Distribution of Sample Means, the Central Limit Theorem

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Distribution of Sample Means, the Central Limit Theorem • If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called the sampling distribution. • Central Limit Theorem says that as sample size, n, gets larger, the distribution of sample means is approximately – Normal, and has – Same mean as original distribution; that is, Mean = – Standard deviation = original standard deviation over square root sample size; that is, Standard Deviation =

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Distribution of Sample Means, the Central Limit Theorem. If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called the sampling distribution . - PowerPoint PPT Presentation

Transcript of Distribution of Sample Means, the Central Limit Theorem

Page 1: Distribution of Sample Means, the Central Limit Theorem

Distribution of Sample Means, the Central Limit Theorem

• If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called the sampling distribution.

• Central Limit Theorem says that as sample size, n, gets larger, the distribution of sample means is approximately– Normal, and has– Same mean as original distribution; that is, Mean = – Standard deviation = original standard deviation over square root

sample size; that is, Standard Deviation =

Page 2: Distribution of Sample Means, the Central Limit Theorem

Normal with varied µ and σ = 1

Page 3: Distribution of Sample Means, the Central Limit Theorem

Normal with varied σ and µ = 0

Page 4: Distribution of Sample Means, the Central Limit Theorem

Standard Normal with µ = 0 and σ = 1

Symmetric: Mean = 0

Stretches from about -3 to 3


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