What happens when a blonde walks from Austria to Germany?

In both countries the average IQ rises.

The reverse procedure cant’be done. So case 2 is not possible.

Case C, interestingly enough, can be done.

Let A={2,4} B={5,5,6,6,35} C={1}

Moving 2 from A to B, and the two 5’s from B to C all 3 averages increase.

REVERSE: Move 1 from set C to B, and the two sixes from B to A. ]]>

1st Case:I will use small sets and numbers, for clarity. A={2,3,4) av.=3 B={5,6,7} av.value=6

If we move 5 from setB to setA ,then we have: A={2,3,4,5) av.=3.5 and B={6,7} with av.=6.5

Both averages went up! The reason is quite obvious. We moved one (or some)members of a set that had av.value smaller than the av.value of the set but greater than the av.value of the new set (immigrating destination)

The reverse procedure (case 2) is also feasible.

Take 6 from set {6,7} and place it in set {2,3,4,5} .Both averages go up again.

Well, this is actually sometimes a sad story in real life. Meaning, the false interpretation of such statistics (surely no real “intelligence” got bigger ,but it would seem so, by someone who looks at “averages” and judges accordingly, without going deeper in the subject…) is common in real life situations (sometimes by sneaky persons (manipulation), or mostly just ignorants who dress up their pseudo-science with some “mathematical prestige”..)

Permit me and forgive me for posting a personal experience . My mother (in Greece) is a chronicle cancer patient, so I’ve been spotting and scrutinizing some relevant statistics for some years now. I was really surprised from the number of statistical “reports” that overlook the very same mathematical property, thus giving the wrong impression.

Let’s assume that set A is a set of “Healthy” people and set B is a set of people with Cancer.

A cancer patient at an early stage, leaves set A,thus increasing the life expectancy of set A , and enters set B (Cancer patients). But being of course (because of the early stage of her disease) “healthier” than the average of set B, her “migration” also increases the life expectancy of set B. That means, that someone who just got cancer-ill , being treated as a “statistical unit” this way, improves the “average health level” overall!!

Well, I don’t mean to say that medical or pharmaceutical statistics are mistrustful , but care and skepticism must always be there.