The mean valueμ of a population is a single fixed number. Explain why the mean ¯X of

a sample of a particular size n can vary, using a diagram to assist your explanation if you

wish.

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- Apr 23rd 2008, 08:32 PM #1

- Apr 23rd 2008, 09:14 PM #2

- Joined
- Feb 2008
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it seems that they would like you to explain randomness. This can be easily explained by any normal distribution. Though the mean is in the middle the variation shows that not all people lie on the mean. So taking a random sample may have you lie on either side of the mean. The easiest way to show this is from a sample size of n=1. In this case, unless the person is at the mean, the average of the sample will be on one side or the other. However, as n grows large the mean will begin to move to the middle, and its true value.

Hopefully this answers your question.

-Ryan