# Sigma 6

From wikikotten

Revision as of 01:47, 2 April 2007 by 62.58.98.194 (Talk)

### Rules for normally distributed data

In practice, one often assumes that the data are from an approximately normally distributed population. If that assumption is justified, then about 68% of the values are within 1 standard deviation of the mean, about 95% of the values are within two standard deviations and about 99.7% lie within 3 standard deviations. This is known as the **"68-95-99.7 rule"**, or **"the empirical rule"**

The confidence intervals are as follows:

σ | 68.26894921371% |

2σ | 95.44997361036% |

3σ | 99.73002039367% |

4σ | 99.99366575163% |

5σ | 99.99994266969% |

6σ | 99.99999980268% |

7σ | 99.99999999974% |

For normal distributions, the two points of the curve which are one standard deviation from the mean are also the inflection points.