In today’s world, data plays an important role in the decision-making process, and understanding it is critical for any business. The analysis of data involves a variety of techniques, one of which is plotting numbers from a normal distribution. A normal distribution is a common probability distribution, also known as the Gaussian distribution or bell curve. In this article, we will explore the problem of plotting random numbers from a normal distribution using Python, understand the libraries involved and dissect the code to understand each step.

## Libraries and Functions for Normal Distribution

Python offers several libraries that can help us with generating and plotting numbers from a normal distribution. Two of the most widely used libraries for this purpose are NumPy and Matplotlib.

**NumPy** is a powerful library for handling arrays and performing various numerical computations. We will use it to generate the random numbers from a normal distribution. Some important functions in NumPy for our problem include np.random.normal() and np.linspace().

**Matplotlib** is a library for creating static, interactive, and animated visualizations in Python. We will use it to visualize the normal distribution of the generated random numbers. The primary function we will use from this library is plt.hist().

Now let’s delve into the solution for plotting these random numbers and understand the code step-by-step.

## Solution: Plotting Numbers from a Normal Distribution

To showcase the solution, we will use the following Python code:

import numpy as np import matplotlib.pyplot as plt mu = 0 sigma = 1 n = 1000 samples = np.random.normal(mu, sigma, n) x = np.linspace(mu - 3 * sigma, mu + 3 * sigma, 100) plt.hist(samples, bins=x, density=True, alpha=0.6, color='g') plt.xlabel('Random Numbers') plt.ylabel('Frequency') plt.title('Plotting Numbers from a Normal Distribution') plt.show()

Now let’s break down the code and understand it in detail.

1. We start by importing the necessary libraries: NumPy and Matplotlib.

2. We set the parameters needed for generating the random numbers. Here, **mu** represents the mean, **sigma** represents the standard deviation, and **n** represents the number of random numbers we want to generate.

3. We generate the random numbers using the np.random.normal() function by providing the mean, standard deviation, and the number of random numbers.

4. We create a linspace using np.linspace() for values ranging from mu-3*sigma to mu+3*sigma, which represents the range for the x-axis covering approximately 99.7% of the data points.

5. We use the plt.hist() function from Matplotlib to plot the histogram. We specify the bins by providing the linspace we created, and we set the density to true for normalization. The alpha parameter is set to 0.6 for transparency and color to ‘g’ for green.

6. We set the x-axis label, y-axis label, and the title of the histogram using plt.xlabel(), plt.ylabel(), and plt.title() functions, respectively.

7. Finally, we display the histogram using plt.show().

## Understanding the np.random.normal() function

The np.random.normal() function is a versatile function within the NumPy library. It allows us to generate random samples from a normal (Gaussian) distribution. The function takes three arguments:

– loc (float): Mean (“centre”) of the distribution.

– scale (float): Standard deviation (spread or “width”) of the distribution.

– size (int or tuple of ints): Output shape, which determines the number of random numbers to generate.

By using this function, we can generate random numbers with ease and plot them using a histogram, as demonstrated in the above code.

In conclusion, Python, along with its powerful libraries like NumPy and Matplotlib, makes plotting numbers from a normal distribution an easy task. Understanding these libraries and their functions is essential for handling data and visualizing it effectively. With a few lines of code, we can generate random numbers and visualize their distribution, making Python an excellent choice for statistical analysis and data visualization.