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# -*- coding: utf-8 -*-
"""
Created on Sun Oct 11 18:47:35 2015
@author: Camil Staps (s4498062)
Run with Python 2.7
"""
import matplotlib.pyplot as plt
import numpy as np
def all_samples(data, n):
"""All samples without replacement or ordering with n elements from data"""
if n == 0:
return [[]]
else:
samples = []
for i, d in enumerate(data):
samples = samples + [[d] + s for s in all_samples(data[i+1:], n-1)]
return samples
def nearly_equal(m, n, sig_fig = 5):
"""Determine whether two numbers are nearly equal"""
# http://stackoverflow.com/a/558289/1544337
return m == n or int(m * 10 ** sig_fig) == int(n * 10 ** sig_fig)
data = np.array([2,3,6,8,11,18])
# i
print("Mean: %f\nStandard deviation: %f" % (data.mean(), data.std()))
samples_2 = all_samples(data, 2)
samples_4 = all_samples(data, 4)
# ii
print([(s, np.mean(s)) for s in samples_2])
print([(s, np.mean(s)) for s in samples_4])
# iii
samples_2_means = [np.mean(s) for s in samples_2]
samples_4_means = [np.mean(s) for s in samples_4]
print("Mean of 2-sample means: %f" % np.mean(samples_2_means))
print("Standard deviation of 2-sample means: %f" % np.std(samples_2_means))
print("Mean of 4-sample means: %f" % np.mean(samples_4_means))
print("Standard deviation of 4-sample means: %f" % np.std(samples_4_means))
# iv
print("Means are equal (2): %r" % (np.mean(samples_2_means) == data.mean()))
print("Means are equal (4): %r" % (np.mean(samples_4_means) == data.mean()))
print("σ2 ≈ σ/√2×√(4/5): %r" % nearly_equal(
np.std(samples_2_means), data.std() / np.sqrt(2.) * np.sqrt(4./5.)))
print("σ4 ≈ σ/√4×√(2/5): %r" % nearly_equal(
np.std(samples_4_means), data.std() / np.sqrt(4.) * np.sqrt(2./5.)))
# v
plt.figure(figsize=(10,4))
plt.subplot(1, 3, 1)
plt.hist(data)
plt.title('Population distribution')
plt.subplot(1, 3, 2)
plt.hist(samples_2_means)
plt.title('2-Sample mean distribution')
plt.subplot(1, 3, 3)
plt.hist(samples_4_means)
plt.title('4-Sample mean distribution')
plt.show()
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