For a normal distribution (the theoretical distribution which closely matches experimental measurement of human intelligence) mean and median are the same. For others such as the distribution in personal income (Almost a reverse Laplace distribution) the mean (the sum of measured property divided by the population measured) and median (the point in the measured value distribution that 50 % of the population falls below or above) are very different because a small portion at one end contains most of the measured value.

A general form of my question would more accurately be phrased in terms of median than mean.

Regards,
Mark