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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.