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Let's explore sampling distributions of the means
further by looking at the means from a much larger sample. The graph
on the left below is for a sample size of 2 (the same graph we saw earlier)
and the one on the right is for a sample size of 12.
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Click on the "Roll One Set" button in each graph to see what is
happening. Then click on "Roll 10 Sets" a number of times to see
what the sampling distribution will look like for each sample size.
Sample Size = 2
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Sample Size = 12
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There are several important things to notice in the graphs above after
you've generated a large number of samples for each graph:
- The distribution of "means" with sample size = 2 is peaked, but it
doesn't quite have the shape of a normal distribution.
- When the sample size = 12, the distribution of the means looks
much like a normal distribution. It is peaked in the center and values
of the mean far from the center are decreasingly likely.
- As the sample size increases from 2 to 12, it is more
difficult for the
mean to be far away from 3.5 (which is the average of the six face values:
1, 2, 3, 4, 5, 6).
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File:
© 1999, Duxbury Press.
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