This is partly related to the question at Visualising the variance which I haven't accepted an answer yet, partly because I have become unsure if I'm asking the correct question.
The case is this, we have a population P that consists of 50 people. These have answered questions on a scale of 1-5, which our software normalizes to a 0-100 scale. We also have a reference population R which consists of several hundred, if not thousands of people. The reference data is "pre-rendered" to have an average score, a standard deviation, and an average standard deviation (ASD). The last value is found by doing the standard deviation per survey, then the average of those standard deviations. (The reference population contains a representative collection of previous surveys)
We then generate a value for what we directly translated call "variation", but I have started to believe is more a comparison of spread... This is where my issues lie. The formula related to this is
(((((stdev(P) - ASD) / ASD) * 100) + 100) / 2)
(The last part is to adapt to a 0-100 scale, where 50 means that the spread in your result is the same as the spread in the reference population)
What are we really calculating with this formula?
(I have taken over this system as a developer, and statistics are not my strong side)