# demonstrates the concept of variance using scatter plots

population.size = 1000000
population.mean1x = 0
population.mean1y = 0
population.std1x = 50
population.std1y = 50
population.mean2x = 0
population.mean2y = 0
population.std2x = 500
population.std2y = 500

sample.size = 10000

axis.limit = 5000

population.data1x = rnorm(population.size,population.mean1x,population.std1x)
population.data1y = rnorm(population.size,population.mean1y,population.std1y)
population.data2x = rnorm(population.size,population.mean2x,population.std2x)
population.data2y = rnorm(population.size,population.mean2y,population.std2y)

population.mean = mean(population.data)

par(mfrow=c(2, 1))
par(mar=c(1,1,1,1))

sample.data1x = sample(population.data1x,sample.size,replace = TRUE)
sample.data1y = sample(population.data1y,sample.size,replace = TRUE)
sample.data2x = sample(population.data2x,sample.size,replace = TRUE)
sample.data2y = sample(population.data2y,sample.size,replace = TRUE)

plot(sample.data1x,sample.data1y,xlim = c(-axis.limit,axis.limit),,ylim = c(-axis.limit,axis.limit))
plot(sample.data2x,sample.data2y,xlim = c(-axis.limit,axis.limit),,ylim = c(-axis.limit,axis.limit))