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Sahithyan's S2
Sahithyan's S2 — Methods of Mathematics

Empirical Rule

Applies to normal distributions.

  • The probability of area between mean and +or – 1sd is 0.68.
  • The probability of area between mean and +or – 2sd is 0.95.
  • The probability of area between mean and +or – 3sd is 0.997.

Graphical illustration of the Empirical Rule

Image by Statistics By Jim

Chebyshev’s Theorem

For any k>1k\gt 1, at least 1−1k21-\frac{1}{k^2} of the values lie within kσk\sigma of the mean.

P(−kσ<X<kσ)≤1−1k2P(-k\sigma < X < k\sigma) \le 1-\frac{1}{k^2}