Variable standardization / scaling for PCA when all dimensions already have same scale Often when PCA is performed on exam results where all variables (dimensions) have the same $0$ to $100$ scale, scaling is none the less applied. For different scales I can see the purpose of it, but not in this case. Why is it done?
 A: Scaling (for PCA) is kind of a personal matter. Some people always do it, others won't, whatever the data.
It is not just a question of measuring scale (°C vs °K, km vs miles), not scaling leads to giving more importance to variables that have larger variance (such variables would contribute more to dimensions construction than other variables). Some people exactly want that as they reckon that variables with small variance are of little interest. On the other hand, people that do scale their variables often state that all variables are of equal interest: a variable with small variance may even be more interesting - for exemple in sensometrics, a difficult item (umami for european people) to evaluate and thus be a key item to separate your products while other items (sweet taste) will have larger variance as it is easily recognized and people give notes on a much more individual level-
When you have variables on different scales, for exemple $m$ and $km$, the difference of scale often leads to difference in variance that may not be relevant (just an artificial product of scale) but scaling in a PCA is much more than just getting rid of that problem.
