Generalized Statistical Means and New Price Index Formulas, Notes on some unexplored index formulas, their interpretations and generalizations

The theory of (increasingly more generalized types of) statistical means can be used to create a plethora of index formulas. Some of them are new and some were indeed discussed in the past but fallen into oblivion, because their rationale was not well understood. Surprisingly many possess interesting interpretations and attractive properties that deserve being unveiled. We begin with unweighted indices with implications to what now is called "low level aggregation" and proceed to weighted index formulas that lend themselves to productive generalizations and thereby to some new formulas. It turns out that contrary to popular belief the Laspeyres and Paasche formula are not equally well justified and that some indices from the more comprehensive system of statistical means are attractive regarding their economic interpretation and how they are related to indices of "quantity" and purchasing power of money.