequency of a class?of a class?

AArelative frequency distribution?relative frequency distribution?AArelative frequency distribution?relative frequency distribution?

Relative Frequency DistributionRelative Frequency Distribution


11/68

Percent Frequency DistributionPercent Frequency Distribution

TheThe percent frequencypercent frequency of a class?of a class?TheThe percent frequencypercent frequency of a class?of a class?

AApercent frequency distribution?percent frequency distribution?AApercent frequency distribution?percent frequency distribution?


12/68

Relative Frequency andRelative Frequency and

Percent Frequency DistributionsPercent Frequency Distributions

PoorPoorBelow AverageBelow Average

AverageAverage


ExcellentExcellent

.10.10

.15.15

.25.25

.45.45

.05.05TotalTotal 1.001.00

10101515

2525

4545

55100100

RelativeRelative

FrequencyFrequency

PercentPercent

FrequencyFrequencyRatingRating

.10(100) =.10(100) =

1010

1/20 = .051/20 = .05


13/68

Bar GraphBar Graph

AAbar graphbar graph: graphical device: graphical device

On horizontal axis (usually): labels of the classes.On horizontal axis (usually): labels of the classes.

On vertical axis (usually): scaleOn vertical axis (usually): scale(frequency, relative frequency, percent frequency)(frequency, relative frequency, percent frequency)

Using fixed-width barUsing fixed-width bar

Bars are separatedBars are separated


14/68

PoorPoor BelowAverage

BelowAverage

AverageAverage AboveAverage

AboveAverage

ExcellentExcellent

Frequency

Frequency

Ratingating

Bar GraphBar Graph

11

22

33

44

5566

77

88

991010

Marada Inn Quality RatingsMarada Inn Quality Ratings


15/68

Pie ChartPie Chart

TheThe pie chartpie chart: commonly used graphical device: commonly used graphical device

s First draw aFirst draw a circlecircle; then subdivide the; then subdivide the

circle into sectors/partscircle into sectors/parts

s A relative frequency of .25 wouldA relative frequency of .25 would

consume ? degrees of the circle.consume ? degrees of the circle.


16/68

BelowAverage

15%

BelowAverage

15%

Average

25%

Average

25%

AboveAverage

45%

AboveAverage

45%

Poor10%

Poor10%

Excellent5%

Excellent5%

Marada InnMarada InnQuality RatingsQuality RatingsMarada InnMarada InnQuality RatingsQuality Ratings

Pie ChartPie Chart


17/68

s Insights Gained from the Preceding Pie Chart?Insights Gained from the Preceding Pie Chart?



18/68

II. Summarizing Quantitative DataII. Summarizing Quantitative Data

Frequency DistributionFrequency Distribution Relative Frequency and Percent FrequencyRelative Frequency and Percent Frequency

DistributionsDistributions

Dot PlotDot Plot

HistogramHistogram

Cumulative DistributionsCumulative Distributions

OgiveOgive


19/68

1. Simple frequency distribution1. Simple frequency distribution

Simple frequency distributionSimple frequency distribution

Applicable to?Applicable to?

Not suitable for?Not suitable for?


20/68

ExampleExample

The following data record the number ofThe following data record the number ofchildren in the families of the 47 workers in achildren in the families of the 47 workers in a

company:company:

11 11 33 22 00 22 00 11 22 22 11 33

55 22 44 00 00 22 44 11 11 22 22 00

33 00 00 22 11 33 66 00 22 11 00 33

22 22 22 11 00 00 11 11 33 11 44


21/68

Constructing a simple frequencyConstructing a simple frequency

distribution using a tally chartdistribution using a tally chart

Data valueData value Tally marksTally marks TotalTotal

0

12

3

45

6

||||||||||||||||||||||

||||||||||||||||||||||||||||||||||||||||||||||||||

||||||||||||||

||||||||

||

1111

12121313

66

3311

11


22/68

Frequency distribution tableFrequency distribution table

Number of childrenNumber of children

in familyin familyNumber of workersNumber of workers

00 1111

11 1212

22 1313

33 66

44 33

55 11

66 11


23/68

Disadvantage of simple frequencyDisadvantage of simple frequency

distribution?distribution?


24/68

2. Grouped frequency distributions2. Grouped frequency distributions

A large number of values.A large number of values.

A grouped frequency distribution?A grouped frequency distribution?


25/68

Example: Hudson Auto RepairExample: Hudson Auto Repair

The manager of Hudson AutoThe manager of Hudson Auto

would like to have a betterwould like to have a better

understanding of the costunderstanding of the cost

of parts used in the engineof parts used in the engine

tune-ups performed in thetune-ups performed in theshop. She examines 50shop. She examines 50

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

rounded to the nearest dollar, are listed on the nextrounded to the nearest dollar, are listed on the next

slide.slide.


