For example, if you take a number of random samples from a population and form a distribution of the means of the samples for some variable, you will often get something close to the normal distribution.

Typically,
something close to a normal distribution is produced
by adding the results of a number of independent events
over a large number or trials;
for example,
repeating `n` flips of a coin many times.

There are four ways a coin can land in 2 flips, and, if the flips are fair, each of these is equally likely:

# | Flips | Number of heads |
---|---|---|

1 | 0 | |

2 | 1 | |

3 | 1 | |

4 | 2 |

Because each way the coin can land is equally likely, we would expect on average to see the results appear as follows over a long series of trials:

Frequency | |

Number of heads |

As we increase the number of coin tosses per trial, the shape of the normal curve begins to emerge. For example, at four tosses, we have

Frequency | |

Number of heads |

Frequency | |

Number of heads |

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Last updated November 1, 2000.

This page maintained by Prof. Tim Craven

E-mail (text/plain only): t.craven@uwo.ca

Faculty of Information and Media Studies

University of Western Ontario,

London, Ontario

Canada, N6A 5B7