##### Script for SlideDeck b4
###
###   Measures of Spread
###




### Preamble

# Load additional functions
source("https://rfs.kvasaheim.com/stat200.R")





### ### ###
# Load and attach the data
dt = read.csv("http://rfs.kvasaheim.com/data/geography.csv")
attach(dt)




### Ex1: Geography Quiz

# sample statistics
mean(Score)
median(Score)
modal(Score)

var(Score)
sd(Score)
IQR(Score)

cv(Score)
hildebrand.rule(Score)




# Empirical rule: %within 1stdev of the mean
vv = Score
wi2 = sum( isBetween( vv, min=mean(vv)-sd(vv), max=mean(vv)+sd(vv) ) )
wi2/length(vv)

# %within 2stdev of the mean
wi2 = sum( isBetween( vv, min=mean(vv)-2*sd(vv), max=mean(vv)+2*sd(vv) ) )
wi2/length(vv)





### The Histogram/Barplot

par(cex.axis=0.9, mar=c(4,1,1,1) )
par(cex.lab=1.2, font.lab=2)

hist(Score, breaks=seq(0,7,1)-0.5, 
	col=rgb(1-0:8/8,0,0), border="white", xaxt="n",yaxt="n",
	xlab="", ylab="", main="")
title(xlab="Score on the Geography Quiz", line=2.25)
mtext(side=1, at=0:6, text=0:6)
segments(-0.49,0, 6.5,0)

# 	








### ### ###

# Deatch geography datasest
detach(dt)


# Load and attach the crime dataset
dt = read.csv("http://rfs.kvasaheim.com/data/crime.csv")
attach(dt)



### Ex2: School Enrollment in 1990

mean(enroll90)
median(enroll90)
modal(enroll90)

var(enroll90)
sd(enroll90)
IQR(enroll90)
cv(enroll90)

hildebrand.rule(enroll90)


# Empirical rule: %within 1stdev of the mean
vv = enroll90
wi2 = sum( isBetween( vv, min=mean(vv)-sd(vv), max=mean(vv)+sd(vv) ) )
wi2/length(vv)

# %within 2stdev of the mean
wi2 = sum( isBetween( vv, min=mean(vv)-2*sd(vv), max=mean(vv)+2*sd(vv) ) )
wi2/length(vv)






### Histograms

par(cex.axis=0.9, mar=c(4,1,1,1) )
par(cex.lab=1.2, font.lab=2)

histogram(enroll90, breaks=seq(80,115,2), 
	col="green4", border="white", xaxt="n",xlab="")
title(xlab="School Enrollment Rate (1990)", line=2.25)
axis(1, at=seq(0,120,10))








### Ex3: School Enrollment in 2000

mean(enroll00)
median(enroll00)
modal(enroll00)

var(enroll00)
sd(enroll00)
IQR(enroll00)
cv(enroll00)

hildebrand.rule(enroll00)



# Empirical rule: %within 1stdev of the mean
vv = enroll00
wi2 = sum( isBetween( vv, min=mean(vv)-sd(vv), max=mean(vv)+sd(vv) ) )
wi2/length(vv)

# %within 2stdev of the mean
wi2 = sum( isBetween( vv, min=mean(vv)-2*sd(vv), max=mean(vv)+2*sd(vv) ) )
wi2/length(vv)



# Histogram

par(cex.axis=0.9, mar=c(4,1,1,1) )
par(cex.lab=1.2, font.lab=2)

histogram(enroll00, breaks=seq(80,115,2), 
	col="blue4", border="white", xaxt="n",xlab="")
title(xlab="School Enrollment Rate (2000)", line=2.25)
axis(1, at=seq(0,120,10))












### Ex4: Violent Crime rate in 2000

# Sample statistics

mean(vcrime00)
median(vcrime00)
modal(vcrime00)

var(vcrime00)
sd(vcrime00)
IQR(vcrime00)
cv(vcrime00)

hildebrand.rule(vcrime00)



# Empirical rule: %within 1stdev of the mean
vv = vcrime00
wi2 = sum( isBetween( vv, min=mean(vv)-sd(vv), max=mean(vv)+sd(vv) ) )
wi2/length(vv)

# %within 2stdev of the mean
wi2 = sum( isBetween( vv, min=mean(vv)-2*sd(vv), max=mean(vv)+2*sd(vv) ) )
wi2/length(vv)



# histogram
par(cex.axis=0.9, mar=c(4,1,1,1) )
par(cex.lab=1.2, font.lab=2)

histogram(vcrime00, breaks=seq(0,1800,100), 
	col="red4", border="white", xaxt="n",xlab="")
title(xlab="Violent Crime Rate (2000)", line=2.50)
axis(1, at=seq(0,2000,200))












#####
### Graphic for the Empirical Rule

rv = rnorm(1e6, m=0, s=20)
summary(rv)
hh = hist(rv, breaks=seq(-100,100,10), plot=FALSE )
names(hh)

#

par(bg="transparent")
par(cex.axis=0.9, mar=c(4,1,1,1) )
par(cex.lab=1.2, font.lab=2)

plot.new()
plot.window( xlim=c(-80,80), ylim=c(0,0.02))

rect(-60,0, -50,hh$density[5], col="red4")
rect(-50,0, -40,hh$density[6], col="red4")

rect(-40,0, -30,hh$density[7], col="purple")
rect(-30,0, -20,hh$density[8], col="purple")

rect(-20,0, -10,hh$density[9], col="lightblue")
rect(-10,0, -00,hh$density[10], col="lightblue")

rect(10,0, 00,hh$density[11], col="lightblue")
rect(20,0, 10,hh$density[12], col="lightblue")

rect(30,0, 20,hh$density[13], col="purple")
rect(40,0, 30,hh$density[14], col="purple")

rect(50,0, 40,hh$density[15], col="red4")
rect(60,0, 50,hh$density[16], col="red4")

title(xlab="Random Variable", line=2.50)

axis(1, at=0, label=expression(mu) )

axis(1, at=-20, label=expression(mu - 1*sigma) )
axis(1, at=+20, label=expression(mu + 1*sigma) )

axis(1, at=-40, label=expression(mu - 2*sigma) )
axis(1, at=+40, label=expression(mu + 2*sigma) )

axis(1, at=-60, label=expression(mu - 3*sigma) )
axis(1, at=+60, label=expression(mu + 3*sigma) )