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

quote:

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Go reread what I said, clown.

When we are getting testing values for schools, we are averaging the testing of the students in that school.

Then by computing the mean value to determine central tendency, we are also computing a mean.

By computing the mean of the means for a large number of students nested within schools and then calculating the central tendency of that higher population we are doing exactly what you suggest by

taking the average of a population of polls. Each school is a population.

good god man.

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Again, you misunderstand statistics.

The central limit theorem only applies to randomly selected samples. Selecting your samples by school isn't random. Seriously dude, that's kinda obvious.