# MandysNotes

## Sampling Distribution (2)

Saturday, 23 January 2010 22:09

### Population Distribution vs. Sample Distribution

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{module [79]}

Saturday, 23 January 2010 03:01

### Sampling Distribution of the Sample Mean

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I admit: "sampling distribution of the sample mean" sounds a little creepy, not only because the term is too long-winded for its own good, but also because it feels like you're running in an endless loop.

The best way to explain this one is to give an example:

Suppose you have a population of 5 basketball players:

A, B, C, D and E.

Let us suppose that their respective heights are:

76, 78, 79, 81 and 86

If we had a sample size of 2, then we would be able to derive the following combinations of these players and their heights:

 SAMPLE (size 2) HEIGHTS X - Bar Values A, B 76, 78 77.0 A, C 76, 79 77.5 A, D 76, 81 78.5 A, E 76, 86 81.0 B, C 78, 79 78.5 B, D 78, 81 79.5 B, E 78, 86 82.0 C, D 79, 81 80.0 C, E 79, 86 82.5 D, E 81, 86 83.5

The X-bar column values represent the Sampling Distribution of the Sample Mean, because they are the MEAN of the values for each SAMPLE.

Now let's try a different sample size.  Let's try a sample size of 4.

 SAMPLE (size 4) HEIGHTS X - Bar Values A, B, C, D 76, 78, 79, 81 78.50 A, B, C, E 76, 78, 79, 86 79.75 A, B, D, E 76, 78, 81, 86 80.25 A, C, D, E 76, 79, 81, 86 80.50 B, C, D, E 78, 79, 81, 86 81.00

The X-bar column values represent the Sampling Distribution of the Sample Mean, because they are the MEAN of the values for each SAMPLE.

And that's all it is!