Statistics plots

In this notebook (which covers roughly the same ground as this video) we plot various statistical graphs. For this we need the matplotlib library as well as numpy. The standard way to import these is as below. There is comprehensive documentation for matplotlib at matplotlib.org, including tutorials, examples and detailed references. Also, you can just tell Google Gemini in English what you want to do, and it will often be able to supply the right matplotlib commands.

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

matplotlib can also generate pie charts, bar charts, histograms and so on.

labels = ['Those belonging to the Emperor', 
          'Embalmed ones', 
          'Mermaids', 
          'Stray dogs', 
          'Those that tremble as if they were mad',
          'Those that, at a distance, resemble flies']
short_labels = ['A', 'B', 'C', 'D', 'E', 'F']
sizes = [1, 4, 5, 6, 7, 8]
cols = ['red', 'green', 'blue', 'cyan', 'purple', 'orange']
None

plt.pie(sizes, labels=labels, colors=cols)
plt.title('Celestial Emporium of Benevolent Knowledge')
None

fig, ax = plt.subplots(figsize=(10, 5))
ax.bar(short_labels, sizes, color=cols, label=labels)
ax.set_title('Celestial Emporium of Benevolent Knowledge')
ax.legend()

def heads(N=10):
    """Generate N random coin tosses and return the number of heads."""
    return sum(np.random.randint(0,2,N))

def make_coin_histogram(N = 16, M = 2 ** 15):
    """
    Generate M sets of N random coin tosses and plot the histogram of the 
    number of heads in each set.  Also plot the numbers predicted by the 
    binomial distribution.
    """
    X = [heads(N) for _ in range(M)]
    H = np.histogram(X, bins=N+1, range=(-0.5,N + 0.5), density=True) # unused
    plt.hist(X, bins=N+1, range=(-0.5,N + 0.5), density=True)
    plt.plot(range(N+1),[math.comb(N,i) * 0.5 ** N for i in range(N+1)],color='red')

    

make_coin_histogram(64, 2 ** 16)