# Some issues with standardized variable in a regression analysis

I'm solving this multiple choice question on the properties of a standardized variable. Two of the possible options (which are wrong but look right to me) are 1. It is always normally distributed and 2. it has a bell shaped distribution.

I've been googling and apparently, standardizing a variable does not change the shape of the curve. So if we have a non normal distribution- standardizing it wont change its shape. However, I thought one of the defining characteristic of a Z distribution was that it was symmetric.

If a normal distribution is always symmetric, and a Z distribution is always symmetric, how can we have a non normal standard distribution? Can we have a distribution that is not bell shaped and still standardized? I'm trying to think of examples but can't.

• Is the variable normally distributed before the standardization? – Cagdas Ozgenc Mar 13 '15 at 12:54
• Its a general multiple choice question. Is it possible to standardize a non normally distributed variable? Because our teacher told us that we convert a variable to Z value only if its normally distributed. – dexter Mar 13 '15 at 13:04
• Standardization is a general term. But as analog to normal distribution, any distribution in the class of distributions called location-scale distributions can be location centered and set to unit scale. Therefore if the variable is not normal before standardization both #1 and #2 are false. – Cagdas Ozgenc Mar 13 '15 at 14:10