Introductory Statistics

# Formula Review

### 7.1The Central Limit Theorem for Sample Means (Averages)

The Central Limit Theorem for Sample Means: $X ¯ X ¯$ ~ N

The Mean $X ¯ X ¯$: μx

Central Limit Theorem for Sample Means z-score and 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 ($X ¯ X ¯$)): $σ x n σ x n$

### 7.2The Central Limit Theorem for Sums

The Central Limit Theorem for Sums: ∑X ~ N[(n)(μx),($n n$)(σx)]

Mean for Sums (∑X): (n)(μx)

The Central Limit Theorem for Sums z-score and standard deviation for sums:

Standard deviation for Sums (∑X): $( n ) ( n )$(σx)