Statistics

Mean and Median

The mean is the center of gravity of the data

Variability

Deviations:

Why so? Standard normal distribution!

Quantiles

Also, see Quantile - Wikipedia

Carbon<-read.table("http://stat4ds.rwth-aachen.de/data/Carbon.dat", header=TRUE)

summary(Carbon$CO2) # 1stQu=lowerquartile, 3rd Qu=upperquartile

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   4.350   5.400   5.819   6.700   9.900 

c(mean(Carbon$CO2),sd(Carbon$CO2),quantile(Carbon$CO2,0.90))

                       90% 
5.819355 1.964929 8.900000 

boxplot(Carbon$CO2,xlab="CO2values",horizontal=TRUE)

Crime<-read.table("http://stat4ds.rwth-aachen.de/data/Murder2.dat", header=TRUE)
boxplot(Crime$murder~Crime$nation,xlab="Murder Rate",horizontal=TRUE)

tapply(Crime$murder,Crime$nation,summary)

$Canada
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   1.030   1.735   1.673   1.875   4.070 

$US
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   2.650   5.000   5.253   6.450  24.200 

Bivariate Data

GS<-read.table("http://stat4ds.rwth-aachen.de/data/Guns_Suicide.dat", header=TRUE)
Guns<-GS$guns;Suicides<-GS$suicide
plot(Guns,Suicides) # scatterplot with arguments x, y

cor(Guns,Suicides) # correlation

[1] 0.7386667

PID<-read.table("http://stat4ds.rwth-aachen.de/data/PartyID.dat", header=TRUE)
table(PID$race,PID$id) #forms contingency table (not shown here;see Table 1.1)

       
        Democrat Independent Republican
  black      281          65         30
  other      124          77         52
  white      633         272        704

options(digits=2)
prop.table(table(PID$race,PID$id),margin=1) #Formargin=1, proportions

       
        Democrat Independent Republican
  black     0.75        0.17       0.08
  other     0.49        0.30       0.21
  white     0.39        0.17       0.44

mosaicplot(table(PID$race,PID$id)) #graphical portrayalof cell sizes

Does the sample portray the population well?

y1<-rnorm(30,100,16)# randomly sample normal distribution (Sec.2.5.1)
mean(y1);sd(y1);hist(y1)#histogram(not shown)

[1] 102

[1] 18

y2<-rnorm(30,100,16)# another random sample of size n=30
mean(y2);sd(y2);hist(y2)

[1] 101

[1] 18

Why not? High standard deviation, and low sample size!

Important

Exercises

www.nejm.org/doi/full/10.1056/NEJMon1211064