Histogram allows us to visualize the frequency distribution of our data. It breaks the data into a few smaller bins according to the value of the data, and then count the number of occurences (i.e., the frequency) in each bin.

We can obtain the frequency and bins for a given data using the histogram() function from numpy. Let’s consider the following example:

import numpy as np

# generate 1000 random numbers
x = np.random.rand(1000, 1)

# count the occurences in each bin in x
frequency, bins = np.histogram(x, bins=10, range=[0, 1])


for b, f in zip(bins[1:], frequency):
    print(f'value: {(round(b,1))} >> frequency: {f}')

Output:

value: 0.1 >> frequency: 80
value: 0.2 >> frequency: 80
value: 0.3 >> frequency: 98
value: 0.4 >> frequency: 91
value: 0.5 >> frequency: 123
value: 0.6 >> frequency: 97
value: 0.7 >> frequency: 105
value: 0.8 >> frequency: 102
value: 0.9 >> frequency: 117
value: 1.0 >> frequency: 107

Here, we used numpy.random.rand() function to generate 1000 uniformly distributed values, ranging from 0 to 1. An array x is defined to store the generated values. We would like to know how many data is within 0-0.1, how many occurs at 0.1-0.2, and so on. These can be obtained by calling numpy.histogram() function.

Histogram with Matplotlib

Matplotlib allows us to plot the histogram with pyplot.hist() function. Let’s continue with the above example, and use the histogram function in Matplotlib to visualize the data distribution.

import matplotlib.pyplot as plt 

plt.hist(x, bins = 10)
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

Let’s generate another set of random number, but with normal distribution. Instead of numpy.random.rand(), we can use numpy.random.randn() to generate a series of values that follow standard normal distribution with zero mean and standard deviation equals to 1.

Notes: if we would like to have a normal distribution with specific mean and standard deviation, we can use the following formula: \(\sigma * numpy.random.randn() + \mu\)

# generate 1000 random numbers
x = np.random.randn(1000, 1)

plt.hist(x, bins = 10)
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

Multiple Histograms in a Single Plot

We can plot multiple histograms for easy comparison. Let’s create 3 numpy arrays each consists of 1000 normally distributed random numbers based on different mean and standard deviation.

x1 = 3 * np.random.randn(1000,1) + 3
x2 = 2 * np.random.randn(1000,1) + 7
x3 = x 

plt.figure(figsize=(12, 5))
plt.hist(x1, bins = 10, alpha = 0.5, color = 'red', label = 'x1')
plt.hist(x2, bins = 10, alpha = 0.5, color = 'green', label = 'x2')
plt.hist(x3, bins = 10, alpha = 0.5, color = 'blue', label = 'x3')
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.legend()
plt.show()

Density Distribution

Instead of using the number of occurences as the y-axis, we can normalize the occurences frequency by setting density to True, as shown below:

plt.figure()
plt.hist(x, bins = 10, density= True)
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Probability")
plt.show()

Style the Histogram

We can create spacing between each bin in the histogram using the set_style() function from seaborn. Note that seaborn is built upon matplotlib, so we can use seaborn and matplotlib together.

import seaborn as sns 
sns.set_style("white")

plt.figure()
plt.hist(x, bins = 10, density= True)
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Probability")
plt.show()

We can also use the seaborn.histplot() function to visualize the histogram and density curve on the same plot.

plt.figure()
# sns.histplot(x, bins = 10, hist_kws={'alpha': 0.5}, kde_kws={'linewidth': 2})
sns.histplot(x, bins = 10, alpha = 0.5, stat="probability", kde = True, legend = False)
plt.title("Data Distribution")
plt.xlabel("Value")
plt.ylabel("Probability")
plt.show()