Download - Lab 01 NOTES on Scientific Data and Graphs

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.


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


Defineoutlier.OrganizeDr.Lopez’sdataonHerculesbeetlesbodylengthsintoadatatable.Yourtableshouldincludethefollowingheadings:gender,bodylength(mm),andhornlength(mm).Definerange.

OUTLIER:Somethingthatissituatedawayfromorclasseddifferentlyfromamainorrelatedbody,statisticalobservationthatisnoticeablydifferentinvaluefromtheothersofthesample.

EXERCISES:ExerciseA:DataTables

ExcerptsformDr.Lopez’sfieldresearchnotesonHerculesbeetles(Dynastesherculues)inMexico.

StatisticalDescriptionofData:RANGE:


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.


Calculatetherange,mean,medianandstandarddeviationforthehornlengthsamongthemalebeetles.Whydoweoftenturndataintochartsorgraphs?Inamxyscatterplotwhatdoesthex-axisrepresent?Inanxyscatterplotwhatdoestheyaxisrepresent?

Standarddeviation:EXERCISEB:DATACHARTS/GRAPHS

• Oftenturndatatablesintochartsorgraphstoquicklycompareorcontrastourresults.

o x-axis(horizontal):Displaystheindependentvariables,factorsthatyoubelievetoinfluenceordetermineyourexperimentalresults.

o Y-axis(vertical):Displaysthedependentvariables,themeasurementsthatyourecordedinyourexperiments.


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.


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


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


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.