Diagramatic and graphical representation of data Notes on Statistics.ppt

I BSc II Semester notes

1. DIAGRAMATIC AND
GRAPHICAL
REPRESENTATION OF
DATA

2. •Diagramsareanessentialoperationaltoolforthe
purposeofpresentationof
statisticaldata.Theyareobjects,mainlygeometrical
figuressuchaslines,circles,bars,etc.
•Statisticselaboratedwiththehelpofdiagramsmakeit
easierandsimpler,therebyenhancingtherepresentation
ofanytypeofdata.

3. DiagrammaticRepresentationofData
Representationofdataassistedby
diagramstoincreasethesimplicityofthestatistics
surroundingtheconcerneddataisdefinedas
diagrammaticrepresentationofdata.Thesediagramsare
nothingbuttheuseofgeometricalfigurestoimprovethe
overallpresentationandoffervisualassistanceforthe
reader.

4. TypesofDiagramsusedinDataPresentation
Thetypeofdiagramsuitablefordata
presentationsolelydependsontheparticulardatasetandits
statisticalelements.Therearemultipletypesofdiagramsusedin
datapresentation.Theycanbebroadlycategorizedinthefollowing
typesofone-dimensionaldiagrams–
a.LineDiagram
ALinediagramisusedtorepresentaspecificdataacrossavarying
parameter.Alinerepresentsthesequenceofdataconnected
togetheragainstaparticularvariable.

5. PropertiesofLineDiagram
•TheLinescanbeusedinverticalandhorizontal
directions.
•Theymayormaynothaveuniformscaling
•Thelineconnectingthedatapointsstatethestatistical
representationofdata.

6. b.BarDiagram
BarDiagramisusedmostlyforcomparison
ofstatisticaldata.Itisoneofthemoststraightforwardrepresentation
ofdatawiththeuseofrectangularobjectsofequalwidth.
PropertiesofBarDiagram
TheBarscanbeusedinverticalandhorizontaldirections.
TheseBarsallhaveauniformwidth.
AlltheBarshaveacommonbase.
TheheightoftheBarusuallycorrespondstotherequiredvalue.

7. c.PieChart
Forthestatisticalrepresentationofdata,thesectorsofa
circleareusedasthedatapointsofaparticulardataset.
Asectoristheareaofacircleformedbytheseveral
divisionsdonebytheradiiofthesamecircle.

8. AdvantagesofDiagrammaticPresentation
Thereareseveraladvantagesinthe
presentationofdatawiththevarioustypesofdiagrams.Theyare–
1.MakesitMuchEasiertoUnderstand
•Presentationofdatawiththehelpofdiagramsmakeseasierforeverybody
tounderstand,whichtherebymakesiteasiertograspthestatisticsbehind
thedatapresented.
•Diagrammaticdatapresentationisquitecommon innewspapers,
magazinesandeveninadvertisingcampaignssothatthecommonmassis
abletounderstandwhatthedataistryingtoreveal.

9. 2.PresentationismuchSimpler
Withthehelpofdiagrams,presentationofextremevalues–
extensiveunstabledataaswellassmallcomplicateddatacomplex
canbesimplifiedexponentially.
3.ComparisonoperationsaremoreInteractive
Datasetswhichrequirecomparisonofitselementsinbetween
themselvesusetheapplicationofdiagramsforrepresentation.Not
onlythepresentationisattractive,butitisalsotheidealof
showcasingacomparisoninstatistics.

10. 4.AcceptedUniversally
Everyacademicandprofessionalfield,
letitbeEconomics,Commerce,Science,Engineering,Statistics,etc.
maketheuseofdiagramsacrosstheworld.Hence,thismetricofdata
presentationisuniversallyaccepted.
5.ImprovestheRepresentationofDataasaWhole
Statisticsareincompleteifdiagramsandtablesthatarenotimplementedfor
thepresentationofdata.Hence,theuseofdiagramshelpsintheoverall
statisticalconceptofdatarepresentation.

11. GraphicalRepresentation
Graphicalrepresentationrefersto
theuseofintuitivechartstoclearlyvisualizeandsimplifydata
sets.
Dataisingestedintographicalrepresentationofdata
softwareandthenrepresentedbyavarietyofsymbols,such
aslinesonalinechart,barsonabarchart,orslicesonapie
chart,fromwhichuserscangaingreaterinsightthanby
numericalanalysisalone.

13. Representationalgraphicscanquicklyillustrate
generalbehaviorandhighlight
phenomenon,anomalies,andrelationshipsbetweendata
pointsthatmayotherwisebeoverlooked,andmay
contributetopredictionsandbetter,data-driven
decisions.
Thetypesofrepresentationalgraphicsusedwill
dependonthetypeofdatabeingexplored.

14. TypesofGraphicalRepresentation
Datachartsareavailableinawidevarietyofmaps,diagrams,and
graphsthattypicallyincludetextualtitlesandlegendstodenotethe
purpose,measurementunits,andvariablesofthechart.
Choosingthemostappropriatechartdependsonavarietyof
differentfactors--thenatureofthedata,thepurposeofthechart,
andwhetheragraphicalrepresentationofqualitativedataora
graphicalrepresentationofquantitativedataisbeingdepicted.

