How to Make a Bell Curve in Python

A “bell curve” is the nickname given to the shape of a normal distribution, which has a distinct “bell” shape:

This tutorial explains how to make a bell curve in Python.

How to Create a Bell Curve in Python

The following code shows how to create a bell curve using the numpy, scipy, and matplotlib libraries:

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

#create range of x-values from -4 to 4 in increments of .001
x = np.arange(-4, 4, 0.001)

#create range of y-values that correspond to normal pdf with mean=0 and sd=1 
y = norm.pdf(x,0,1)

#define plot 
fig, ax = plt.subplots(figsize=(9,6))
ax.plot(x,y)

#choose plot style and display the bell curve 
plt.style.use('fivethirtyeight')
plt.show()

How to Fill in a Bell Curve in Python

The following code illustrates how to fill in the area under the bell curve ranging from -1 to 1:

x = np.arange(-4, 4, 0.001)
y = norm.pdf(x,0,1)

fig, ax = plt.subplots(figsize=(9,6))
ax.plot(x,y)

#specify the region of the bell curve to fill in 
x_fill = np.arange(-1, 1, 0.001)
y_fill = norm.pdf(x_fill,0,1)
ax.fill_between(x_fill,y_fill,0, alpha=0.2, color='blue')

plt.style.use('fivethirtyeight')
plt.show()

Note that you can also style the graph in any way you’d like using the many matplotlib styling options. For example, you could use a “solar light” theme with a green line and green shading:

x = np.arange(-4, 4, 0.001)
y = norm.pdf(x,0,1)

fig, ax = plt.subplots(figsize=(9,6))
ax.plot(x,y, color='green')

#specify the region of the bell curve to fill in 
x_fill = np.arange(-1, 1, 0.001)
y_fill = norm.pdf(x_fill,0,1)
ax.fill_between(x_fill,y_fill,0, alpha=0.2, color='green')

plt.style.use('Solarize_Light2')
plt.show()

You can find the complete style sheet reference guide for matplotlib here.

Additional Resources

How to Make a Bell Curve in Excel