6
th
InClassWorksheetName_________________
GraphPractice Teacher_______________
Due____________________________________
MakingScience
Graphsand
InterpretingData
ScientificGraphs:
Mostsc ientificgraphsaremadeaslinegraphs.Theremaybetimeswhenothertypes
wouldbeappropriate,buttheyarerare.
Thelinesonscientificgraphsareusuallydrawneitherstraight orcurved.These
"smoothed"linesdonothavetotouchallthedatapoints,butt heyshouldatleast get
closetomostofthem.The yarecalled bestfitlines.
Ingeneral, scientificgraphsarenotdrawninconnectthedotfashion.
Herearetwoexamplesof bestfitgraphlines.
Oneisdr awncorrect ly,theotherisnot.
BestFitLine#1 BestFitLine#2
· Agraphisavisualrepresentationof
arelationshipbetweentwo
variables,xandy.
· Agraphconsistsoftwoaxescalled
thex( horizontal)andy (vertical)
axes.Theseaxescorrespondtothe
variableswearerelating.In
economicswewillusuallygivethe
axesdifferentname s, suchasPrice
andQuantity.
· Thepointwherethetwoaxes
intersectiscalledtheorigin.The
originisalsoidentifiedasthepoint
(0,0).
InitialPractice:PointsonaGraph
Usethegraphbelowtoanswerthethreequestionsforthisproblem.
1. Whic hpointis(0,6)?
2. What istheycoordinateofpointS?
3. What arethecoordinatesofpointT?
Answers: 1.
2.
3.
AdditionalPractice:PointsonaGraph
Usethegraphbelowtoanswerthefour questio ns forthisproblem.
1. Whic hpoint(s)lieonthexaxis?
2. What istheycoordinateofpointS?
3. What arethecoordinatesofpointQ?
4. What arethecoordinatesofpointT?
Answers: 1.
2.
3.
4.
LocatingPointsonaGraph
Example
1. Whic hpointisontheyaxis?
2. Whic hpointislabeled(20,60) ?
3. Whic hpoint(s)haveay
coordinateof30?
Answer: 1.
2.
3.
VariablesandConstants
Thecharacteristicorelementthatremainsthesame iscalledaconstant. Example:
thenumberofdonutsinado zenisalways12. So,thenumber ofdonutsinadozenisa
constant.
Otherthesevaluescanvary(E xample:thepriceofadozendonutscanchangefrom
$2.50to$3.00).Wecallthesecharacteristicsorelementsvariables.Variableis
thetermforanycharacteristicorelementthatchanges. Youshould
beabletodeterminewhichcharacteristicsorelementsareconstantsandwhichare
variables.
PracticeExample
Whic hofthefollowingarevariablesa ndwhichareconstants?
Thetemperatureoutsideyourhou se.
Thisisa________________________________
Thenumberofsquarefeetinaroom12feetby12feet.
Thisisa________________________________
Thenoiselevelataconcert.
Thisisa_______________________________
Whichofthefollowingarevariablesandwhichareconstants?
Priceofagallonofgas. ___________________________
Numberofinchesinafoot. ___________________________
Numberofleavesona tree . ___________________________
Capacityofthegastankofyourca r. ___________________________
Graphsareausefultoolinscie nce.Thevisualcharacteristicsofa graphmaketrends
indataeasyto see.Oneofthemo stvaluableusesforgraphsisto"predict"datathat
isnotmeasuredonthegraph.
· Extrapolate:extendingthegraph,alongthesameslope,aboveorbelow
measureddata.
·
· Interpolate:predictingdatabetweentwomeasuredpointsonthegraph.
HowToConstructaLineGraphOnPaper
Step WhatToDo HowToDoIt
1
Identifythe
variables
a. IndependentVariable
(Controlledbythe experimenter)
· GoesontheXaxis(h orizontal)
· Shouldbeontheleftsideofadata
table.
b. DependentVariable 
(Changeswiththeindependentvariable)
· GoesontheYaxis( vertical )
· Shouldbeontherightsideofadata
table.
2
Todeterminet he
variablerange.
a. Subtractthelowestdatavaluefrom
thehighestdat avalue.
b. Doeachvariableseparately.
3
Todeterminet he
scaleofthegraph.
a. Determineascale,
(Thenumericalvalueforeachsquare ),
thatbestfitstherangeofeach
variable.
b. SpreadthegraphtouseMOSTofthe
availablespace.
4
Numberandlabel
eachaxis.
· Thistellswhatdatathelinesonyour
graphrepresent.Labelboththexand
yaxis.
5
Plotthedata
points.
a. Ploteachdatavalueonthegraphwith
adot.
b. Youcanputthedatanumberbythe
dot,ifitdoesnotclutteryourgraph.
