Lab 8 – zScore and Normal Distribution Hofstra People实验8–Z值和正态分布霍夫斯特拉的人

《Lab 8 – zScore 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，更多相关内容在学术论文-天天文库。

1、Lab8–z-ScoreandNormalDistributionDescriptivestatistics,likethemeanandstandarddeviation,describedistributionsbysummarizingthecenter(centraltendency)andspread(variability).Whilethisisn'teverydetailaboutadistribution,itdoesgiveusaprettygoodpictureofwhatthedistributionlookslike.Formostbell-shapedcurve

2、s(e.g.,symmetricandunimodal),themeanshouldbeatthemid-pointandthestandarddeviationshouldbesomewherehalfwaybetweenthemeanandthemostextremevalues.Ourgoalistobeabletofindourrawscoreswithinthedistribution,andtobeabletodescribewhereitfalls.LocatingaScoreWhereisourrawscorewithinthedistribution?·Agoodpoin

3、tofreferenceisthemean(sinceitisusuallyeasytofind).Soanaturalchoicefordescribingthelocationofadatapointwouldbethedeviationscore,subtractthemeanfromthescore(X-m).oThedirectionisindicatedbythenegativeorpositivesignonthedeviationscoreoThedistancefromthemeanisthevalueofthedeviationscore·Ifweareonlyconc

4、ernedaboutasingledistribution,thenthisseemstobeprettyeasytodo.But,ifwewanttocomparetwoscoresfromtwodistributions,thenthesituationgetsmuchharder.ConsiderthefollowingsituationYoutaketheACTtestandtheSATtest.Yougeta26ontheACTanda620ontheSAT.Thecollegethatyouapplytoonlyneedsonescore.Whichdoyouwanttosen

5、dthem(thatis,whichscoreisbetter,26or620?)?·Itishardtodoadirectcomparisonherebecausethetwodistributionshavedifferentproperties:differentmeans,anddifferentvariability.·Howmightwegoaboutit?oLookatthedistributiongraphs,locatethescoresandcompare--stillhardtotell.oThinkaboutcumulativepercentilesandperce

6、ntileranks--thismightwork.oTryandtakethedeviationsandstandarddeviationsintoaccount--letstrythisout!Rememberourexample:yougota26ontheACTanda620ontheSATandyouwanttoknowwhichscoreisbetter.ThepopulationmeansandstandarddeviationsfortheACTandSATareprovided.ACT:Meanm=18,SDs=6Deviation=26(orXvalue)–18=8Th

7、endividethedeviationbytheSD=8/6=1.33YourACTscoreis1.33SDabovethemeanSAT:Meanm=500,SDs=100Deviation=620(orXvalue)–500=120ThendividethedeviationscorebytheSD=120/100=1.20YourSATscoreis1.20SDabovethemeanWiththisinfor