# What is difference between Standard Normal Distribution and Mean Normalization approaches to feature-scaling?

The tag feature-scaling seems to convey that one of the scaling methods is Standard Normal Distribution. Further, I read an Answer on this site saying that Mean Normalization is a form of feature scaling.

What is the difference between two approaches to scaling?

Note: I think that statistics and mathematics of normalization do differ.

• Can you link to the answer you're referring to? – Itamar Mushkin Aug 3 '20 at 13:52

The terms standardization and normalization are often used interchangeably. However, strictly speaking they do refer to distinct feature transformations.

# Normalization

Normalization, also called feature scaling usually means scaling the data between 0 and 1. There are many approaches that can be used to achieve this. One common way is by

$$x' = \frac{x - x_{min}}{x_{max} - x_{min}}$$

# Standardization

Standardization transforms the feature to have a mean 0 and a standard deviation of 1. This is also called z-scoring and can be achieved by

$$x_i' = \frac{x_i - \bar{x}}{s}$$

where $$\bar{x}$$ is the mean of the feature and $$s$$ is the standard deviation of the feature.

• normal means conforming to a standard; usual, typical, or expected. The definition varies with respect to discipline of study. Scaled data could be Normalized by computing Z- scores or standard scores which allows the application of inferential statistics such as z -statistic. The normalization produces individual data for each question item or each individual. It generates weights / values for each scale point/category. Normalization is processing of data and has nothing to do with standard normal distribution.The latter is based on statistics. – Subhash C. Davar Jul 22 '20 at 5:22