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# Central Limit Theorem: Summary of Formulas

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

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## Formula 1: Mean for Averages

X¯ ~ N ( μ X , σ X n ) X ~N( μ X , σ X n ) Mean for Averages ( X¯ ) : μ X ( X ): μ X

## Formula 2: Standard Error of the Mean

z = x¯ - μ X ( σ X n ) z= x - μ X ( σ X n ) Standard Error of the Mean (Standard Deviation for Averages (X¯)( X )): σ X n σ X n

## Formula 3: Mean for Sums

ΣX ~ N [ ( n ) μ X , n σ X ] ΣX~N[(n) μ X , n σ X ] Mean for Sums ( ΣX ) : n μ x (ΣX):n μ x

## Formula 4: Standard Deviation for Sums

z = Σx n μ X n σ X z= Σx n μ X n σ X Standard Deviation for Sums ( ΣX ) : n σ X (ΣX): n σ X

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