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<p>Not always true. You seem to be describing the range (difference between highest and lowest). </p>
<p>Consider the following sets: </p>
<p>S1 = {1, 5, 5, 5, 5, 5, 5, 9}
S2 = {1, 2, 3, 4, 5, 6, 7, 8} </p>
<p>According to your argument, S1 would have a higher standard deviation because the biggest number is bigger than the smallest number by a larger margin. </p>
<p>Standard deviation is a measure of variability, i.e. how “clustered” the data are around the mean (low SD) vs. how “spread out” the data are (high SD). </p>
<p>Computing the standard deviations (by hand or by calculator) will tell you that S2 has a larger standard deviation than S1. </p>
<p>@OP: I have never seen a SD question on the SATII (although it doesn’t hurt to know it!). IMO it is much likelier that you will see a question on (linear) regression than a question on standard deviation, although both are pretty unlikely. Never seen histograms or boxplots either, but those are really easy topics. Why not just learn them anyway?</p>