Sigma 6

Rules for normally distributed data

File:Standard deviation diagram.svg

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27% of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45%; and three standard deviations (light, medium, and dark blue) account for 99.73%.

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.