The whole argument about "the bell curve" to measure intelligence by IQ tests is based upon nonsense and misuse of measurement scales (described at this Website)!

You see, the "bell curve", or Gaussian probability function requires calculating the arithmetic mean of the given data, to be used as the "center" of the curve, whose "range" or standard deviation is then derived from the arithmetic mean.

But I. Q. Scores belong only to the ordinal measurement scale, which puts items in ordering but DOES NOT SAY HOW MUCH AN ITEM IS GREATER IN THE ORDER THAN THE ITEM IT DOMINATES!

For example, I could list the numerals on the uniforms of all the baseball players of the National and American Major Leagues. We could arbitrarily add these numerals-as-numbers and calculate their arithmetic mean; then use this mean to find the standard deviation; and plot the results. It might possibly fit a "bell-curve". BUT WOULD THIS MEAN ANYTHING?

If Popup's uniform has numeral 12 and Dropsy's uniform has numeral 15, does this mean that Dropsy is a better player than Popup (or worse)? If Stiffneck on another team has numeral 27 on his uniform, would you (as owner) treat Popoff and Dropsy as an equal trade for Stiffneck?

The most familiar example of the purely ORDINAL SCALE is HARDNESS OF A MINERAL. CHALK is at the BOTTOM OF THIS SCALE, and DIAMOND at its PEAK. Now, diamond is one of three forms of NATURAL CARBON, along with graphite (pencil lead) and "buckballs" (recently discovered). If we could ADD ON THE HARDNESS SCALE, THEN ENOUGH PENCIL LEAD WOULD EQUAL A DIAMOND! Try it!

Equivalent to adding "hardness" is the fallacy of calculating the arithmetic mean of IQ scores! This assumes combining two persons (allegedly) with IQ 50 to execute the performance of a person of IQ 100 (for an extensive measure), or at least better than IQ 50 (for an intensive measure)! But the IQ measure -- if it has any meaning! -- is solely an ordinal measure -- to ORDER ELEMENTS, but NOT TO ADD THEIR MEASURES -- and its only permissible average statistic is the median.

So CALCULATING A BELL CURVE FROM IQ SCORES MAKES AS MUCH SENSE AS CALCULATING A BELL CURVE FROM NUMERALS ON UNIFORMS OF ATHLETES OR COMPOUNDING HARD MINERALS!

If you can ADD I.Q. SCORES to construct a "Bell Curve", then you can compound enough pencil lead to make a diamond!

ELEMENTARY AND SECONDARY SCHOOL STUDENTS ARE PUNISHED FOR THE FUDGING OF PSYCHOMETRICIANS! IS THIS FAIR???

All of this would be EXPOSED if we implemented my concept of NO MEASURE WITHOUT A PREDICTION! Any one claiming to add I.Q. Scores (to build a "Bell Curve") would have to predict that he could find two "low" I. Q. scorers who, combined, would best a "high" scorer!