Quan%fying central tendency and variability

Outline for today

BigDataBaseball–chapter3Be2erknowaplayer:BoJacksonReview:

•  Plo=ngcategoricalandquanAtaAvedata

MoredescripAvestaAsAcs:•  MeasuresofcentraltendencyforquanAtaAvedata•  Measuresofvariability

Worksheet2:duemidnightWednesdayFeb15th

DataFest2017•  March31sttoApril2nd

Amherstishavingpre-DataFestworkshops•  Firstoneisat7:30onFebruary15th

IfyouareinterestedinparAcipaAnginDataFestletmeknow

Big Data Baseball Chapter 3

•  Thoughts?

Be=er know a player

BoJackson

Review

Categorical and quan%ta%ve data

Descrip(vesta(s(csdescribesthesampleofdatayouhaveCategoricalvariables:fallintodisAnctcategories

E.g.,team(RedSox,Yankees,Mets,etc.)

Quan(ta(vevariables:numericaldataE.g.,Numberofhomeruns

Categorical variables: propor%on

Thepropor(onofacategoryisfoundby:

ProporAonofcategory=Numberinthatcategory totalnumber

Example:proporAonofhitsthatarehomeruns160hitstotal30/160=.1875

1B 2B 3B HRCount 90 38 2 30ProporAon 0.56 0.24 0.01 0.19

>hit.typeshit.types/sum(hit.types)

R: barplot(x)

R: pie(x)

PloDng categorical data

Describing quan%ta%ve variables

R: stem(x)

R: hist(x)

hist(player.data.2013$HR,n=30,xlab="HR",main="HistogramofHRsfor2013playerswithover300PA")

ObservaAonsaboutthedistribuAon?

Dotplot for individuals’ HR in 2013

Whenwehavediscretedata,wecanalsousedotplotstogetasenseofhowthedataisdistributed

Dotplot for individuals HR in 2013

OnewaytogetasenseoftheshapeofadistribuAonistouseadotplot

R: mosaic::dotPlot(x)

MiguelCabrera

ChrisDavis

Common shapes for Distribu%ons

sta%s%cs measuring the center of distribu%on

Graphsareusefulforvisualizingdatatogetasenseofwhatofwhatthedatalooklike

Wecanalsosummarizedatanumerically

Anumericalsummary(funcAon)ofsampleiscalledsta(s(c

TwoimportantstaAsAcsthatcanbeusedtodescribethecenterofthedataarethemeanandthemedian.

The mean

Mean=SumofalldatavaluesNumberofdatavalues

Mean=x1+x2+x3+…+xn= Σxin n

R: mean(x) Ifyoudatahasmissingvaluesuse:

mean(x, na.rm = TRUE)

Mean number of games played (G)

Canyoucalculatethemeannumberofgamesplayedforplayerswhohad300plateappearancesin2013>players.2013mean(players.2013$G)

Doyouthinkthemeannumberofgamesplayedwouldbehigherifwecalculateditfromonlyplayerswhohad500plateappearances?

Sample vs. Popula%on mean

Themeanforasampleisdenotedx̄(pronounced“x-bar”)Themeanforapopula)onisdenotedμ,whichistheGreekle2er“mu”

μ

x̄

Give the proper nota%on: μ vs. x̄ ?̄

Werandomlyselect50baseballplayersandtaketheirmeanheight?

Welookatallprofessionalbaseballplayersandtaketheirmeanheight?

The median

Themedianofadatasetofsizenis

•  Ifnisodd:Themiddlevalueofthesorteddata

•  Ifniseven:Theaverageofthemiddletwovaluesofthesorteddata

ThemediansplitsthedatainhalfR: median(x)

Resistance

WesaythatastaAsAcsisresistantifitisrelaAvelyunaffectedbyextremevalues(outliers).

Themedianisresistantwhenthemeanisnot

Football player salary examples

SomeNFLfootballplayersarepaidalotmorethanothers(starquarterbackscanbepaidmorethan$20million)

MeanNFLsalary=$1.87millionMedianNFLsalary=$838,000

MeanandmediansalaryforallUSworkers?DistribuAonofsalariesforUSworkers?

Which is the mean A or B?

A B

Summary sta%s%cs quan%fying the spread of quan%ta%ve variables

Standard devia%on

R: sd(x)

In class worksheet: compu%ng the standard devia%on

54 35 23 28 3229 23 30 35 3738

Values DeviaAons SquaredDeviaAons

54 20.91 437.19

35 1.91 3.64

NumberofhomerunsDavidOrAzhadinthelast11seasons: