Central Limit Theorem: Summary of Formulas 1.5 2008/06/06 15:07:49 GMT-5 2008/07/18 16:06:25.021 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics Central Limit Theorem for Sample Means (Averages) X ~ N ( μ X , σ X n ) Mean for Averages ( X ) : μ X Central Limit Theorem for Sample Means (Averages) Z-Score and Standard Error of the Mean z = x - μ X ( σ X n ) Standard Error of the Mean (Standard Deviation for Averages ( X )): σ X n Central Limit Theorem for Sums ΣX ~ N [ ( n ) ⋅ μ X , n ⋅ σ X ] Mean for Sums ( ΣX ) : n ⋅ μ X Central Limit Theorem for Sums Z-Score and Standard Deviation for Sums z = Σx − n ⋅ μ X n ⋅ σ X Standard Deviation for Sums ( ΣX ) : n ⋅ σ X