ODF 1.2 Part 2 CD01 5.18.72-5.18.75 STDEV* DANGEROUS EXTRA FORMULAS

For each of the STDEV, STDEVA, STDEVP, and STDEVPA, there is an extra formula in the definitiions.

The first formula is a definition for s^2 or sigma^2 depending on whether we are talking about a sample or a set of equiprobable values. The second formula is mathematically equivalent but it is computationally worse. (It has the advantage that the mean does not have to be computed in advance. However, it is even worse as a computational method than the so-called "naive" mathematical definition. The second formula is equivalent to the formula 4.2.2(14) that Donald Knuth gives as an approach to be avoided because of its computational instability.)

I recommend that the second form of the formula, the one that subtracts n X xbar^2, be stricken, because it raises more questions than it answer and we have no business even suggesting it.

Furthermore, I would use the formulas to explain how the mathematical standard-deviation (or variance in the STDEVP and STDEVPA cases) is mathematically defined. I would say that the result is a computational approximation to the mathematical value, not that it returns the mathematical result.

I would then add, perhaps,

Note: Special computational methods are generally used to produce more-reliable results than achievable by direct implementation of the formula as a computational method.

A non-normative reference to the treatment in the Art of Computer Programming might be useful here (and perhaps many other places).

PS: These are also nice codefest challenges for assessing the ways that OpenFormula functions can be implemented reliably as computations from the specification and available expert materials.