Q 1 andQ 3,

(1)

Statisti sis thes ien eof olle ting,organizingandinterpretingthedata.

1. Thedieren ebetweenProbabilityandStatisti s

(a) PopulationvsSample

(b) populationmeanandpopulationvarian eandstandarddeviation.

i. Measuring enter: themean(

µ, x ¯

^),^median ⁽

M

^),^mode

ii. Measuringspread: thequartiles,thepth per entile,

Q 1

^and

Q 3

^,

theinterquartilerange(IQR)

iii. Theve-numbersummary andboxplots

mean(x);var(x), median(x), quantile(x,0.25),

( ) Skewtoright,Skew toleft,symmetri ;

(d) The(100p)thper entileof adistribution isoften alledthequantile

oforder

p

^.

q-q quantile-quantileplot,weexpe tthepoints

(y r , ˜ π r )

^lie^lose^to^a^line

throughtheoriginwithslopequalto1. (ex 3.2-7,3.5-4)

2. Displayingdatawithgraphs: barplot,pie hart,(ordered)stem-and-leaf

plot,histograms,

3. Somebasi R ommands

barand pie hart

>pie.sales<- (0.12, 0.3,0.26,0.16,0.04,0.12)# orpie.sales=s an()

>names(pie.sales)<- ("Blueberry","Cherry","Apple","BostonCream",

"Other","VanillaCream")

>barplot(pie.sales)

>pie(pie.sales)

>stem(pie.sales)

histograms(ex 3.1Mark M Gwire's HomeRuns)

>x= (364,368,364,419,424,347,462,419,437,419,

+371,362,358,527,381,545,478,440,471,451,

+425,366,477,397,433,388,423,409,356,409,

+438,437,449,433,461,431,472,485,405,415,

+511,425,458,452,408,374,464,398,409,369,

+385,477,393,509,501,450,472,497,458,381,

+430,341,385,417,423,375,403,435,377,370)

>plot(x)

>mean(x)

>var(x)

>sqrt(var(x))

>summary(x)

(2)

341.0385.0423.0423.8456.5545.0

>venum(x)

[1℄341385423458545

>stem(x)

Thede imalpointis1digit(s)to therightofthe|

34|1768

36|24468901457

38|11558378

40|35899957999

42|3345501335778

44|0901288

46|124122778

48|57

50|191

52|7

54|5

>par(mfrow= (2,2))

>hist(x)

>hist(x,br=seq(337.5,547.5,30))

>hist(x,br=seq(337.5,547.5,30),prob=TRUE)

>hist(x,br=20)

>par(mfrow= (1,1))

>hist(x,br=seq(337.5,547.5,30),prob=TRUE)

>lines(density(x), ol="red")# adensityestimateofx

>rug(x)

q-q plot

>qqnorm(x) #quantilesof xwith respe tto thevaluesof expe ted under

anormallaw

>qqline(x, ol=2) #drawaline withslop=1

>qqplot(y,x);abline(0,1, ol=2)#quantilesofxw.r.t. thequantilesofy

(3)

Histogram of x

x

Frequency

350 400 450 500 550

0 2 4 6 8 10 12 14

Histogram of x

x

Frequency

350 400 450 500 550

0 5 10 15

Histogram of x

x

Density

350 400 450 500 550

0.000 0.002 0.004 0.006 0.008

Histogram of x

x

Frequency

350 400 450 500 550

0 2 4 6 8

Figure1: Exampleforhistogram

(4)

−2 −1 0 1 2

350 400 450 500 550

Normal Q−Q Plot

Theoretical Quantiles

Sample Quantiles

Figure2: q-qnormalplot