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Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Definerawdata.Whatarethestepstoorganizerawdata?Whatcanbedonetohelpvisualizedata?Whatisthepurposeoflab01–scientificdataandgraphs?Defineaverage.Definemedian.
INTRODUCTION:
RAWDATA:Measurementscollectedduringascientificexperiment.Unorganizeddata,whichdoesn’ttellyoumuchaboutthemselves.
•Stepstoorganizerawdata:
• Enterdataintoadatatablesoyoucanfindtheinformationeasily.
• Summarizetheminstatisticalterms(range,mean,median,andstd.Deviation)soitiseasiertocompareandcontrastlater.
•Tohelpvisualizedata:
turndatatablesintochartsorgraphs.Makesiteasiertospottrendsorcorrelationsinourdataiftheyexist.
PURPOSE
Introductiontodataorganization,datadescriptions,anddatacharts/graphconstruction.
OBJECTIVES:
• Organizedataintotablesandcalculatestatisticaldescriptorsofthedata
• Creategraphs/chartsfromgivendatasets• Analyzedataandinterprettrendsfromvarious
graphs.VOCABULARY:
AVERAGE:Anumberthatiscalculatedbyaddingquantitiestogetherandthendividingthetotalbythenumberofquantities.𝐴𝑉𝐺 = &'(&)(&*(⋯(&,
-
MEDIAN:
The“midpoint”valueinasortedlistofvaluesFirstrankallofthevaluesinthedatasetfrommin.tomax.•forodd#values:themedian=thevaluethatliesinthemiddleofthesortedlistofvalues.
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Definebargraph.DefineXYscatterplot.Defineindependentvariable.Definedependentvariable.Definequalitativevariable.Definequantitativevariable.Defineslope.
•foreven#values:themedian=theaverageofthetwovaluesthatlieinthemiddleofthesortedlistofvalues.
BARGRAPH:
Agraph/chartthatusesnarrowcolumnsofdifferentheightstoshowandcomparedifferentamounts.
XYSCATTERPLOT:
Agraphofplottedpointsthatshowtherelationshipbetween2setsofdata.
INDEPENDENTVARIABLE:Thevariableinafunctionalrelationwhosevalueisindependent,notaffectedbyothervariables.Thevariablethatismanipulatedinanexperiment.
DEPENDENTVARIABLE:
Thevariableinafunctionalrelationwhosevalueisdependentupon,orinfluencedbyanindependentvariable.Afactorwhosevaluechangeswhentheindependentvariableischanged.
QUALITATIVEVARIABLE:Categoricalvariables,arevariableswithnonaturalsenseofordering.Arenotmuchnumericalinnature.
Color,names,gender,etc.
QUANTITATIVEVARIABLE:Variablethataremeasuredonanumericscale.Numericalinnature
Ordinal,interval,ratioscales,height,weight,length,etc.
SLOPE:
TheratiooftheamountthatYincreaseasXincreasessomeamount.
𝑠𝑙𝑜𝑝𝑒 = 345637&
= 89
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Defineoutlier.OrganizeDr.Lopez’sdataonHerculesbeetlesbodylengthsintoadatatable.Yourtableshouldincludethefollowingheadings:gender,bodylength(mm),andhornlength(mm).Definerange.
OUTLIER:Somethingthatissituatedawayfromorclasseddifferentlyfromamainorrelatedbody,statisticalobservationthatisnoticeablydifferentinvaluefromtheothersofthesample.
EXERCISES:ExerciseA:DataTables
ExcerptsformDr.Lopez’sfieldresearchnotesonHerculesbeetles(Dynastesherculues)inMexico.
StatisticalDescriptionofData:RANGE:
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Definemean.Definestandarddeviation.Whatisthemin.amountofvariablesneededtodothestandarddeviationforadataset?Calculatetherange,mean,medianandstandarddeviationforbodylengthsforeachdateofDr.Lopez’sdataandorganizethemintoadatatable.
Theareacoveringtheupperandlowerlimitsonaparticularscale𝑅𝑎𝑛𝑔𝑒 = max 𝑣𝑎𝑙𝑢𝑒 − min 𝑣𝑎𝑙𝑢𝑒
MEAN(average):Anumberexpressingthetypicalvalueinasetofdata
𝑚𝑒𝑎𝑛 = 𝑆𝑢𝑚𝑜𝑓𝑎𝑙𝑙𝑣𝑎𝑙𝑢𝑒𝑠𝑖𝑛𝑑𝑎𝑡𝑎𝑠𝑒𝑡
#𝑜𝑓𝑣𝑎𝑙𝑢𝑒𝑠𝑖𝑛𝑑𝑎𝑡𝑎𝑠𝑒𝑡
STANDARDDEVIATION(Std.Dev.):Ameasureofhowvariablethevaluesinadatasetare.
𝑆𝑡𝑑𝐷𝑒𝑣 = (𝑥 − 𝑚𝑒𝑎𝑛)Q
(#𝑜𝑓𝑣𝑎𝑙𝑢𝑒𝑠𝑖𝑛𝑑𝑎𝑡𝑎𝑠𝑒𝑡 − 1)
Σ=summation;x=theindividualvaluesinthedataset.
• Min.#ofvaluestodostd.Dev.Mustbeat
least3.
