notes for graph topic for Bpharm 8th semester

notes of graph for bpharm 8th sem

1. Graphs
UNIT -III
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2. •Sometimessignificanceiffigures(i.e.numbers)in
tabularpresentationisnoteasilyunderstood.
•Insuchcases,healthresearchersandotherexecutive
preferdiagrammaticpresentationwhichisreadily
understoodwiththehelpofgraphs,chartsor
diagrams.
•Graphsofstatisticaldatabringoutclear&relative&
arehelpfulinfindingouttherelationshipbetweentwo
ormoresetsofdata.•
•Diagrammaticrepresentationofdata.
3
Graphs
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3. •Imagineyoujustdidasurveyofyourfriendstofindwhichkindof
movietheylikedbest:
Table: Favorite Type of Movie
3
Graphs
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Comedy Action Romance Drama SciFI
4 5 6 1 4
•Itisareallygoodwaytoshowrelativesizes:wecansee
whichtypesofmoviearemostliked,andwhichareleast
liked,ataglance.

4. 3
Types of Graphs
4
•Histogram
•Pie Chart
•Bar Diagram
•Statistical Map
•Frequency Polygon
•Time series plot
•Cubic Graph
•Response Surface Plot
•Counter plot Graph
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5. 3
Histogram
5
❖Histogram:
❖Agraphshowingthedifferencesinfrequenciesor
percentagesamongcategoriesofaninterval-ratiovariable.
❖Thecategoriesaredisplayedascontiguousbars,with
widthproportionaltothewidthofthecategory&height
proportionaltothefrequencyorpercentageofthat
category.
❖Ahistogramisagraphicaldisplayofdatausingbarsof
differentheights.
❖Inahistogram,eachbargroupsnumbersintoranges.
❖Tallerbarsshowthatmoredatafallsinthatrange.
❖Ahistogramdisplaystheshapeandspreadofcontinuous
sampledata.
❖Ahistogramisanapproximaterepresentationofthe
distributionofnumericaldata.
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6. Histogram
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•Histogramisonetypeofgraphicalpresentationofdata
obtainedfromanysource.
•Thisiseasymethodtorepresentthedataandquick
understandingway.
•Histogramshouldbedesignedinvariousotherwayto
revealmorecomplicateddatainsinglesheet.
•Histogramhavinggreatimportanceinindustrialand
educationalpointofview.
•Differentstatisticalsoftwareplayingmajorroleto
showtheresults&reportsinhistogramsindifferent
organizations.

7. Types of Histogram
Thehistogramcanbeclassifiedbasedondifferenttypes
ofdistributions,suchas
✓Normaldistribution,
✓Skeweddistribution,
✓Bimodaldistribution,
✓Multimodaldistribution,
✓Combdistribution,
✓Edgepeakdistribution,
✓Dogfooddistributions,
✓Heartcutdistribution,andsoon.
Usedtorepresentthesedifferenttypesofdistributions.
Differenttypesofahistogramare
❑Uniformhistogram,
❑Symmetrichistogram,
❑Bimodalhistogram,
❑Probabilityhistogram.
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8. Types of Histogram
UniformHistogram
•Auniformdistributionrevealsthatthenumber
ofclassesistoosmall,andeachclasshasthe
samenumberofelements.
•Itmayinvolvedistributionthathasseveral
peaks.
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Uniform Histogram

9. Types of Histogram
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BimodalHistogram
•Ifahistogramhastwopeaks,itissaidtobebimodal.
•Bimodalityoccurswhenthedatasethasobservations
ontwodifferentkindsofindividualsorcombined
groupsifthecentresofthetwoseparatehistograms
arefarenoughtothevariabilityinboththedatasets.

10. Types of Histogram
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SymmetricHistogram
❖Whenyoudrawtheverticallinedownthecentreof
histogram,andthetwosidesareidenticalinsizeand
shape-Symmetrichistogram.
❖Thediagramisperfectlysymmetriciftherighthalf
portionoftheimageissimilartheleft.
❖Thehistogramthatarenotsymmetricareknownas
skewed.

