Illustration with Python Central Limit Theorem | sample size increases the mean of sample is close to population mean

sampleSizeIncreaseDot.py

import numpy as np
import random
import matplotlib.pyplot as plt

# Step 1
## show that as the sample size increases the mean of sample is close to population mean
# build gamma distribution as population
shape, scale = 2., 2.  # mean=4, std=2*sqrt(2)
s = np.random.gamma(shape, scale, 1000000)

# Step 2
# set expected values of population
mu = shape*scale # mean
# sample size
samplesize = []
# collect difference between sample mean and mu
diflist = []
# for each sample size
for n in range(10,20000,20): 
    # sample n sample
    rs = random.choices(s, k=n)
    # start count
    c = 0
    # calculate mean
    mean = sum(rs)/len(rs)
    # collect difference between sample mean and mu
    diflist.append(mean-mu)
    samplesize.append(n)

# Step 3
# set figure size.
plt.figure(figsize=(20,10))
# plot each diference.
plt.scatter(samplesize,diflist, marker='o')
# show plot.
plt.show()