#chapitre 2


#1

x=c(3.88,3.9,3.93,3.9,3.93,3.96,3.88,3.94,3.96,3.88,3.94,3.99,3.98)
n=length(x)
tableau=table(x)/n
plot(tableau, ylab="relative frequency")
plot(tableau, type="l",ylab="relative frequency")



#3

pie(c(38.7,22.6,8.8,60), labels =c("United States","South America","Canada","Mexico"))
title("Estimated Oil Reserves")


#4

#a

time=c(19,21.9,18,22.7,19.2,21.1,28.6,25.3,21.6,20.7,20.4,25.1,21.2,18.3,19.1,
16.2,21.6,13,13.8,15.8,17.2,20,27,24,21,19.8,20.5,22.7,21.8,20.7,21.5,21.2,20.6,
19,22.3,19.3,22.2,14.8,17.3,15.4,20.7,19.1,21.6,18.9,19.8,22,19.6,24.6,16.7,23.8)
length(time)
hist(time,main="Average Travel Time to Work (minutes)",ylab="Relative frequency")
plot(ecdf(time),verticals=TRUE)

#b

percent=c(.9,.7,.7,8.3,2.5,3.9,24.8,8.8,6.4,2.5,1.3,10.1,1.6,2.5,3.6,1.2,2,.6,.3,
1.2,.6,2.4,8.1,4,1.1,1,1.1,2.8,2,1.6,1.3,.8,.8,.5,3,.6,2.2,.6,1.9,1.4,2.9,1,2.1,
2.3,2.7,4.5,3.4,4.9,2.4,7.4)
length(percent)
stem(percent)


plot(time,percent)
cor(time,precent)

#6

#a

accidents=c(4,2,4,3,11,6,4,4,1,4,2,3,3,1,2,2,6,0,2,1,3,2)
tableau=table(accidents)

#b

plot(tableau) #graphique de fréquences
plot(tableau,type="l") #polygone de fréquences

#c

plot(ecdf(accidents),verticals=TRUE)

#d

mean(accidents)

#e

n=length(accidents)
n/2
sort(accidents)
median(accidents)

#f

#du tableau le mode est 2

#g

sd(accidents)
sqrt(var(accidents))

#7

fatalities=c(197,5,231,285,278,39,62,33,1,239,166,342,3,1,12,89,531,0,22,13,22,50)
n=length(fatalities)

#a

hist(fatalities,main="Yearly Airline Fatalities")

#b

sort(fatalities)
stem(fatalities)

#c

mean(fatalities)

#d

sort(fatalities)
n/2
median(fatalities)

#e

sd(fatalities)
sqrt(var(fatalities))

#10 

x=runif(99,0,100) # 99 obs suivant une loi uniforme entre 0$ et 100$
x=c(x,1000000) #salaires chez A
y=runif(110,0,1000) #salaires chez B
sum(x) # masse salariale de A
sum(y) # masse salariale de B
median(x)
median(y) 
#médiane chez A peut être plus petite que celle chez B même si la masse salaire chez A est  #plus grande

#11

age=c(2.5,7.5, 12.5,17.5,25,35,45,55,65,75,90)
freq.male=c(120,184,44,24,23,50,60,102,167,150,49)
freq.fem=c(67,120,22,15,25,22,40,76,104,90,27)

#a

n.male=sum(freq.male)
sum(age*freq.male)/n.male

weighted.mean(age,freq.male)

#b

n.fem=sum(freq.fem)
sum(age*freq.fem)/n.fem

weighted.mean(age,freq.fem)

#c

age.all.male=rep(age,freq.male)
n.male*c(.25,.5,.75)
sort(age.all.male)[c(244,487,730)]


quantile(age.all.male,probs=c(.25,.5,.75))

#d


age.all.fem=rep(age,freq.fem)
n.fem*c(.25,.5,.75)
mean(sort(age.all.fem)[c(152,153)])
mean(sort(age.all.fem)[c(304,305)])
mean(sort(age.all.fem)[c(456,457)])


quantile(age.all.fem,probs=c(.25,.5,.75))

#15

pay1992=c(22340,31825,23153,20108,28902,25040,32603,26596,23145,24373,25538,20649,27910,
23570,20937,21982,21858,22342,21808,27145,29664,27463,25324,19237,23550,19378,20355,24743,
24866,32073,21051,32399,22249,18945,24845,21698,23514,25785,24315,21398,18016,22807,25088,
21976,22360,24940,25553,22168,23008,21215)

#on enleve la donnee sur Washington D.C. qui n'est pas un etat.

#a

mean(pay1992) #different de la moyenne globale des Etats-Unis.

#b 

#Il nous faudrait connaitre le poids relatif (population) de chaque etat dans le pays.

#c

sort(pay1992)
n=length(pay1992)
n/2

median(pay1992)

#d

mean(c(22340,31825,23153,20108,28902,25040,32603,26596,23145,24373))
mean(pay1992[1:10])

#17

percent=c(18.2,20.8,16.4,16.6,17.4,19.3,20.5,21.2,19.6,18,21.2,19.4,18.7,24,23.6,18.5,19,20.4,
20.6,20.8,23.1,15.4,18.2,17.6,17.5,19.3,17.6,21.4,14.8,15.8,18.5,21.2,19.6,17.8,20.3,21.2,22.3,
20.3,19.7,23.1,15.6,13.4,14.3,20.2,16.6,13.9,18.4,20.1,20.5,17)

#a

stem(percent)

#b

mean(percent)
median(percent)
table(percent) # mode=21.2

#c

var(percent)

#d

hist(percent,13:24)

#e

mid.point=(13:23)+.5
freq=c(2,2,3,4,6,7,6,10,5,1,4)
length(mid.point)
length(freq)
sum(freq)
length(percent)

weighted.mean(mid.point,freq)

var(rep(mid.point,freq))

#18

#a

mv=function(x){
m=x[1]
v=0
n=length(x)
for(i in 1:(n-1)){
print(c(m,v))
mp=m
m=mp+(x[i+1]-mp)/(i+1)
v=(1-1/i)*v+(i+1)*(m-mp)^2
}
list(moyenne=m,variance=v)
}

x=c(3,4,7,2,9,6)
mv(x)

#b

mean(x)
var(x)

#19

score=c(283,278,276,271,276,277,280,275,280,284,280,277,282,279,285,281,283,278,277,275,277,
279,274,276,270,279,280,278,272,276,281,279,276,281,289,280)
quantile(score,probs=c(.1,.9))