To calculate the mean we add up the observed values and divide by the number ... One clue to lack of symmetry from derived statistics is when the mean and the ...IntendedforhealthcareprofessionalsOurCompanySubscribeMyAccountLogincovid-19ResearchEducationNews&ViewsCampaignsJobsArchiveForauthorsHostedSearchHome/AboutBMJ/Resourcesforreaders/Publications/Statisticsatsquareone/2.Meanandstandarddeviation2.Meanandstandarddeviation Themedianisknownasameasureoflocation;thatis,ittellsuswherethedataare.Asstatedin,wedonotneedtoknowalltheexactvaluestocalculatethemedian;ifwemadethesmallestvalueevensmallerorthelargestvalueevenlarger,itwouldnotchangethevalueofthemedian.Thusthemediandoesnotusealltheinformationinthedataandsoitcanbeshowntobelessefficientthanthemeanoraverage,whichdoesuseallvaluesofthedata.Tocalculatethemeanweadduptheobservedvaluesanddividebythenumberofthem.ThetotalofthevaluesobtainedinTable1.1was22.5,whichwasdividedbytheirnumber,15,togiveameanof1.5.Thisfamiliarprocessisconvenientlyexpressedbythefollowingsymbols:(pronounced“xbar”)signifiesthemean;xiseachofthevaluesofurinarylead;nisthenumberofthesevalues;andσ,theGreekcapitalsigma(our“S”)denotes“sumof”.Amajordisadvantageofthemeanisthatitissensitivetooutlyingpoints.Forexample,replacing2.2by22inTable1.1increasesthemeanto2.82,whereasthemedianwillbeunchanged.Aswellasmeasuresoflocationweneedmeasuresofhowvariablethedataare.Wemettwoofthesemeasures,therangeandinterquartilerange,inChapter1.Therangeisanimportantmeasurement,forfiguresatthetopandbottomofitdenotethefindingsfurthestremovedfromthegenerality.However,theydonotgivemuchindicationofthespreadofobservationsaboutthemean.Thisiswherethestandarddeviation(SD)comesin.Thetheoreticalbasisofthestandarddeviationiscomplexandneednottroubletheordinaryuser.WewilldiscusssamplingandpopulationsinChapter3.Apracticalpointtonotehereisthat,whenthepopulationfromwhichthedataarisehaveadistributionthatisapproximately“Normal”(orGaussian),thenthestandarddeviationprovidesausefulbasisforinterpretingthedat