In [109]:

    

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt


    

In [110]:

    

population = np.random.randint(1,high=100,size=50)


    

In [111]:

    

mean = np.mean(population)
print(mean)


    

    




51.46

In [112]:

    

sem = np.std(population) / np.sqrt(len(population))
print(sem)


    

    




3.91460955907

In [113]:

    

replicates = np.empty(10000)
for i in range(10000):
    sample = np.random.choice(population, size=len(population))
    replicates[i] = np.mean(sample)


    

In [114]:

    

# mean of the sampled data.
sampled_mean = np.mean(replicates)

print(sampled_mean)


    

    




51.491052

In [115]:

    

# std of the sampled distr.
replicates_std = np.std(replicates)

print(replicates_std)


    

    




3.93361555993

In [116]:

    

# 95% confidence interval 
percentiles = np.percentile(replicates,[2.5,97.5])

print(percentiles)


    

    




[ 43.8595  59.26  ]

In [117]:

    

sns.set()

_ = plt.hist(replicates,bins=int(np.sqrt(len(replicates))),normed=True)
_ = plt.xlabel('data')
_ = plt.ylabel('%')

# add mean
plt_x_mean = np.repeat(sampled_mean, 2)
plt_y_mean = [0, 0.14]
_ = plt.plot(plt_x_mean,plt_y_mean,color='red')

plt.margins(.02)
plt.show()