STATISTICS

      EQUATIONS

      Some Statistics Equations

      Parameters

      Population mean

      Population standard deviation

      Population variance

      Variance of population proportion

      Standardized score

      Population correlation coefficient

      Statistics

      Sample mean

      Sample standard deviation

      Sample variance

      Variance of sample proportion

      Pooled sample proportion

      Pooled sample standard deviation

      Sample correlation coefficient

      Correlation

      Pearson product-moment correlation

      Linear correlation (sample data)

      Linear correlation (population data)

      Simple Linear Regression

      Simple linear regression line

      Regression coefficient

      Regression slope intercept

      Regression coefficient

      Standard error of regression slope =

      Counting

      n factorial

      Permutations of n things, taken r at a time

      Combinations of n things, taken r at a time

      Probability

      Rule of addition

      Rule of multiplicatio

      Rule of subtraction

      Rule of multiplication

      Rule of subtraction

      Formula

      μ = (Σ Xi ) / N

      σ = sqrt [ Σ ( Xi - μ )2 / N]

      σ2 = Σ ( Xi - μ )2 / N

      σP2 = PQ / n

      Z = (X - μ) / σ

      ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }

      Formula

      x = ( Σ xi ) / n

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

      s2 = Σ( xi - x )2 /( n - 1 )

      sp2 = pq / (n - 1)

      p = (pl * nl + p2 * n2) / (nl + n2)

      sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (nl + n2 - 2) ]

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

      r = Σ (xy) / sqrt [ (Σ x2 ) * (Σ y2 ) ]

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

      ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) σy ] }

      ŷ = b0 + b1x

      b1 = Σ [ (xi - x) (yi - y)] / Σ [ (xi - x)2]

      b0 = y - b1 * x

      b1 = r * (sy / sx)

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

      n! = n * (n-1) * (n – 2) * … * 3 * 2 * 1. By convention, 0! = 1.

      nPr = n! / (n - r)!

      nCr = n! / r!(n - r)! = nPr / r!

      Formula

      P(A U B) = P(A) + P(B) - P(A n B)

      P(A n B) = P(A) P(B|A)

      P(A’) = 1 - P(A)

      P(A n B) = P(A) P(B|A)

      P(A’) = 1 - P(A)