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《lab 8 – z-score and normal distribution - hofstra people实验8–z值和正态分布-霍夫斯特拉的人》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Lab8–z-ScoreandNormalDistributionDescriptivestatistics,likethemeanandstandarddeviation,describedistributionsbysummarizingthecenter(centraltendency)andspread(variability).Whilethisisn'teverydetailaboutadistribution,itdoesgiveusaprettygoodpictureofwhatthedistrib
2、utionlookslike.Formostbell-shapedcurves(e.g.,symmetricandunimodal),themeanshouldbeatthemid-pointandthestandarddeviationshouldbesomewherehalfwaybetweenthemeanandthemostextremevalues.Ourgoalistobeabletofindourrawscoreswithinthedistribution,andtobeabletodescribew
3、hereitfalls.LocatingaScoreWhereisourrawscorewithinthedistribution?·Agoodpointofreferenceisthemean(sinceitisusuallyeasytofind).Soanaturalchoicefordescribingthelocationofadatapointwouldbethedeviationscore,subtractthemeanfromthescore(X-m).oThedirectionisindicated
4、bythenegativeorpositivesignonthedeviationscoreoThedistancefromthemeanisthevalueofthedeviationscore·Ifweareonlyconcernedaboutasingledistribution,thenthisseemstobeprettyeasytodo.But,ifwewanttocomparetwoscoresfromtwodistributions,thenthesituationgetsmuchharder.Co
5、nsiderthefollowingsituationYoutaketheACTtestandtheSATtest.Yougeta26ontheACTanda620ontheSAT.Thecollegethatyouapplytoonlyneedsonescore.Whichdoyouwanttosendthem(thatis,whichscoreisbetter,26or620?)?11·Itishardtodoadirectcomparisonherebecausethetwodistributionshave
6、differentproperties:differentmeans,anddifferentvariability.·Howmightwegoaboutit?oLookatthedistributiongraphs,locatethescoresandcompare--stillhardtotell.oThinkaboutcumulativepercentilesandpercentileranks--thismightwork.oTryandtakethedeviationsandstandarddeviati
7、onsintoaccount--letstrythisout!Rememberourexample:yougota26ontheACTanda620ontheSATandyouwanttoknowwhichscoreisbetter.ThepopulationmeansandstandarddeviationsfortheACTandSATareprovided.ACT:Meanm=18,SDs=6Deviation=26(orXvalue)–18=8ThendividethedeviationbytheSD=8/
8、6=1.33YourACTscoreis1.33SDabovethemeanSAT:Meanm=500,SDs=100Deviation=620(orXvalue)–500=120ThendividethedeviationscorebytheSD=120/100=1.20YourSATscoreis1.20SDabovethemeanWiththisinf
