## Distribution of Sample Means

Move the slider to change the sample size, n .
Notice how the normal distribution with standard
deviation 1 divided by the square root of n
changes as the sample size changes.

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The Central Limit Theorem says that, for
samples of a given size n taken from a
distribution with mean μ and standard
deviation σ , the mean of the sample
means is also μ , but the standard deviation
of the sample means is σ divided by the
square root of n.

The Central Limit Theorem also says that if
the samples came from a normal distribution
then the distribution of the sample means will
also be normal.

Consequently, as the sample size increases,
the standard deviation of the sample means
decreases and the resulting normal
distribution curve becomes taller and
narrower as most of the area of the curve
is forced toward the center of the distribution.

David Gurney, Created with GeoGebra