# What is a simple teachable example where normalization/standardization of data is necessary or convenient for valid inference?

Many students come across normalization and standardization as a easy to understand, but hard to grasp/motivate problem. Often times reasons for why we should normalize or standardize data range from the fact we want to do PCA (variance sensitive) or want to make the results more readable. I was wondering if anyone had a simple, nearly trivial example that is teachable to students where the motivation behind normalization or standardization is justified?

• A client ran into severe numerical problems (total loss of numerical precision in computing sums of squares and products), as well as issues in reporting results, in making simple regressions of monitoring data over time. Her problem stemmed from using her software's default method of representing time as seconds since 1970. That put the values of her times around $10^9$ and the rates of change (which were a few percent per year) were expressed as values less than $10^{-8}$. The solution was not necessarily standardization, but expressing times in years since 2000 worked nicely.
– whuber
Oct 24, 2017 at 16:05