So, forexample, youcanhaveonevariablegrasswhereyouonlylookatonethingandyouonlywanttolookatthisandyouwanttoseehowthesehowthischanges, youhaveyourtypicaltovariablegrouse, whichyouprobablyknowwhereyouhavethis X and a Y axis.
Thenwehavethecontinuouspart, andnowthecontinuouspartisreallythatvaluescouldjusttakeonanynumber, andthey'renotinlimitedbydecimalplace, So a valuethatcanyouknowitcouldbelike 1.1, andthenthenextvaluewouldbe 1.2.
So, forexample, let's sayyouhave a bottleofwaterinthisbottleofwatercanholdoneleader.
Now, ifyoufillyourbottleupandstartsoffemptyandyoufillitallthewayuptothetop, theamountofwaterthatyou'vehadneededtotakeoneverysinglenumberbetweenzeroandonebecauseyoucan't justfillupwater, youknow, a kindofsmallincrementsofsay, Hey, I'm gonnaputin 0.2 leaderseverysingletimebecausethewaterdoesn't just, youknow, teleportfrom A to B.
Butit's stillimportantforyoutoknowthatyou'redealingwithcontinuousdatahereratherthandiscreetsothatyouknowhey, therecanstillbeotherstuffinbetweenhere m orallofthesethingsratherthan, youknow, havingspecificsteps, sizesandallyouseeisjustkindof a bunchoflinesateverystepsize.
Butlet's go a littlebitdeeperandsay, Istheheightof a childdiscreet?
Oristheheightof a childcontinuous?
Well, eventhoughwhenyoumeasureheight, yougetsomething, like, youknow, fivefoot 53 or 160 centimetersorsomethinglikethat.
Um, it's not a discretevalue, becausetogetthatheight, youhavetohavereachedeverysingleheightbefore, Umandsoeventhoughatthemomentyoumaybemeasuringit, you'rekindofroundingitofftohowmuchyourmeasuringtapecanmeasure.
So, likeyourmeasuringtape, it's kindoflimitingtheheight.
Butifyouhad a supersuperpressedheistmeasuringinstrument, youcouldmeasurenotjust, youknow, fivefootthreeorsomethinglikethat.
Anothergoodexampleofthemeanwouldbetosay, howmuchchocolatedoyourequirewhenyougetthiskindofsweetcravingandyou'renotgoingtosaylike, Oh, youknow, I'm requiredonechocolatebartocheckwithbarsorthree, butlikeyou'regoingtosayonaverage, youknow, I require, youknow, maybe 3/4 of a chocolatebar, andsometimestheymaywant a littlebitmore, Um, because I feellikeit.
Andwhen I starteatingchocolatecravingevenmoresometimes, youknow, I haveitupfirstand, like, thetastersdoesn't sitrightwithmerightnow.
Butifyouweretousethemeetinginsteadthanallofthebillionairesandallthemillionairesinthecountry, theywouldchangethathouseholdincome, andthenyouwouldsay, Oh, youknow, theaveragehouseholdincomeperfamilywouldlooklike 60 K.
Andthat's a badrepresentation, becausethatdoesn't actuallygiveyou a realisticlookatwhattheaveragehouseholdfamilyhasontheaveragehouseholdfamilyreallydoes.
It's, youknow, centeredatlike 40 K andsure, therewerepeoplebelowtheirpeoplebehigh, butthat's what's inthemiddle.
Whatdoyouusuallyspendwhenyoubuy a newitemofclothing?
Andsosure, youknow, sometimesmaygotothatexpensiveclothingstoreandyoucouldget a jacketthatcosts, I don't know, northof a couple 100 eurosordollars, whateversystemyouwanttouse.
Andsometimesyoucangoto a secondhandstoreandgetitforverycheap.
Butusuallyifyougointostores, a jacket, I don't know, maybecostyou, like, $100 orsomethinglikethat.
So, youknow, ifyougoout, youcanexpecttopayabout $100.
Beacontechnicallyalsoappliedtwocategoriesortwocardinalnumbersifhewanted, sothatyoucansaythemostcommoncountrythatwehave, wheretheaveragekindofcountrythatwewouldexpecthereisthe U.
