Understanding Gaussian Distribution: A Beginner's Guide - Statistics in Tamil
Gaussian distribution, also known as normal distribution, is a continuous probability distribution that describes the likelihood of a random variable taking on a specific value within a range of values. The distribution is symmetrical around its mean (average) and is bell-shaped.
The Gaussian distribution is often used in statistical modeling and analysis because of its ubiquity in natural phenomena, as well as its mathematical convenience. Many real-world phenomena, such as the heights of people, the weights of objects, and the errors in measurements, can be approximated by a Gaussian distribution.
The empirical formula, also known as the 68-95-99.7 rule or the three-sigma rule, is a shorthand way to remember the approximate percentages of values that fall within one, two, and three standard deviations from the mean in a Gaussian distribution. Specifically:
Approximately 68% of values fall within one standard deviation of the mean.
Approximately 95% of values fall within two standard deviations of the mean.
Approximately 99.7% of values fall within three standard deviations of the mean.
These percentages can be useful for quickly estimating the distribution of data and identifying outliers.