## Sampling Distribution (2)

{module [79]}

**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!**