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Stats 240, Week 3 Notes

by: Vanessa Olivo

Stats 240, Week 3 Notes JUST 240_04

Vanessa Olivo
GPA 3.6

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About this Document

These notes cover the measure of central tendency and the measure of dispersion.
Statistics for Social Research
Venezia Michalsen
Class Notes
Stats, 240
25 ?




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This 4 page Class Notes was uploaded by Vanessa Olivo on Sunday October 2, 2016. The Class Notes belongs to JUST 240_04 at Montclair State University taught by Venezia Michalsen in Fall 2016. Since its upload, it has received 17 views. For similar materials see Statistics for Social Research in Justice Studies at Montclair State University.


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Date Created: 10/02/16
Chapter4:MeasuresofCentralTendency • Measuresofcentraltendencyaredescriptivestatisticsthatofferinformationaboutwherethescoresinaparticular datasettendtocluster. Ø Examplesinclude:Mode,MedianandMean • Normaldistributionisasetofscoresthatclusterinthecenterandtapersofftotherightandleftsideofthenumber line. • PositiveSkewisasetofscoresthatclusteronthelefthandsideofthenumberline. • NegativeSkewisasetofscoresthatclusterontherighthandsideofthenumberline. • Mode Ø Thevaluethatoccursthemostfrequentlyinasetofscores Ø Levelofmeasurement:nominal,ordinal,intervalorratio Ø Shapeofdistribution:bimodal(twohighpointsinanumberline) Ø Adatacanhavemorethanonemode,butcanalsohaveNOmodeifallthevaluesinadatasetonlyoccur once Ø ModeàMo. • Median Ø Thescorethatcutsthedistributioninhalf.50%ofthescoresareabovethatvalueand50%arebelowthat value. Ø Continuousandordinaldata (▯▯▯) Ø MP= ▯ Ø N=samplesizewhenthelevelofmeasurementisratio,howeverwhenit’sordinalyouaddthefrequencies Ø Putranksinascendingordescendingorder Ø Whenthereisanevennumber,youhavetofindthetwomiddlenumbers,addthemtogetheranddivideby 2 Ø Varyeffectivebyoutliers(numbersthataren’taroundthesamenumbersastheothers) Ø MedianàMD • Mean Ø Arithmeticaverageofadataset Ø Levelofmeasurement:rationorintervalONLY Ø ???? = ▯ ▯ Ø x=valuesinagivenset; = ???????????? ???????????? ????ℎ???? ???????????????????????????? ???????? ????ℎ???? ????????????ℎ???? ???????? ???????? Ø Tocalculatethemeanusingfrequencies,addanewcolumntothetabletitledfx(productofxandf columns) v Multiplyeachvaluebyitsfrequencyandthensumtheproductstofindtheetotalsumofallthe values. ▯▯ v ???? = ▯ v N=thesumofthenumberoffrequencies; = ????ℎ???? ???????????? ???????? ???????? • Deviationscoreisthedistancebetweenthemeanandanygivenrawscore Ø Example:ifthemeanis24andarawscoreis22then22-24=-2 Chapter5:MeasureofDispersion/MeasureofVariability • Dispersionistheamountofvariabilityamongthescoresinadistribution • Kurtosisisameasureofhowmuchadistributionwidthcurvesthatdepartsitfromnormality • Leptokurtosisisameasureofhowclusteredorpeakedadistributionis • Platykurtosisisameasureofhowspreadoutorflatadistributionis • Variationratio Ø Calculatestheproportionofthecaseslocatedoutsidethemodalcategory Ø Levelofmeasurement:nominalandordinal ▯▯▯▯▯ Ø ???????? = 1.00 − ▯ Ø f modethenumberofcasesinthemodalcategory Ø VariationratioàVR • Bondingruleisarulestatingthatallproportionsrangefrom0.00to1.00 • Quartiles Ø Usequartilestodescribethemedian Ø Usefulforintervalorratio Ø Dividesdistributioninquarters:25,50(median),75 Ø Discussesthetop25%andthebottom25% • Range Ø Iscalculatedbysubtractingthesmallestscorefromthelargest v Ex.Highestvalue:27,Lowestvalue:19 v Threewaystocalculatetherange: 19to27 27-19=8 27.8-18.5=9 Ø RangeàR • Variance Ø Ameasureofdispersioncalculatedasthemeanofthesquareddeviationscores Ø Levelofmeasurement:ratioandinterval Ø Variationàs 2 Ø d =i -xi v d (ieviationscore:differencebetweenrawscoreandthemean) v x =aiivendatapoint v x=themeanofthesample Ø Populationvarianceequationis: Ø Samplevarianceequationis: Ø 1 :findthemean v 2 :subtracttherawscorefromthemeantoproducepositiveornegativedeviationscores 3 :inordertogetridofthenegativedeviationscore,wemustsquareallthescores th § 4 :addallthescorestogetheraftersquaringeachandthendividethesumby N(samplesize)-1 Ø StandardDeviation v Thesquarerootofthevariance Ø Standarddeviationàsorsd Ø Populationstandarddeviationequationis: Ø Samplestandarddeviationequationis:


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