MandysNotes

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!

Read 2105 times Last modified on Friday, 14 February 2014 03:07
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