We'llcoverthatin a laterlecturetowomen, gointodatavisualization, butthepeakof a hist a gramthat's goingtoshowyouthemodeofthedata, themostoccurringdata, Um, a goodanotheruseofthemodewouldbeifyoulookatemployeeandcomeon a companybecausethataccompanyyouknow, youcanagainhavetheboss, whichtakesoffthemeanandyoucanhave, youknow, higherlevelemployeestowhichwekindofshiftinthemedian.
Or, say, 40% ofyouremployeesearnminimumwageorprobablynotyouremployees, becausethatwouldn't be a verygoodsystemtohavebut a 40% oftheemployeesthatthecompanythatyou'relookingat a veryminimumwagethat's not a reallygoodthingtoehave.
Solet's justkindofgothroughthiswith a workexample.
Let's setup a companyinthetownandThisistheonlycompanyinthetownandtheownerofthecompanyearns a salaryof 200 K a yearandthentheemployees, youknow, theyallhavedifferentsalaries, butthelowestemployeesormaybetheparttimeworkers.
Theyearnsomethinglike 50 k a year.
Sowe'vegotdataonkindofrangingfrom 15 K upto 200 K.
Andnowwecancombinethisifweknowtherangeofourdatatokindofget a betterfeelfordatum.
Andsolet's useanexamplewherewehavetwodifferentcountries, justcountries A and B andtheyhavethesamemeanheightforwomen, whichinthiscasewillsayis 165 centimetersorfivefeetformonwillsaythattherangeofheightsforthemcouldbeidentical.
Now, ifcountry A has a standarddeviationoffivecentimeters, whichisapproximatelytwoinches, andcountry B has a standarddeviationof 10 centimeters, whichisapproximatelyfourintereststhanwhatyoucanexpect, knowingthesevaluesisthatifyougointocountry, eh, thepeoplethatyou'regoingtoseearegonnabemuchmoresimilarandheights.
Soourstandarddeviationislower.
ThatmeansourvaluesdifferlowerfromthemeanandSothatmeans a lotofthewomenthatyou'regoingtoseearegoingtobeverycloseto 165 centimetersorfivefeetfourplusminustwoinches.
Whereasifyougotocountrybe, theyhave a muchlargerstandarddeviation.
Andsoyoucan't reallyexpecteveryonetobeabout 54 becauseitfluctuates a lotmore.
Andsoifyougotothatcountry, youcanexpecttosee a lotmorewomenofdifferentheights, bothtallerandshorter.
Then 54 allright.
Andsothat's howwecankindofusethevarianceinthestandarddeviationorthestandarddeviationtogiveus a littlebitmoreperspectiveonourdataandkindofallowustoandfirstsomestuffaboutourdata.
Sowhatthatmeansiswegetthecovarianceformydrinkingcoffeeversusfeelingtired, andthenwewouldjustdividebythestandarddeviationofmetricandcoffeeand a standarddeviationofmefeelingtired.
Theirdomainisbetweennegativeoneandone, and a correlationofonemeans a perfectpositivecorrelation.
Sothatmeanswhenonevariablegoesup, theothergoesup.
Soformycoffeeexample, thatwouldbeif I havecoffeeinthemorning, then I alsofeelmorehappy.
Sothemorecoffee I havemorehappy I feel.
Andofcourse, there's gonnabe a limit.
Butlet's say I onlydrinkuptotwocupsofcoffeeorsomethinglikethat, and I candrinkanythinginbetween, andthemore I have, themorehappy I amaboutit.
Sothatwouldbe a positivecorrelation.
Themore I haveofcoffee, theMaurahalfofhappiness, andsotheywouldkindofgouptogether, andthenwegetclosertozero.
Um, zeropointisgonnameannocorrelationtous.
Soanythingbetweenzeroandoneisgoingtobe a kindofslightlypositivecorrelation.
It's notgonnabe a superstrong, andwe'llactuallyseesomeexamplesonthenextline, butyeah, Soanythingbetweenzeroandoneisgonnabe a kindofslightpositivecorrelation, notsuperstrong.