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Calculatetherange,mean,medianandstandarddeviationforthehornlengthsamongthemalebeetles.Whydoweoftenturndataintochartsorgraphs?Inamxyscatterplotwhatdoesthex-axisrepresent?Inanxyscatterplotwhatdoestheyaxisrepresent?
Standarddeviation:EXERCISEB:DATACHARTS/GRAPHS
• Oftenturndatatablesintochartsorgraphstoquicklycompareorcontrastourresults.
o x-axis(horizontal):Displaystheindependentvariables,factorsthatyoubelievetoinfluenceordetermineyourexperimentalresults.
o Y-axis(vertical):Displaysthedependentvariables,themeasurementsthatyourecordedinyourexperiments.
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Whatarethetwomostcommonlyusedcharts/graphsinscience?GenerateabargraphshowingthemeanandmedianHerculesbeetlebodylengthfromDr.Lopez’sdata.Besuretoincludeatitle,axislabelsforbothaxes.Generateaseparatebargraphshowingthedailymeanandmedianbodylengthswiththedatesbeingtheindependentvariable.Besuretoincludealegendtoclearlyindicatehowtheseriesarerepresented.Whatarethe3essentialpartsofachart/graph?
• Thetwomostcommonlyusedcharts/graphin
science:• Bargraphs:
Forcategoricalvariables• XYscatterplots:
Forcontinuousvariables.
PartsofCharts/Graph:
• Chart/graphtitle:Titleshouldbedescriptivebutnotinterpretative.
Tellthereaderwhatthechart/graphisabout.
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Whatisapositivetrend?Whatisanegativetrend?
• Axislabels:Axislabelstellyourreaderwhattheindependentanddependentvariablesareonthechart/graph,aswellaswhatistheunitofmeasurement.
• Legend:Providealegendonyourgraphwhenyouhavemorethanoneseries.Tellsyourreaderswhichbar(onbargraphs)ordots(onXYscatterplots)arerepresentingwhichgroupofdata.
EXERCISEC:TRENDSPOTTING
• Wheninterpretingdatathroughcharts/graphs,wecanoftenvisuallyseeatrendorcorrelationbetweentheindependentanddependentvariables.
• Positivetrend:upwardtrend
o Astheindependentvariable(x)increases,thedependentvariable(Y)increasesaswell
o Hasapositiveslope
• Negativetrend:Downwardtrend
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Whatdoestheslopeofthetrendlineimply?OrganizeadatatablefromDr.Lopez’sdataonthemaleHerculesbeetles.Calculatethehorn-to-bodyratio.Andgraphbodylengthvs.Hornlengthanddrawtrendatrendline.Graphbody/lengthvs.Horn/bodyratioanddrawatrendline.WhatwerethemeanandmedianbodylengthofallHerculesbeetlesinDr.Lopez’sstudy?
o Astheindependentvariable(x)
increases,thedependentvariable(y)decreases.
o Hasanegativeslope.
• Theslopeofthetrendline,regardlessofbeingpositiveornegative,impliesthestrengthofthetrendbetweenthetwovariables.
o Thesteepertheslope,thestrongerthetrend.
o Ifthetrendlineisflatorbarelyhasaslope,thenthereisnocleartrendorthetrendisweakbetweenthetwovariables.
𝑚𝑒𝑎𝑛 = 𝑏𝑜𝑑𝑦𝑙𝑒𝑛𝑔𝑡ℎ𝑓𝑜𝑟𝑒𝑎𝑐ℎ𝑏𝑒𝑡𝑡𝑙𝑒
𝑡𝑜𝑡𝑎𝑙#𝑜𝑓𝑏𝑒𝑒𝑡𝑙𝑒𝑠 = 80.1𝑚𝑚
𝑚𝑒𝑑𝑖𝑎𝑛 = 73.4 + 72.2
2 = 72.8𝑚𝑚
Lab01 SCIENTIFICDATA&GRAPHS LABNOTES
Didthedailymeansandmediansforbodylengthsdiffersignificantlyfromoneanother?WhatwerethemeanandmedianhornlengthofallthemaleHerculesBeetlesinDr.Lopez’sstudy?Whatdoestherange&standarddeviationstellyouaboutDr.Lopez’sdataset?Wasthereatrendbetweenbodylengthandhornlengthamongstmalebeetles?Wasitstrong/weak?Positive/negative?Whatkindoftrendexistsbetweenbodylengthsandhorn-to-bodyratio?Arethetrendsthesame?
Yes,theydifferedsignificantly,rangefrodailymean=6.4mm.Therangefordailymedians=15.1mm.Thesebeetlesarenotverylarge∴1mmwillmakesignificantdifference.Mean=40.6mm,Median=39.8mm.Therangefordailymean=21.1mm,andformedian=22.4mm.∴hornlengthsaresignificantlydifferentfromoneanother.ThatthereisasignificantdifferencebetweenbodylengthandhornlengthsinHerculesbeetles.Overallthereisalargedeviationbetweenthelengthsamongthebeetles.Thedataisspreadoutoveralargerangeofvalues.Thereisaweak,positivetrendbetweenhornlengthandbodylength.Thereisanegative,strongtrendbetweenhorn-to-bodyratioandbodylength.Thetrendlinesareoppositeofeachother.