Good question. I don't really know, although based on most schools' middle-80% ranges (which are readily available for most schools), you're probably not too far off. It may be a bit larger than 20, but not too much larger.
If the std dev for a given school is 20 and its average score is 690, then 68% of scores will fall between 670 and 710, and 95% of scores will fall between 650 and 730. These bands are fairly consistent with school's published ranges. They're maybe a tad narrow (leading me to think that the actual std dev is more than 20), but not by too much.
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