If a sample of 100 is equally valid whether the population is 100,000 or 100 trillion, then why are so many studies conducted with thousands of samples? Even “random” political polls conducted with between 500-1,500 respondents were proved by this last election to have been so inept. Why? Because the sampling was too low.
I would offer a simple example. When the FDA finally releases a drug for public use, it is only after thousands of subjects have been tested. Yet, even after so large a sampling, they’ve been known to pull a drug off the market years later when, after hundreds of thousands of patients have used it, harmful side-effects begin to develop (even with new users). If your theory is inviolable (as pertaining to human physiology), then why weren’t these issues known after only 100 test subjects?
I’m afraid you’re confusing the discipline of statistics (as applied to mathematical probabilities, physics, etc.) with the more “unpredictable” field of human physiology.
Consider that the largest penis ever measured was 33.5 cm (about 13.2”). If you consider the low end to be “retractable penis,” you’d have to allow maybe a 0.5” EL (or less). That gives a range of 12.7 inches. If you chose to measure in even 1/8” increments, you’re still talking about a possible 100 different measurements (providing that no subject is found longer than 33.5 cm).
And that doesn’t even address the frequency of recurrence. If you wanted to assemble a thorough graph in which you charted at least 10 instances of each of those 100 measurements (with the exception, of course, of the “longest”), you’d have to allow that in order to get 10 for some sizes, you’d need 20, 30, 50, 100 or more measurements of more “common” sizes. Even a low estimate of such a compilation would involve thousands of subjects.
Furthermore, if you conducted such a survey in a quite homogenous society (like Israel, Japan, etc.) vs. a pluralistic society (like the U.S.), you’re furthering skewing the results due to ethnic/racial peculiarities.
It’s not my lack of understanding of the Central Limit Theory that’s at issue, but rather your overzealous application to it regarding this issue - a mistake, by the way, that the professionals researchers of the established institutions do not make.