To plot a normal distribution in Python, you can use the following syntax:
#x-axis ranges from -3 and 3 with .001 steps x = np.arange(-3, 3, 0.001) #plot normal distribution with mean 0 and standard deviation 1 plt.plot(x, norm.pdf(x, 0, 1))
The x array defines the range for the x-axis and the plt.plot() produces the curve for the normal distribution with the specified mean and standard deviation.
The following examples show how to use these functions in practice.
Example 1: Plot a Single Normal Distribution
The following code shows how to plot a single normal distribution curve with a mean of 0 and a standard deviation of 1:
import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm #x-axis ranges from -3 and 3 with .001 steps x = np.arange(-3, 3, 0.001) #plot normal distribution with mean 0 and standard deviation 1 plt.plot(x, norm.pdf(x, 0, 1))
You can also modify the color and the width of the line in the graph:
plt.plot(x, norm.pdf(x, 0, 1), color='red', linewidth=3)
Example 2: Plot Multiple Normal Distributions
The following code shows how to plot multiple normal distribution curves with different means and standard deviations:
import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm #x-axis ranges from -5 and 5 with .001 steps x = np.arange(-5, 5, 0.001) #define multiple normal distributions plt.plot(x, norm.pdf(x, 0, 1), label='μ: 0, σ: 1') plt.plot(x, norm.pdf(x, 0, 1.5), label='μ:0, σ: 1.5') plt.plot(x, norm.pdf(x, 0, 2), label='μ:0, σ: 2') #add legend to plot plt.legend()
Feel free to modify the colors of the lines and add a title and axes labels to make the chart complete:
import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm #x-axis ranges from -5 and 5 with .001 steps x = np.arange(-5, 5, 0.001) #define multiple normal distributions plt.plot(x, norm.pdf(x, 0, 1), label='μ: 0, σ: 1', color='gold') plt.plot(x, norm.pdf(x, 0, 1.5), label='μ:0, σ: 1.5', color='red') plt.plot(x, norm.pdf(x, 0, 2), label='μ:0, σ: 2', color='pink') #add legend to plot plt.legend(title='Parameters') #add axes labels and a title plt.ylabel('Density') plt.xlabel('x') plt.title('Normal Distributions', fontsize=14)
Refer to the matplotlib documentation for an in-depth explanation of the plt.plot() function.
Excellent thank you! How do we plot a guassian /bell curve ?
Also, can we plot a Guassian curve if we only have the mean and the standard deviation (no other data)?
import numpy as np
import matplotlib.pyplot as plt
# Parameters of the normal distribution
mean = 50
std_dev = 10
# Generate x values for the distribution curve
x = np.linspace(mean – 3 * std_dev, mean + 3 * std_dev, 100)
# Calculate y values for the distribution curve
y = (1 / (std_dev * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x – mean) / std_dev) ** 2)
# Plot the distribution curve
plt.plot(x, y)
# Shade the area to the left of 40
x_shade = np.linspace(mean – 3 * std_dev, 40, 100)
y_shade = (1 / (std_dev * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x_shade – mean) / std_dev) ** 2)
plt.fill_between(x_shade, y_shade, alpha=0.5)
# Add labels and title
plt.xlabel(‘Number of Reported Burglaries’)
plt.ylabel(‘Probability Density’)
plt.title(‘Distribution of Reported Burglaries in a Month’)
# Show the plot
plt.show()
Hi Matebogo…Thank you for you post! Let us know if you have any questions we can help with!