Part of ALG-08 — Statistics: Mean, Variance & Standard Deviation

Shortcut for Symmetric Data

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For symmetric data (e.g., a-2d, a-d, a, a+d, a+2d), the mean is the middle value (a), and variance simplifies because sum of deviations from mean has a pattern. For equally spaced data centered at a with spacing d and n terms: Var = d2d^2n2112\frac{n^2-1}{12}. This is extremely useful for MCQ speed. Example: {3,5,7,9,11} → a=7, d=2, n=5, Var = 425112\frac{25-1}{12} = 4*24/12 = 8.

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