Normal and Gaussian Distribution

By Admin Published in Machine Learning 3-4 mins
Table of content
Related Posts
Win the COVID-19

April 24, 2021

Model vs Algorithm in ML

April 29, 2021

Is AI a threat to humanity?
Akash Kumar

August 18, 2019

Tuples - An Immutable Derived Datatype
Vineeth Kumar

August 18, 2022

Young Data Scientists

December 17, 2021

Random forest model(RFM)

December 20, 2020

Data Science is Important!

December, 2021

Data Science at Intern Level

January 7, 2022

Text Stemming In NLP

July 5, 2022

Clustering & Types Of Clustering

November 17, 2020

Support Vector Machine

November 25, 2020

Operators in Python - Operation using Symbol
Vineeth Kumar

September 14, 2022

Basics of Functions In Python - A Glance
Vineeth Kumar

September 9, 2022

Gaussian Distribution

Gaussian distribution is a bell-shaped curve, it follows the normal distribution with the equal number of measurements right side and left side of the mean value. Mean is situated in the centre of the curve, the right side values from the mean are greater than the mean value and the left side values from the mean are smaller than the mean. It is used for mean, median, and mode for continuous values. You all know the basic meaning of mean, median, and mod. The mean is an average of the values, the median is the centre value of the distribution and the mode is the value of the distribution which is frequently occurred. In the normal distribution, the values of mean, median, and are all same. If the values generate skewness then it is not normally distributed. The normal distribution is very important in statistics because it fits for many occurrences such as heights, blood pressure, measurement error, and many numerical values.

A gaussian and normal distribution is the same in statistics theory. Gaussian distribution is also known as a normal distribution. The curve is made with the help of probability density function with the random values. F(x) is the PDF function and x is the value of gaussian & used to represent the real values of random variables having unknown distribution.

There is a property of Gaussian distribution which is known as Empirical formula** **which shows that in which confidence interval the value comes under. The normal distribution contains the mean value as 0 and standard deviation 1.

The empirical rule also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Python code for plotting the gaussian graph:

import matplotlib.pyplot as plt

import numpy as np

import scipy.stats as stats

import math

mu = 0

variance = 1

sigma = math.sqrt(variance)

x = np.linspace(mu - 3sigma, mu + 3sigma, 100)

plt.plot(x, stats.norm.pdf(x, mu, sigma))


The above code shows the Gaussian distribution with 99% of the confidence interval with a standard deviation of 3 with mean 0.

Learnbay provides industry accredited data science courses in Bangalore. We understand the conjugation of technology in the field of Data science hence we offer significant courses like Machine Learning, Tensor Flow, IBM Watson, Google Cloud platform, Tableau, Hadoop, time series, R and Python. With authentic real-time industry projects. Students will be efficient by being certified by IBM. Around hundreds of students are placed in promising companies for data science roles. Choosing Learnbay you will reach the most aspiring job of present and future.

Learnbay data science course covers Data Science with Python, Artificial Intelligence with Python, Deep Learning using Tensor-Flow. These topics are covered and co-developed with IBM.


#Data Science#Machine Learning