Standard Normal Variate (Z), standardization of data

If we have a random variable(RV) with mean = 0 & variance σ² = 1, then that RV is called z i.e. Standard Normal Variate.

Say,

X = N ( u, σ² ) is any normal dist with mean as u & variance as σ²

then we can apply standardization to this dist & we will perform

x' = ( xi - u ) / σ 

x' will be called standard normal variate.

The transformation performed on the initial RV is called standardization. 

Why do we standardize data?

It makes sure that 68% of the data in hand now lies within -1 & 1. Makes analysis easier. 

The process of transforming this X = N ( u, σ² ) into X = N ( 0, 1 ) is called Standardization.