Standard deviation of SAT?

This has ran through my mind if the average score for the sat is 1500 does that mean 68.2% of test takers score between 1400-1600? That means something like 16% test takers score over 1600 which seems pretty low. Obviously it doesn’t take into consideration super scoring. Can some mathematicians way in and tell me if this is correct or what i did wrong

Here are the percentiles for the composite score
https://secure-media.collegeboard.org/digitalServices/pdf/sat/sat-percentile-ranks-composite-crit-reading-math-writing-2014.pdf

The SD of each subject is around 100. The SD for the sum of the scores should be larger.

@MITer94 ah so the SD of scores is 1200-1800?

@FloridaBoy954 do you mean 300?

If so, I’m not actually sure, but it could be a good approximation. Note that if we treat CR, W, M as independent random variables with mean 500 and SD 100, then Var(CR+W+M) = 3*100^2, so SD would be about 170.

However there should be at least some correlation between CR, W, M, so the SD should be higher. I’m not sure what it actually is…

Edit: SD = 322, stated at bottom

@miter94 yea i mean 300 this SD is always something that i was interested in finding out thanks for providing some insight

From the info provided by milkweed (thank you) 37% sore over 1600. In discussing SD. IF S.D =322 & Mean =1497 (per milkweed chart), it means at a certain confidence level 70% of the population will score between 1175-1819. (mean of 1497 plus or minus one SD (322) . Which means likely . If you go out two SD’s or plus or minus 644, you can likely get a higher confidence level that 95% that test takers will score between 853 and 2141.

The SAT is a statistical measurement of intelligence within the population as a whole, which is why a test score within 100 points is virtually the same score, which is also why it cannot be relied on by itself.