Ap Statistics formulas

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Forumulas for stats

Sample mean

x = ( Σ xi ) / n

Sample standard deviation

s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ]

Pooled sample standard error

s pooled = sqrt [ (n1 - 1) s12 + (n2 - 1) s22 ] / (n1 + n2 - 2) ]

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

Sample correlation coefficient

r = [ 1 / (n - 1) ] Σ { [ (xi - x) / sx ] [ (yi - y) / sy ] }

Standard error of regression slope

sb1 = sqrt [ Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]

Rule of addition

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Rule of multiplication

P(A ∩ B) = P(A) P(B|A)

Expected value of X

E(X) = μx = Σ [ xi * P(xi) ]

Variance of X

σ2 = Σ [ xi - E(x) ]2 P(xi) = Σ [ xi - μx ]2 P(xi)

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