So what you say with your example is that in a layered sample (say separate the population by heigh or muscle mass), the weighted mean is a better estimator tha

So what you say with your example is that in a layered sample (say separate the population by heigh or muscle mass), the weighted mean is a better estimator than the arithmetic mean of a sample ? It is not ignored by statistics. http://en.wikipedia.org/wiki/Weighted_mean http://en.wikipedia.org/wiki/Weighted_mean