re: "Half the schools are below average" - not always true

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Tests are designed to have an underlying normal distribution. Furthermore, test scores are then converted from raw scores to another scale so that the scores are truly normal.

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That may or may not be true for a given exam, but it doesn't matter. School performance does necessarily follow a normal distribution - therefore neither will the average test scores that indicate that performance.

Just look our our own public education system. It is way skewed! There are a couple of exceptionally good public high schools - the Louisiana School for Math, Science, and the Arts comes to mind - a few places with decent high schools - and a lot of places with crap schools. The distribution is in no way normal!

Now - I agree - if you transform school performance measures themselves onto a normal scale - the distribution is normal.
That would be a statement like "half the schools are below the 50th percentile" - which is a tautology. That's not what I meant though.

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Then maybe the score that represents the average will be different but since these are norm-referenced tests, they usually adjust accordingly when converted (e.g., Flynn Effect for IQ stores). Although the distribution may be slightly impacted, it should still be relatively normal because there will be ceiling and floor effects (i.e., usually can't go lower than a 200 on SAT composite or higher than an 800. Not to mention, there are so many other variables at play in your hypothetical that aren't accounted for (e.g., demographics, developmental limitations, cognitive limitations).

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And its your idea that those unaccounted for variables will just happen to add up in exactly the right way to cancel out the skewed distribution of resource allocation in the 90/10 example? Come on man!