**standardization**may sound a little weird at first but understanding it in the context of statistics is not brain surgery. It is something that has to do with

**distributions**. In fact, every

**distribution**can be standardized. Say the

**mean**and the

**variance**of a variable are

**and**

*mu***squared respectively.**

*sigma***Standardization**is the process of transforming a variable to one with a

**mean**of 0 and a

**standard deviation**of 1. You can see how everything is denoted below along with the formula that allows us to standardize a

**distribution**.

## Standard Normal Distribution in Statistics: Definition and Formulas

Logically, a**normal distribution**can also be standardized. The result is called a

**standard normal distribution.**

**standardization**goes down here. Well, all we need to do is simply shift the

**mean**by

**, and the**

*mu***standard deviation**by

**.**

*sigma***to denote it. As we already mentioned, its**

*Z***mean**is 0 and its

**standard deviation**: 1.

**z-score**. It is equal to the original variable, minus its

**mean**, divided by its

**standard deviation**.

**A Case in Point**

Let’s take an approximately normally distributed set of numbers: 1, 2, 2, 3, 3, 3, 4, 4, and 5.
**mean**is 3 and its

**standard deviation**: 1.22. Now, let’s subtract the

**mean**from all data points. As shown below, we get a new data set of: -2, -1, -1, 0, 0, 0, 1, 1, and 2.

**mean**is 0, exactly as we anticipated.

**The Next Step of the Standardization**

So far, we have a new **distribution**. It is still normal, but with a mean of 0 and a

**standard deviation**of 1.22. The next step of the

**standardization**is to divide all data points by the

**standard deviation**. This will drive the

**standard deviation**of the new data set to 1. Let’s go back to our example. The original dataset has a

**standard deviation**of 1.22. The same goes for the dataset which we obtained after subtracting the

**mean**from each data point.

**Important:**Adding and subtracting values to all data points does not change the

**standard deviation**. Now, let’s divide each data point by 1.22. As you can see in the picture below, we get: -1.6, -0.82, -0.82, 0, 0, 0, 0.82, 0.82, and 1.63.

**standard deviation**of this new data set, we will get 1. And the

**mean**is still 0!

## Standardization of Normal Distribution: Next Steps

This is how we can obtain a**standard normal distribution**from any normally distributed data set. Using it makes predictions and inferences much easier. This is exactly what will help us a great deal in the next tutorials. So, if you want to use the knowledge you gained here, feel free to jump into the linked tutorial. The article first appeared on: https://365datascience.com/standardization/

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