Normal Distribution / Gaussian Distribution
A Random Variable (X) having mean () and standard deviation () is said to be Normally Distributed if it has the following properties:
Properties of Normal Distribution
- The mean, median and mode are all at the centre point.
- There is no skewness.
- It has a kurtosis of 3.
- It follows Bell Curve.
- It is symmetrical on both sides of the mean.
- 50% data lies before the mean and the other 50% is on the right side of the mean.
- The data near the mean is more frequent in occurrence than the data far from it.
- If you go one standard deviation to the left and one standard deviation to the right, it covers 68% of the total data.
- If you go two standard deviations to the left and two standard deviations to the right, it covers 95% of the total data.
- If you go three standard deviations to the left and three to the right, it covers 99.7% of the total data.
Standard Normal Distribution
Standard Normal Distribution is a particular type of Normal Distribution where the mean is 0 and the standard deviation is 1.
How to convert Normal Distribution into Standard Normal Distribution?
Normal Distribution can be converted to Standard Normal Distribution by using a z-score. This process is also called Standardization.
- = mean
- = standard deviation
- = current value
Central Limit Theorem
The Normal Distribution is key to the central limit theorem. According to it, if multiple samples are taken from a population then the distribution of their sample means will follow a normal distribution as the sample size increases.
Applications of Normal Distribution
- All kind of variables in nature is nearly normally distributed like height, weight, job satisfaction, body temperature, strength etc.
- The central limit theorem is based on the concept of normal distribution.
- The assumption behind statistical tests is that data follows a normal distribution.
- If a variable is not normally distributed, it can be converted into normal distribution by a simple transformation.
You can check other probability distributions here.