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Ladder

Concentration — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. -6-4-202460.000.100.200.300.400.50valueprobability1.5σ2σ3σthe meanmean 0.300, standard deviation 1.847; beyond 1.5 of them lies 0.2000 against a bound of 0.4444, beyond 2 ofthem lies 0.1000 against a bound of 0.2500, beyond 3 of them lies 0.0000 against a bound of 0.1111the bound knows only the variance — not the shape, not the number of values, not whether the distribution issymmetric — which is why it is so far from tight here and cannot be improved in general

    How far from the average a thing can be

    Knowing only an average and a spread — nothing about the shape, nothing about the number of outcomes, nothing about symmetry — the chance of landing three standard deviations out is at most one in nine. And there is a distribution that lands there exactly that often, so the bound cannot be improved.

    rung 1 · probability

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