Histograms

Histograms are used to represent graphically the frequency of a set of measurements.

See the matplotlib user manual for more details: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.hist.html

import numpy
import matplotlib.pyplot as plt
%matplotlib inline

data = [-1.17, -1.23, -2.94, 0.36, -0.63,  0.09, -0.42, -0.39,  1.03, -1., 
 1.12,  0.25, -0.84,  0.47,  0.42, -0.15,  1.36, -0.7,  -0.71,  
 0.13, -0.77,  0.44,  0.41, -0.52, -0.59,  0.25, -0.69, -1.34, -0.96,  
 0.17, -1.78,  0.08,  0.53,  0.35, -1.37, -0.05, -0.24, -0.36,  1.49,  
 0.16,  1.26, -0.08,  1.25,  0.19,  1.37,  0.96, -1.45,  0.11,  1.67,  
 1.28, -0.61, -0.43, -1.01,  0.11,  0.59, -0.62,  0.21,  0.94, -0.88, 
 -0.95, -0.65, -0.42, -1.24,  0.53, -0.38, -1.05, -1.68, -1.95, -1.07,  
 0.38,  0.09, -0.24, -1.74,  0.23,  0.11,  0.9,   0.07, -0.45,  0.25,  
 1.81,  0.23,  0.01, -2.77, -0.14,  0.26, -0.73, -1.82, -0.52, -0.1,  
 -0.5,   0.79, -0.74,  1.2,   1.,   -0.5,  -2.19, -2.01, -0.86, -0.41,  0.8 ]


# Define range and number of bins
min_range = -5
max_range = 5
num_bins = 20

# Normalized to unit area ?
norm = True

# Plot histogram
plt.figure(figsize=[6,6])
entries, bin_boundaries, patches = plt.hist(data, bins=num_bins, range=(min_range, max_range), facecolor='green', density=norm)

print ("Entries =", entries)
print ("Bin boundaries =", bin_boundaries)

plt.title('Histogram of Data Points')
plt.xlabel('Data Points')
plt.ylabel('Frequency')
plt.show()

Entries = [0.   0.   0.   0.   0.04 0.04 0.1  0.18 0.38 0.34 0.52 0.16 0.2  0.04
 0.   0.   0.   0.   0.   0.  ]
Bin boundaries = [-5.  -4.5 -4.  -3.5 -3.  -2.5 -2.  -1.5 -1.  -0.5  0.   0.5  1.   1.5
  2.   2.5  3.   3.5  4.   4.5  5. ]

Any time you in your data you lose information: data are now represented by a vector of size nbins. On the other hand you can see this as a simple (lossy) information compression.

Physical example of bins: Galton machine https://en.wikipedia.org/wiki/Galton_board