### Handout 1

# Problem 1.3

# start web based help

help.start()

# enter data

x <- c(0.74, 0.647, 1.90, 2.69, 0.75,
	0.32, 9.99, 1.77, 2.41, 1.96,
	1.66, 0.70, 2.42, 0.54, 3.36,
	3.59, 0.37, 1.09, 8.32, 4.06,
	4.55, 0.76, 2.03, 5.70, 12.48)

# compute the sample size

n <- length(x)

# get help on hist(), the command to produce a histogram

help(hist)

# plot a frequency histogram

X11()
hist(x, freq = TRUE)

# plot a relative frequency histogram

X11()
hist(x, freq = FALSE)

# Problem 1.12

# a.

# get help on mean()

help(mean)

# get help on sd()

help(sd)

# Compute the mean and sd of x

x.mean <- mean(x)
x.mean

x.sd <- sd(x)
x.sd

# b.

x.1u <- x.mean + x.sd
x.1u
x.1d <- x.mean - x.sd
x.1d

x.2u <- x.mean + 2*x.sd
x.2u
x.2d <- x.mean - 2*x.sd
x.2d

x.3u <- x.mean + 3*x.sd
x.3u
x.3d <- x.mean - 3*x.sd
x.3d

# count numer of observations in each interval

Count1 <- 0

for(i in 1:n){
	if((x[i] < x.1u) && (x[i] > x.1d)) Count1 <- Count1 + 1
}

Count1
Count1/n

Count2 <- 0

for(i in 1:n){
        if((x[i] < x.2u) && (x[i] > x.2d)) Count2 <- Count2 + 1
}

Count2
Count2/n

Count3 <- 0

for(i in 1:n){
        if((x[i] < x.3u) && (x[i] > x.3d)) Count3 <- Count3 + 1
}

Count3
Count3/n