Example R programs and commands
		      5. Box plots, confidence intervals

# All lines preceded by the "#" character are my comments.
# All other left-justified lines are my input.

# Plot 3 data points specifying mean, confidence interval, and range 
x1 <- c( 1.0, 1.1, 1.5, 1.7, 1.9)
x2 <- c( 2.0, 2.1, 2.5, 2.7, 2.9)
x3 <- c( 3.0, 3.1, 3.5, 3.7, 3.9)
boxplot(list(x1,x2,x3),range=0)

# Compute the 95% confidence interval given the mean, standard deviation,
# and number of samples:
xbar<-3.3    # example mean value
xsd<-0.44    # example standard deviation
quantiles<-c(0.025,0.975)  # 95% lies between 2.5% and 97.5% marks
n <- 18     # Number of samples
xdf <- n-1  # Degrees of freedom
qt(quantiles,xdf)    # t values for 95% confidence interval
#OUTPUT:   [1] -2.109816  2.109816
xbar+ (xsd/sqrt(n))*qt(quantiles,xdf)    # confidence interval
#OUTPUT:   [1] 3.081193 3.518807
# Estimate the standard deviation of the mean from some samples:
x<-c(1.1,1.2,1.1,1.4,1.5,1.3,1.2,1.0)    # samples
mean(x)     # average of samples estimates the population mean
#OUTPUT:   [1] 1.225
sd(x)       # sample standard deviation estimates population sd.
#OUTPUT:   [1] 0.1669046
sd(x)/sqrt(length(x))  # standard deviation of the sample mean
#OUTPUT:   [1] 0.05900968