Statistics Formulas

Parameters

• Population mean = μ = ( Σ X_i ) / N
• Population standard deviation = σ = sqrt [ Σ ( X_i - μ )² / N ]
• Population variance = σ² = Σ ( X_i - μ )² / N
• Variance of population proportion = σ_P² = PQ / n
• Standardized score = Z = (X - μ) / σ
• Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (X_i - μ_X) / σ_x ] * [ (Y_i - μ_Y) / σ_y ] }

Statistics

Unless otherwise noted, these formulas assume simple random sampling.

• Sample mean = x = ( Σ x_i ) / n
• Sample standard deviation = s = sqrt [ Σ ( x_i - x )² / ( n - 1 ) ]
• Sample variance = s² = Σ ( x_i - x )² / ( n - 1 )
• Variance of sample proportion = s_p² = pq / (n - 1)
• Pooled sample proportion = p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)
• Pooled sample standard deviation = s_p = sqrt [ (n₁ - 1) * s₁² + (n₂ - 1) * s₂² ] / (n₁ + n₂ - 2) ]
• Sample correlation coefficient = r = [ 1 / (n - 1) ] * Σ { [ (x_i - x) / s_x ] * [ (y_i - y) / s_y ] }

Correlation

• Pearson product-moment correlation = r = Σ (xy) / sqrt [ ( Σ x² ) * ( Σ y² ) ]
• Linear correlation (sample data) = r = [ 1 / (n - 1) ] * Σ { [ (x_i - x) / s_x ] * [ (y_i - y) / s_y ] }
• Linear correlation (population data) = ρ = [ 1 / N ] * Σ { [ (X_i - μ_X) / σ_x ] * [ (Y_i - μ_Y) / σ_y ] }

 

Reference: http://stattrek.com/Lesson1/Formulas.aspx?Tutorial=Stat