For practical purposes, if the distribution is according to the standard "bell curve," the average, mean, and median coincide.

If ONE "genius" appears to distort the curve, then the "average" is moved up, while the median remains unchanged, leaving 50% of the total population "below average."

Similarly, a small group of "total duds" could pull the average down, leaving the appearance that a larger percentage of those in the sample are "above average." Failures can make the statistics look better (if one tells the right lies) as long as the failures can be confined to a small group that fails in grand style.

Of course, one would never accuse schools, administrators, and politicians of studying how to "look better without doing anything."

???

John