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IntroductionToScientificAnalysis(BIO100) ASSIGNMENT:DESCRIPTIVESTATISTICS Name:_______________KEY______________________ Calculatethemean,medianandmodefortheheadcircumferencedata.Answerthe questionsbelowbasedonyourcalculations. 1. Arethe3measuresofcentraltendencysimilartoeachother?Explaintheirrelationship tooneanother. Mean:57.1,Median:57.0,Mode:58.5.Thethreemeasuresareverysimilartoone another.Infact,themeanandmedianarealmostidentical.Themodeisslightlylarger thanthemeanandmedian. 2. Basedonwhatyouknowaboutdistributions,whydoyouthinkthesemeasuresof centraltendencyexhibitthispattern? Ifthemean,median,andmodearederivedfromanormalcurve,thentheywillbeequal tooneanother.Becausethestatisticsforheadcircumferenceareveryclosetoone anothersuggeststhattheyarederivedfromanormalcurve. 3. UsingExcelorotheranalyticalsoftware, constructafrequencydistribution (histogram)graphofthisdata(printthe graphonaseparatesheetofpaper).Does itbackupyourinterpretationabove? Yes.Theshapeofthefrequency distributionforheadcircumference(bars) appearstoresembleanormalcurve(solid line). Calculatetherange,standarddeviation,andstandarderrorfortheheightdataformalesand females. 4. Howdothesemeasuresofdispersioncompareacrossgenders? Female Male Range 30.4 22.9 StDeviation 8.2 6.6 StError 1.5 1.6 Bothrangeandstandarddeviationarelargerforfemalesthanmales.Thestandard errorsareverysimilar. IntroductionToScientificAnalysis(BIO100) Name:_______________KEY______________________ 5. Constructabarorbox-plotgraph. Remember,bothofthesekindsof graphsrequirecentraltendencyand dispersion.Howdothegenders comparenow? Onaverage,malesappeartallerthan females,butthereisalotofoverlapin theirheightbetweenthegenders; thatis,tallerfemalesandshorter malesoverlapinheight.Femalesalso appeartohavemorespread(i.e., dispersion)withrespecttoheight comparedtomales. 6. Calculatethecoefficientofvariation(CV)fortheheadandheightdata.Comparethe results.WhatdoestheCVtellyouaboutvariationofthesetwotraits? CVheight:0.061(6.1%);CVhead:0.033(3.3%). Thereisrelativelylowvariationineachofthesetraits.Butvariationinheightisabout twiceasvariableasthatofheadcircumference.Remember,theCVallowsyouto comparetherelativevariabilitybetweenvariablesthathavedifferentmeanssuchas theheadandheightdata. 7. Constructascatterplotoftheheadandheightdata.Istherearelationship?Ifso,does itlooklinearornon-linear?Isitapositiveornegativerelationship?Pleasedescribe. Thereappearstobeapositive linearrelationshipbetweenthe headandheightvariablesoverall forbothgenders.Notsurprisingly, thereisscatterinthedata.Thatis, thepointsdon’tallfallona straightline.Butwewouldn’t expectthateithersinceweknow thatthereisindividualvariability intherelationshipofthesetraits. NOTE:Ilabeledfemalesandmalesseparatelyonthisgraphmerelyforillustration purposes.Itwasnotrequiredthatyoudosoforfullcredit.