# demonstrates the concept of variance using scatter plots
# the script will generate two samples from two populations, each with the same mean but a different
# standard deviation

# the population size, the means of the populations, and the standard deviations of the populations. note
# population1 has a much smaller standard deviation than population2.
population.size = 1000000
population.mean1 = 0
population.std1 = 50
population.mean2 = 0
population.std2 = 500

# create two populations
population.data1 = rnorm(population.size,population.mean1,population.std1)
population.data2 = rnorm(population.size,population.mean2,population.std2)

# draw out a sample from each population in the x and y axis
sample.size = 100
sample.data1 = sample(population.data1,sample.size,replace = TRUE)
sample.data2 = sample(population.data2,sample.size,replace = TRUE)

# plot the output
axis.limit = 1000
par(mfrow=c(2, 1))
par(mar=c(1,1,1,1))
plot(sample.data1,ylim = c(-axis.limit,axis.limit))
plot(sample.data2,ylim = c(-axis.limit,axis.limit))