11. Types of Histogram
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ProbabilityHistogram
•AProbabilityHistogram shows apictorial
representationofadiscreteprobabilitydistribution.
•Itconsistsofarectanglecentredoneveryvalueofx,
andtheareaofeachrectangleisproportionaltothe
probabilityofthecorrespondingvalue.
•Theprobabilityhistogramdiagramisbegunby
selectingtheclasses.
•Theprobabilitiesofeachoutcomearetheheightsof
thebarsofthehistogram.

12. Types of Histogram
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ProbabilityHistogram
Thefollowingtablegivesthelifetimeof400neonlamps.
Drawthehistogramforthebelowdata:
Life time
in Hrs
No of
Lamps
300 –400 14
400 –500 56
500 –600 62
600 –700 86
700 –800 74
800 –900 62
900 –1000 48

13. Pie chart
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Piechart:
•Agraphshowingthedifferencesinfrequenciesor
percentagesamongcategoriesofanominaloran
ordinalvariable.
•Thecategoriesaredisplayedassegmentsofa
circlewhosepiecesaddupto100percentofthe
totalfrequencies.
•Theangleofasectorisproportionaltothe
frequencyofthedata.
•Apiechartisagoodwayofdisplayingdatawhen
youwanttoshowhowsomethingissharedor
divided.

14. Pie chart
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Too many categories can be messy!White
Black
American Indian
Asian
Pacific Islander
Two or more
87.7%
8.3%
2.8%
.5%
.8%
.6%
N = 35,919,174
Annual Estimates of U.S. Population 65 Years & Over by Race, 2003
ThePieChart:TheRaceand
EthnicityoftheElderly

15. Pie chart
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WecanreducesomeofthecategoriesWhite
Black
Other and two or more
87.7%
8.3%
4%
N = 35,919,174
Annual Estimates of U.S. Population 65 Years and Over, 2003

16. Bar Graph
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TheBarGraph:TheLivingArrangementsandLabor
ForceParticipationoftheElderly0
10
20
30
40
50
60
70
80
Living alone Married Other
Series1
Living Arrangements of Males (65
and Older) in US, 2000
Bargraph:
•Agraphshowingthe
differencesinfrequenciesor
percentages among
categoriesofanominaloran
ordinalvariable.
•Thecategoriesaredisplayed
asrectanglesofequalwidth
withtheirheightproportional
tothefrequencyor
percentageofthecategory.

17. Bar Graph
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Candisplaymoreinfobysplittingsex0
10
20
30
40
50
60
70
80
Living alone Married Other
Males
Females
Living Arrangement of U.S. Elderly (65 and Older)
by Gender, 2003

18. Bar Graph
4/9/2024 1877.1
57.2
18
63.4
44.3
9.8
0 20 40 60 80 100
55 to 59
60- to 64
65 +
Women
Men
Percent of Men and Women 55 Years and Over in
the Civilian Labor Force, 2002

19. The Statistical Map: The Geographic
Distribution of the Elderly
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•Wecandisplaydramatic
geographicalchangesin
Americansocietybyusinga
statisticalmap.
•Mapsareespeciallyuseful
fordescribinggeographical
variationsinvariables,such
as
•Populationdistribution,
•Votingpatterns,
•Crimesrates,or
•Laborforceparticipation

20. The Frequency Polygon
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Frequencypolygon:
•Agraphshowingthe
differencesinfrequenciesor
percentages among
categoriesofaninterval-
ratiovariable.
•Pointsrepresentingthe
frequenciesofeachcategory
areplacedabovethe
midpointofthecategoryand
arejointedbyastraightline.
Source:AdaptedfromU.S.Bureauofthe
Census,CenterforInternationalResearch,
InternationalDataBase,2003.
Population of Japan, Age 55 & Over,
2000, 2010, & 2020Population of Japan, Age 55 and Over, 2000,
2010, and 2020
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
55-59 60-6465-69 70-7475-79 80+
2000
2010
2020

