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Distribution of Sample Means

Author: Ryan Backman
Video Transcript
Terms to Know
Central Limit Theorem

A theorem that explains the shape of a sampling distribution of sample means. It states that if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal.

Distribution of Sample Means

A distribution where each data point consists of a mean of a collected sample. For a given sample size, every possible sample mean will be plotted in the distribution.

Standard Deviation of a Distribution of Sample Means

The standard deviation of the population, divided by the square root of sample size.

Standard Error

The standard deviation of the sampling distribution of sample means distribution.

Formulas to Know
Mean of a Sampling Distribution of Sample Means

mu subscript x with bar on top end subscript space equals space mu subscript p o p u l a t i o n end subscript

Standard Deviation of a Sampling Distribution of Sample Means

sigma subscript x with bar on top end subscript space equals space fraction numerator sigma subscript p o p u l a t i o n end subscript over denominator square root of n end fraction