26/68


s Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 74

62 82 98 101 79 105 79 69 62 73


27/68

Grouped Frequency DistributionGrouped Frequency Distribution

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 classesSmaller data sets usually require fewer classes


28/68

Grouped Frequency DistributionGrouped Frequency Distribution

Guidelines for Selecting Width of ClassesGuidelines for Selecting Width of Classes

Use classes of equal width.Use classes of equal width.

Approximate Class WidthApproximate Class Width


29/68


For Hudson Auto Repair, if we choose sixFor Hudson Auto Repair, if we choose six

classes:classes:

50-5950-5960-6960-69

70-7970-79

80-8980-89

90-9990-99100-109100-109

Parts Cost ($)Parts Cost ($) FrequencyFrequency

Approximate Class Width = (109 - 52)/6 = 9.5 ~ 10Approximate Class Width = (109 - 52)/6 = 9.5 ~ 10


30/68



50-5950-59

60-6960-69

70-7970-79

80-8980-89

90-9990-99100-109100-109

PartsParts

Cost ($)Cost ($)

.04.04

.26.26

.32.32

.14.14

.14.14

.10.10

Total 1.00Total 1.00

RelativeRelative

FrequencyFrequency

44

2626

3232

1414

14141010

100100

PercentPercent

FrequencyFrequency

2/502/50 ..

04(10004(100

))

R l i F dR l ti F d


31/68

s Insights Gained from the Percent FrequencyInsights Gained from the Percent Frequency

DistributionDistribution




32/68

Definitions associated with frequencyDefinitions associated with frequency

distribution classesdistribution classes

Class limits:Class limits:

Class boundaries:Class boundaries:

Note: upper boundary of one class will coincidesNote: upper boundary of one class will coincideswith the lower boundary of the next classwith the lower boundary of the next class

Sometimes limits and boundaries will coincideSometimes limits and boundaries will coincidee.g. 12 and up to 13, 13 and up to 14, 14 and upe.g. 12 and up to 13, 13 and up to 14, 14 and upto 15to 15


33/68

Definitions associated with frequencyDefinitions associated with frequency

distribution classesdistribution classes

Class widths (class lengths):Class widths (class lengths):

Class mid-points:Class mid-points:

D Pl


34/68

Dot PlotDot Plot

One of the simplest graphicalOne of the simplest graphicalsummaries of data is asummaries of data is a dot plotdot plot..

A horizontal axis shows the range ofA horizontal axis shows the range of

data values.data values. Then each data value is represented byThen each data value is represented by

a dot placed above the axis.a dot placed above the axis.

D Pl


35/68

5050 6060 7070 8080 9090 100100 1101105050 6060 7070 8080 9090 100100 110110

Cost ($)Cost ($)

Dot PlotDot Plot

Tune-up Parts CostTune-up Parts Cost


36/68

HistogramHistogram

Common graphical presentation of quantitativeCommon graphical presentation of quantitative

datadata

Horizontal axis: values of classesHorizontal axis: values of classes

A rectangle is drawn above each class intervalA rectangle is drawn above each class interval

Unlike a bar graph, a histogram has no gap betweenUnlike a bar graph, a histogram has no gap between

rectanglerectangle

Hi t


37/68

HistogramHistogram

22

44

66

88

1010

1212

1414

1616

1818

Parts

Cost ($)

Parts

Cost ($)

Freque

ncy

Freque

ncy

5059 6069 7079 8089 9099 100-1105059 6069 7079 8089 9099 100-110

Tune-up Parts CostTune-up Parts Cost


38/68

Cumulative frequency distributionCumulative frequency distributionCumulative frequency distributionCumulative frequency distribution

Cumulative relative frequency distributionCumulative relative frequency distributionCumulative relative frequency distributionCumulative relative frequency distribution

Cumulative DistributionsCumulative Distributions

Cumulative percent frequency distributionCumulative percent frequency distributionCumulative percent frequency distributionCumulative percent frequency distribution

C l i Di ib iC l ti Di t ib ti


39/68

Cumulative DistributionsCumulative Distributions Hudson Auto RepairHudson Auto Repair


40/68

OgiveOgive

s A graph of a cumulative distribution.A graph of a cumulative distribution.

s Horizontal axis: data valuesHorizontal axis: data values

s Vertical axisVertical axis

- cumulative frequencies, orcumulative frequencies, or

- cumulative relative frequencies, orcumulative relative frequencies, orcumulative percent frequenciescumulative percent frequencies

s The frequency of each class: plotted as a point.The frequency of each class: plotted as a point.

