### Class examples from Week 4: Variability
### Ken Benoit Feb 2010


## percentiles illustrated
x <- (round(runif(100)*100))  # create 100 random values 0-100
xsorted <- sort(x)            # sort the values
xsorted[c(1,25,50,75,100)]    # min; 25th, 50th, 75th %tile; max
summary(xsorted)              # ask R for same information
summary(x)                    # sorting makes no difference
quantile(x,0.25)              # 25th percentile using quantile()
quantile(x,0.95)              # 75th percentile
quantile(x,0.50)              # 50th percentile (median)
median(x)                     # median (50th percentile)
# compute position of 25th %tile using formula
(p <- (25/100)*(length(xsorted)+1))
x[floor(p)]      # the position before p
x[ceiling(p)]    # the position after p


## variance and standard deviation from L&F Table 4.1
x <- c(9,8,6,4,2,1)
xdev <- x - mean(x)
(s2 <- sum(xdev^2)/length(x))
(s <- sqrt(s2))


## redo figure 4.4 LFF
males <- c(5,2,7,9,3,4,3,1,3,8)
females <- c(3,5,7,4,5,6,7,6,5,4)
boxplot(c(males,females), ylim=c(0,10))
abline(h=c(2,4,6,8), lty="dotted")