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

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You can't even correctly describe what is being measured and analyzed.

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Sure I can. We're measuring how many schools fall below average. Look at the OP. Its not that hard to grasp.

You're asserting that for large enough numbers of schools, half will fall below average. You are basing this on the central limit theorem which applies to random samples - however, the samples are not random, meaning you are wrong. (Not surprising from a guy who thinks ice has no mass.)



Clearly - if a state desired to - it could create a system whereby 90% of the schools performed below average - simply by putting 100% of the resources into 10% of the schools and putting 0% into the remaining 90%. It can do this regardless how many schools. You are asserting this isn't mathematically possible to do given a large enough number of schools. That's hilarious.