#Central Limit Theorem
import numpy as np

# Create population and find population mean
population = np.random.normal(loc=65, scale=100, size=3000)
population_mean = np.mean(population)

# Select increasingly larger samples
extra_small_sample = population[:10]
small_sample = population[:50]
medium_sample = population[:100]
large_sample = population[:500]
extra_large_sample = population[:1000]

# Calculate the mean of those samples
extra_small_sample_mean = np.mean(extra_small_sample)
small_sample_mean = np.mean(small_sample)
medium_sample_mean = np.mean(medium_sample)
large_sample_mean = np.mean(large_sample)
extra_large_sample_mean = np.mean(extra_large_sample)

# Print them all out!
print "Extra Small Sample Mean: {}".format(extra_small_sample_mean)
print "Small Sample Mean: {}".format(small_sample_mean)
print "Medium Sample Mean: {}".format(medium_sample_mean)
print "Large Sample Mean: {}".format(large_sample_mean)
print "Extra Large Sample Mean: {}".format(extra_large_sample_mean)

print "\nPopulation Mean: {}".format(population_mean)