21. Time Series Charts
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Timeserieschart:
Agraphdisplayingchangesin
avariablesatdifferentpoints
intime. Itshowstime
(measuredinunitssuchas
yearsormonths)onthe
horizontalaxisandthe
frequencies(percentagesor
rates)ofanothervariableonthe
verticalaxis.
Source: Federal Interagency Forum on
Aging Related Statistics, Older Americans
2004: Key Indicators of Well Being, 2004.
Percentage of Total U. S. Population 65
Years and Over, 1900 to 20500
5
10
15
20
25
1900192019401960 19802000202020402060

22. Time Series Charts
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Timeserieschart:
Agraphdisplayingchangesin
avariablesatdifferentpoints
intime. Itshowstime
(measuredinunitssuchas
yearsormonths)onthe
horizontalaxisandthe
frequencies(percentagesor
rates)ofanothervariableonthe
verticalaxis.
Source: U.S. Bureau of the Census, “65+
in America,” Current Population Reports,
1996, Special Studies, P23-190, Table 6-1.
Percentage Currently Divorced
Among U.S. Population 65 Years
and Over, by Gender, 1960 to 2040 0
2
4
6
8
10
12
14
16
1960 1980 2000 2020 2040
Males
Females

23. Cubic Graph
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•Acubicgraphisagraphinwhich
allverticeshave degree
three(3D).
•Inotherwords,acubicgraphisa
3-regulargraph.
•Cubicgraphsarealsocalled
trivalentgraphs.
•Ifthesmallestandthelargestmagnitudetobepresented
asintheratioof1:1000,thebardiagramscannotbeused
•Becauseoftheheightofthebiggestbarwouldbe1000
timestheheightofthesmallestbarandthustheywould
lookverydisproportionate.

24. Cubic Graph
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❑Ifwetakesquaresofthesidesifthesquare1:√1000i.e.
1:31.62i.e.1:32(approx.)whichwillagaindisproportionate
diagrams.
❑Ifcubeareusedtothepresentthisdata,thenthevolumeof
cubeofsideis'x'thenwetakethecuberootsi.e.1:3√1000
i.e.1:10,whichwillgivetoareasonablyproportionatediagram
Construction of a cube of side 'AB'
•ConstructasquareofsideABCD.
•DrawEFasbisectorperpendiculartobisectorofAB[thisis
donebyfindingthemidpointofABandthendrawinga
perpendicularatthepointlinetoAB]suchthatEF=AB
•JoinAE,CF,andEF.
•ThroughBdrawalineBGparalleltoAE,suchthatBG-AE.
•JoinEGandthroughGdrawalineGH/EFsuchthatGH=EF
•JoinDH
•RuboffthelinesCF,EFandFH.NowCDHGEAC isthe
requiredcube

25. Cubic Graph
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26. Cubic Graph
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27. Response Surface Plot
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➢Surfaceplotsarediagramsofthree-
dimensionaldata.
➢Ratherthanshowingtheindividual
datapoints,surfaceplotsshowa
functionalrelationshipbetweena
designateddependentvariable(Y),
andtwoindependentvariables(X
andZ).
➢Theplotisacompanionplottothe
contourplot.

28. Response Surface Plot
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➢A2-DgridofXandzis
constructed.
➢Therangeisgridisequaltothe
rangeofthedata.
➢Avalueiscalculatedforeachgrid
point.
➢ThisYvalueisaweightedaverage
ofalldatathatisnearthisgrid
point.
➢The3-Dsurfaceisconstructed
usingtheseaveragesvalues.
➢Hence,thesurfaceplotdoesnot
showthevariationateachgrid
point.

29. Response Surface Plot
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30. Contour Plot Graph
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31. Response Surface Plot
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32. Response Surface Plot
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33. Why use charts and graphs?
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–Whatdoyougain?
–abilitytodirectreaders’attentiontooneaspectoftheevidence
–abilitytoreachreaderswhomightotherwisebeintimidatedbythe
samedatainatabularformat
–abilitytofocusonbiggerpictureratherthanperhapsminor
technicaldetails
–Whatdoyoulose?
–abilitytoexaminenumericdetailofferedbyatable
–potentiallytheabilitytoseeadditionalrelationshipswithinthedata
–potentiallytime:oftenwegetcaughtupinselectingcolorsand
formattingchartswhenasimplyformattedtableissufficient

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