Important Statistics Formulas

Parameters * Population mean = μ = ( Σ Xi ) / N * Population standard deviation = σ = sqrt [ Σ ( Xi - μ )2 / N ] * Population variance = σ2 = Σ ( Xi - μ )2 / N * Variance of population proportion = σP2 = PQ / n * Standardized score = Z = (X - μ) / σ * Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }
Statistics
Unless otherwise noted, these formulas assume simple random sampling. * Sample mean = x = ( Σ xi ) / n * Sample standard deviation = s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ] * Sample variance = s2 = Σ ( xi - x )2 / ( n - 1 ) * Variance of sample proportion = sp2 = pq / (n - 1) * Pooled sample proportion = p = (p1 * n1 + p2 * n2) / (n1 + n2) * Pooled sample standard deviation = sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (n1 + n2 - 2) ] * Sample correlation coefficient = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] }
Correlation
* Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x2 ) * ( Σ y2 ) ] * Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (xi - x) / sx ] * [ (yi - y) / sy ] } * Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }
Simple Linear Regression * Simple linear regression line: ŷ = b0 + b1x * Regression coefficient = b1 = Σ [ (xi - x) (yi - y) ] / Σ [ (xi - x)2] * Regression slope intercept = b0 = y - b1 * x * Regression coefficient = b1 = r * (sy / sx) * Standard error of regression slope = sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]
Counting
* n factorial: n! = n * (n-1) * (n - 2) * . . . * 3 * 2 * 1. By convention, 0! = 1. * Permutations of n things, taken r at a time: nPr = n! / (n - r)! * Combinations of n things, taken r at a time: nCr = n! / r!(n - r)! = nPr / r!
Probability
* Rule of addition: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) * Rule of multiplication: P(A ∩ B) = P(A)