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

Ogive withOgive with


41/68

PartsParts

Cost ($)Cost ($) PartsParts

Cost ($)Cost ($)

2020

4040

6060

8080

100100

CumulativePercentFrequency




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

(89.0,(89.0,

76)76)

Ogive withOgive with

Cumulative Percent FrequenciesCumulative Percent Frequencies

Tune-up Parts CostTune-up Parts CostTune-up Parts CostTune-up Parts Cost


42/68

Chapter 2Chapter 2

Summarizing dataSummarizing data

Exploratory Data AnalysisExploratory Data Analysis

Cross-tabulation and Scatter DiagramsCross-tabulation and Scatter Diagrams

Part B

xx

yy

E l t D t A l iE l t D t A l i


43/68

Exploratory Data AnalysisExploratory Data Analysis

The techniques ofThe techniques ofexploratory data analysisexploratory data analysis consist ofconsist of

simple arithmetic and easy-to-draw pictures that cansimple arithmetic and easy-to-draw pictures that canbe used to summarize data quickly.be used to summarize data quickly.

One such technique is theOne such technique is the stem-and-leaf displaystem-and-leaf display..

St d L f Di lSt d L f Di l


44/68

Stem-and-Leaf DisplayStem-and-Leaf Display

Each digit on a stem is aEach digit on a stem is a leafleaf..

Each line in the display is referred to as aEach 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 isIt is similar to a histogramsimilar to a histogram on its side, but it has theon 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 theA stem-and-leaf display shows both the rank orderrank order

andand shape of the distributionshape of the distribution of the data.of the data.

E l d R iE l H d A t R i


45/68


The manager of Hudson AutoThe manager of Hudson Auto

would like to have a betterwould like to have a better

understanding of the costunderstanding of the cost

of parts used in the engineof parts used in the engine

tune-ups performed in thetune-ups performed in the

shop. She examines 50shop. She examines 50

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

rounded to the nearest dollar, are listed on the nextrounded to the nearest dollar, are listed on the next

slide.slide.

E l H d A R iE l H d A t R i


46/68


s Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups

91 78 93 57 75 52 99 80 97 62

71 69 72 89 66 75 79 75 72 76

104 74 62 68 97 105 77 65 80 109

85 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

St d L f Di lSt d L f Di l


47/68


56789

100

2 72 72 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 stem

a leafa leaf

St t h d St d L f Di lStretched Stem and Leaf Display


48/68

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 - 4, and the secondcorresponds to leaf values of 0 - 4, and the second

value corresponds to leaf values of 5 - 9.value corresponds to leaf values of 5 - 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 cancondensed the data too much, we can stretch thestretch thedisplaydisplay by using two stems for each leading digit(s).by using two stems for each leading digit(s).

St t h d St d L f Di lStretched Stem and Leaf Display


49/68

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

5 5 95 5 91 41 4

7 7 7 8 97 7 7 8 9

1 31 35 8 95 8 90 0 2 30 0 2 3

5 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 4

5 6 7 8 8 8 9 9 95 6 7 8 8 8 9 9 92 2 2 22 2 2 2772255

55

66

66

77

77

88

88

99

991010

1010

St d L f Di lStem and Leaf Display


50/68


s Leaf UnitsLeaf Units

Where the leaf unit is not shown, it is assumedWhere the leaf unit is not shown, it is assumedto 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.

Example: Leaf Unit 0 1Example: Leaf Unit 0 1


51/68

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

99

1010

1111

Leaf Unit = 0.1Leaf Unit = 0.16 86 8

1 41 4

22

0 70 7

8.68.6 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

Example: Leaf Unit 10Example: Leaf Unit 10


52/68

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 = 1088

1 91 9

0 30 3

1 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 is

represented as an 8.represented as an 8.

Crosstabulations and ScatterCrosstabulations and Scatter


53/68

Crosstabulations and ScatterCrosstabulations and Scatter

DiagramsDiagrams

Cross-tabulationCross-tabulation and aand a scatter diagramscatter diagram are twoare two

methods for summarizing the data for two (or more)methods for summarizing the data for two (or more)

variables simultaneously.variables 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 usedto summarize the data forto summarize the data for one variable at a timeone variable at a time..

CrosstabulationCrosstabulation


54/68


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.

s Cross-tabulation can be used when:Cross-tabulation can be used when: one variable is qualitative and the other isone variable is qualitative and the other is

quantitative,quantitative,

both variables are qualitative, orboth variables are qualitative, or both variables are quantitative.both variables are quantitative.

