GRE-Style: Standard Deviation Comparison

GRE Quantitative · Axiom Academy

EXAMPLE Quantitative Comparison: Shift vs. Scale Comparing two standard deviations that hide unknowns inside an additive shift — by spotting structure, not by crunching decimals. Quantitative Comparison. Quantity A: the standard deviation of . Quantity B: the standard deviation of , where x and y are unspecified real numbers. Which quantity is greater? Nice work — you compared two standard deviations built entirely from unknowns, without ever needing a calculator. Shift-invariance: adding a constant c to every value in a set does not change its standard deviation: . Scale rule: multiplying every value by k scales the standard deviation by |k| : . Result: is exactly 2.5 times , so — Quantity B is greater, for every value of x and y . Anytime a GRE Quantitative Comparison hides unknowns inside an additive offset, kill the offset first — standard deviation only sees relative spacing, never absolute position.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.