15. BarGraph--containsaverticalaxisandhorizontalaxisanddisplaysdataas
rectangularbarswithlengthsproportionaltothevaluesthattheyrepresent;
ausefulvisualaidformarketingpurposes
Choropleth--thematicmapinwhichanaggregatesummaryofageographic
characteristicwithinanareaisrepresentedbypatternsofshading
proportionatetoastatisticalvariable
FlowChart--diagramthatdepictsaworkflowgraphicalrepresentationwith
theuseofarrowsandgeometricshapes;ausefulvisualaidforbusinessand
financepurposes
Heatmap--acolored,two-dimensionalmatrixofcellsinwhicheachcell
representsagroupingofdataandeachcell’scolorindicatesitsrelative
value

16. Histogram–frequencydistributionandgraphicalrepresentationusesadjacent
verticalbarserectedoverdiscreteintervalstorepresentthedatafrequency
withinagiveninterval;ausefulvisualaidformeteorologyandenvironment
purposes
LineGraph–displayscontinuousdata;idealforpredictingfutureeventsover
time;ausefulvisualaidformarketingpurposes
PieChart--showspercentagevaluesasasliceofpie;ausefulvisualaidfor
marketingpurposes
Pointmap--CAD&GIScontractmappinganddraftingsolutionthatvisualizesthe
locationofdataonamapbyplottinggeographiclatitudeandlongitudedata
Scatterplot--adiagramthatshowstherelationshipbetweentwosetsofdata,
whereeachdotrepresentsindividualpiecesofdataandeachaxisrepresentsa
quantitativemeasure

17. StackedBarGraph--agraphinwhicheachbarissegmentedintoparts,with
theentirebarrepresentingthewhole,andeachsegmentrepresenting
differentcategoriesofthatwhole;ausefulvisualaidforpoliticalscienceand
sociologypurposes
TimelineChart--alongbarlabelledwithdatesparallelingitthatdisplayalist
ofeventsinchronologicalorder,ausefulvisualaidforhistorycharting
purposes
TreeDiagram--ahierarchicalgenealogicaltreethatillustratesafamily
structure;ausefulvisualaidforhistorychartingpurposes
VennDiagram--consistsofmultipleoverlappingusuallycircles,each
representingaset;thedefaultinnerjoingraphicalrepresentation

18. AdvantagesandDisadvantagesofGraphicalRepresentationofData
Tabularandgraphicalrepresentationofdataareavitalcomponentin
analyzingandunderstandinglargequantitiesofnumericaldataand
therelationshipbetweendatapoints.Datavisualizationisoneofthe
mostfundamentalapproachestodataanalysis,providinganintuitive
anduniversalmeanstovisualize,abstract,andsharecomplexdata
patterns.Theprimaryadvantagesofgraphicalrepresentationofdata
are:

19. Facilitatesandimproveslearning:graphicsmakedataeasyto
understandandeliminatelanguageandliteracybarriers
Understandingcontent:visualsaremoreeffectivethantextinhuman
understanding
Flexibilityofuse:graphicalrepresentationcanbeleveragedinnearly
everyfieldinvolvingdata
Increasesstructuredthinking:userscanmakequick,data-driven
decisionsataglancewithvisualaids

20. Supportscreative,personalizedreportsformore
engagingandstimulatingvisualpresentations
Improvescommunication:analyzinggraphsthat
highlightrelevantthemesissignificantlyfasterthan
readingthroughadescriptivereportlinebyline
Showsthewholepicture:aninstantaneous,fullviewof
allvariables,timeframes,databehaviorand
relationships

21. Disadvantagesofgraphicalrepresentationofdata
typicallyconcernthecostofhumaneffortandresources,
theprocessofselectingthemostappropriategraphical
andtabularrepresentationofdata,greaterdesign
complexityofvisualizingdata,andthepotentialfor
humanbias.

22. ImportanceofGraphicalRepresentationofData
Graphicvisualrepresentationofinformationisacrucialcomponent
inunderstandingandidentifyingpatternsandtrendsintheever
increasingflowofdata.Graphicalrepresentationenablesthequick
analysisoflargeamountsofdataatonetimeandcanaidinmaking
predictionsandinformeddecisions.Datavisualizationsalsomake
collaborationsignificantlymoreefficientbyusingfamiliarvisual
metaphorstoillustraterelationshipsandhighlightmeaning,
eliminatingcomplex,long-windedexplanationsofanotherwise
chaotic-lookingarrayoffigures.

23. Dataonlyhasvalueonceitssignificancehasbeenrevealedand
consumed,anditsconsumptionisbestfacilitatedwithgraphical
representationtoolsthataredesignedwithhumancognitionand
perceptioninmind.Humanvisualprocessingisveryefficientat
detectingrelationshipsandchangesbetweensizes,shapes,colors,
andquantities.Attemptingtogaininsightfromnumericaldataalone,
especiallyinbigdatainstancesinwhichtheremaybebillionsof
rowsofdata,isexceedinglycumbersomeandinefficient.