AAcross-tabulationcross-tabulation is a tabular summary of data foris a tabular summary of data for

two variables.two variables.



55/68

PricePrice

RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame TotalTotal

$99,000> $99,000

18 6 19 1218 6 19 12 5555

4545

3030 20 35 1520 35 15TotalTotal 10010012 14 16 312 14 16 3

Home StyleHome Style


s Example: Finger Lakes HomesExample: Finger Lakes Homes

The number of Finger Lakes homes sold for eachThe number of Finger Lakes homes sold for eachstyle and price for the past two years is shown below.style and price for the past two years is shown below.

quantitativequantitativevariablevariable

qualitativequalitativevariablevariable



56/68


Insights Gained from Preceding Cross-Insights Gained from Preceding Cross-

tabulationtabulation



57/68

PricePrice


$99,000> $99,000

18 6 19 1218 6 19 12 5555

4545

3030 20 35 1520 35 15TotalTotal 100100

12 14 16 312 14 16 3



Frequency distributionFrequency distributionfor the price variablefor the price variable

Frequency distributionFrequency distributionfor the home style variablefor the home style variable

Cross tabulation: Row or Column PercentagesCross-tabulation: Row or Column Percentages


58/68

Cross-tabulation: Row or Column PercentagesCross-tabulation: Row or Column Percentages

Converting the entries in the table into rowConverting the entries in the table into row

percentages or column percentages canpercentages or column percentages canprovide additional insight about theprovide additional insight about the

relationship between the two variables.relationship between the two variables.

b l


59/68

PricePrice


$99,000> $99,000


Crosstabulation: Row PercentagesCrosstabulation: Row Percentages

C b l i C l


60/68

PricePrice

RangeRange Colonial Log Split A-FrameColonial Log Split A-Frame

$99,000> $99,000


TotalTotal

Crosstabulation: Column PercentagesCrosstabulation: Column Percentages

Scatter Diagram and TrendlineScatter Diagram and Trendline


61/68

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.

AAscatter diagramscatter diagram is a graphical presentation of theis a graphical presentation of the

relationship between tworelationship between two quantitativequantitative variables.variables.

Scatter Diagram and TrendlineScatter Diagram and Trendline

AAtrendlinetrendline is an approximation of the relationship.is an approximation of the relationship.

Scatter DiagramScatter Diagram


62/68


A Positive RelationshipA Positive Relationship

x

y



63/68


A Negative RelationshipA Negative Relationship

xx

yy



64/68


No Apparent RelationshipNo Apparent Relationship

xx

yy

Example: Panthers Football TeamExample: Panthers Football Team


65/68



The Panthers football team is interestedThe Panthers football team is interested

in investigating the relationship, if any,in investigating the relationship, if any,

between interceptions made and points scored.between interceptions made and points scored.

11

33

22

11

33

1414

2424

1818

1717

3030

xx= Number of= Number ofInterceptionsInterceptions

yy= Number of= Number ofPoints ScoredPoints Scored



66/68


yy

xx

Number of InterceptionsNumber of Interceptions

Nu

mberofPointsScored

Nu

mberofPointsScored

55

1010

15152020

2525

3030

00

3535

11 22 3300 44



67/68

s Insights Gained from the Preceding Scatter DiagramInsights Gained from the Preceding Scatter Diagram


Tabular and Graphical ProceduresTabular and Graphical Procedures


68/68

Tabular and Graphical ProceduresTabular and Graphical Procedures

Qualitative DataQualitative DataQualitative DataQualitative Data Quantitative DataQuantitative DataQuantitative DataQuantitative Data

TabularTabular

MethodsMethodsTabularTabular



MethodsMethodsGraphicalGraphical




MethodsMethods

FrequencyFrequency

DistributionDistributionRel. Freq. Dist.Rel. Freq. Dist.Percent Freq.Percent Freq.

DistributionDistributionCrosstabulationCrosstabulation

Bar GraphBar GraphPie ChartPie Chart

FrequencyFrequency

DistributionDistributionRel. Freq. Dist.Rel. Freq. Dist.Cum. Freq. Dist.Cum. Freq. Dist.

Cum. Rel. Freq.Cum. Rel. Freq.DistributionDistributionStem-and-LeafStem-and-Leaf

DisplayDisplayCrosstabulationCrosstabulation

Dot PlotDot PlotHistogramHistogramOgiveOgiveScatterScatter

DiagramDiagram

DataDataDataData

chapter 2 (summarizing data)_st

Documents