# 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? Commented Aug 3, 2020 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. Commented Jul 22, 2020 at 5:22

Scaling means quantifying or estimating weights to be assigned to different categories of response to a question item after data had been generated in terms of responses, e.g. Strongly agree,agree,somewhat agree -if standard scale (s) are not available for data-processing and analysis. The tag feature-scaling seems to convey that one of the scaling methods is Standard Normal Distribution.Given the meaning and purpose of scaling it is incorrect to say that standard normal distribution serves as a basis of scaling. Similarly, "normalization" of raw data does not invoke scaling of data generated by an experiment or a survey.(Also, the method of normalization cited by authors is incorrect). In view of observations above, the tag feature scaling should be corrected.