程宏2016 2017學(xué)年統(tǒng)計學(xué)課程 第4次-統(tǒng)計學(xué) 第4章部分內(nèi)容回顧(Grant)

Theempiricalrulehelpstomeasurehowthevaluesdistributeaboveandbelowthemeanandcanhelpidentifyoutliers.Theempiricalruleapproximatesthevariationofdatainabell-shapeddistributionApproximately68%ofthedatainabell-shapeddistributionlieswithin1standarddeviationofthemeanorChap3-1TheEmpiricalRule68%Approximately95%ofthedatainabell-shapeddistributionlieswithintwostandarddeviationsofthemean,orμ±2σApproximately99.7%ofthedatainabell-shapeddistributionlieswithinthreestandarddeviationsofthemean,orμ±3σChap3-2TheEmpiricalRule99.7%95%UsingtheEmpiricalRuleSupposethatthevariableMathSATscoresisbell-shapedwithameanof500andastandarddeviationof90.Then,68%ofalltesttakersscoredbetween95%ofalltesttakersscoredbetween99.7%ofalltesttakersscoredbetweenChap3-3410and590(500±90).320and680(500±180).230and770(500±270).UsingtheEmpiricalRuleSupposetheenergyinformationadministrationreportedthatthemedianretailpricepergallonofregulargradegasolinewas$2.30,thestandarddeviationwas$0.10andthattheretailpricepergallonhasabell-shapeddistribution.a.Whatpercentageofregulargradegasolinesoldbetween$2.20and$2.40pergallon?b.Whatpercentageofregulargradegasolinesoldbetween$2.20and$2.50pergallon?c.Whatpercentageofregulargradegasolinesoldformorethan$2.50pergallon?Chap3-468%81.5%2.5%Regardlessofhowthedataaredistributed,atleast(1-1/k2)x100%ofthevalueswillfallwithinkstandarddeviationsofthemean(fork>1)

Examples:

(1-1/22)x100%=75%…........k=2(μ±2σ) (1-1/32)x100%=89%……….k=3(μ±3σ)Chap3-5ChebyshevRulewithinAtleastChap3-6TheFiveNumberSummaryinIQRThefivenumbersthathelpdescribethecenter,spreadandshapeofdataare:XsmallestFirstQuartile(Q1)Median(Q2)ThirdQuartile(Q3)XlargestFiveNumberSummaryand

TheBoxplotTheBoxplot:AGraphicaldisplayofthedatabasedonthefive-numbersummary:Chap3-7Example:Xsmallest

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Q1

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Median--Q3

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Xlargest25%ofdata25%25%25%ofdata

ofdataofdata Xsmallest

Q1

MedianQ3

XlargestSincethedistancesbetweenmediantoXsmallestisgreaterthanthedistancesbetweenXlargesttothemedi