6
Drawthegraph.
a. Drawacurveor alinethatbestfits
thedatapoints.
b. Mostgr aphsofexperimentaldataare
notdrawnas"connectthedots".
7
Titlethegraph.
a. Yourtitleshouldclearlytellwhatthe
graphisabout.
b. Ifyourgraphhasmorethanonesetof
data,pro videa"key"toide ntifythe
differentlines.
GraphingPractice–Problem1
Ageofthe
treeinyears
Averagethicknessof
theannualringsincm.
ForestA
Averagethicknessof
theannualringsincm.
ForestB
10 2.0 2.2
20 2.2 2.5
30 3.5 3.6
40 3.0 3.8
50 4.5 4.0
60 4.3 4.5
A. Thethicknessoftheannualringsindicateswhattypeofenvironment
wasoccurrin gatthetimeofitsdevelopment. A thinringusually
indicatesalackofwater,forestfires,oramajorinsectinfestation. A
thickringindicatesjusttheopposite.
B. Makealinegraphofthedata.
C. Whatisthedependentvariable?
D. Whatistheindependentvariable?
E. What wastheaveragethicknessoftheann ualringsof40yearoldtrees
inForestA? inForestB?
F. Basedonthisdata,whatcanyouconcludeaboutFore stAandForestB?
The dependentvariableis____________________________
The independentvariableis__________________________
The averagethicknessofannualringsof40yearold treesin
ForestAwas_____________.
ForestBwas_____________.
WhatdoesthistellyouaboutconditionsinForestAandForestB
whenth etreeswere40yearsold?
GraphingPracticeProblem2
pHofwater Numberoftadpoles
8.0 45
7.5 69
7.0 78
6.5 88
6.0 43
5.5 23
A. Makealinegraphofthedata.
B. What isthedependentvariable?
C. Whatistheindependentvariable?
D. Whatistheaveragenumberoftadp olescollectedpersample?
E. What istheoptimum water pHfortadpoledevelopment?
F. BetweenwhattwopHreadingsistherethegrea testchangeintadpole
number?
G. HowmanytadpoleswouldweexpecttofindinwaterwithapHreading
of5.0?
Thedependentvariableis_______________________________
Theindependentvariableis______________________________
The averagenumberoftadpolescollectedpersampleis________
BetweenpH_______andpH__________isthegreatestchangein
tadpolenumber.
Ifthewater’spHwas5 .0,youwouldexpecttofind__________of
tadpoles.
GraphingPracticeProblem3
Amountof
ethyleneinml/m
2
Winesap
Apples:
Daysto
Maturity
Golden
Apples:
Daysto
Maturity
GalaApples:
Daysto
Maturity
10 14 14 15
15 12 12 13
20 11 9 10
25 10 7 9
30 8 7 8
35 8 7 7
A. Ethyleneisaplanthormonethatcausesfruittomature.Thedataabove
concernstheamountoftimeittakesforfruittomaturefromthetimeof
thefirstapplicationofethylenebyspraying afieldoftrees.
B. Makealinegraphofthedata.
C. Makeakeyforthedifferentkindsofapplesbeinggraphed.
D. Whatisthedependentvariable?
E. What istheindependentvariable?
Thedependentvariableis________________________________
Theindependentvariableis______________________________
GraphingPracticeProblem4
WaterTemperaturein
o
C Numberofdevelopingclams
15 75
20 90
25 120
30 140
35 75
40 40
45 15
50 0
A. Aclamfarmerhasbeenkeeping recordsof thewatertemperatureand
thenumberofclamsdevelopingfromfertilizedeggs.Thedatais
recordedabove.
B. Makealinegraphofthedata.
C. Whatisthedependentvariable?
D. Whatistheindependentvariable?
E. What istheoptimumtemperatureforclamdevelopment?
Thedependentvariableis________________________________
Theindependentvariableis______________________________
Theoptimumtemperatureforc lamdevelopmentis____________
GraphingPractice–Problem5
Time(seconds) Distance( meters)
0 0
1 2
2 8
3 18
4 32
5 50
6 72
7 98
8 128
9 162
10 200
A. Graphthedata.
GraphingPractice–Problem 6
Thevolumeofagasdecreasesast hetemperatu reofthegasdecreases.Asampleof
gaswascollectedat100degreesCelsiusandthencooled.Thechangesinthevolume
ofthesampleareshownbelow.
TEMPERATURE(
o
C) VOLUME(ml )
100 317
80 297
60 288
40 278
30 252
20 243
10 236
0 233
10 227
30 202
A. Graphthedata.