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Statistics Tutorial

# Statistics Tutorial - Statistics Tutorial Important...

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Statistics Tutorial: Important Statistics Formulas This web page presents statistics formulas described in the Stat Trek tutorials. Each formula links to a web page that explains how to use the formula. Parameters Population mean = μ = ( Σ X i ) / N Population standard deviation = σ = sqrt [ Σ ( X i - μ ) 2 / N ] Population variance = σ 2 = Σ ( X i - μ ) 2 / N Variance of population proportion = σ P 2 = 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 = s 2 = Σ ( x i - x ) 2 / ( n - 1 ) Variance of sample proportion = s p 2 = pq / (n - 1) Pooled sample proportion = p = (p 1 * n 1 + p 2 * n 2 ) / (n 1 + n 2 )

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Pooled sample standard deviation = s p = sqrt [ (n 1 - 1) * s 1 2 + (n 2 - 1) * s 2 2 ] / (n 1 + n 2 - 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 x 2 ) * ( Σ y 2 ) ] 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 ] } Simple Linear Regression Simple linear regression line: ŷ = b 0 + b 1 x Regression coefficient = b 1 = Σ [ (x i - x) (y i - y) ] / Σ [ (x i - x) 2 ] Regression slope intercept = b 0 = y - b 1 * x Regression coefficient = b 1 = r * (s y / s x ) Standard error of regression slope = s b1 = sqrt [ Σ(y i - ŷ i ) 2 / (n - 2) ] / sqrt [ Σ(x i - x) 2 ] Counting n factorial: n! = n * (n-1) * (n - 2) * . . . * 3 * 2 * 1. By convention, 0! = 1. Permutations of
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Statistics Tutorial - Statistics Tutorial Important...

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