Difference between revisions of "Sigma 6"

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===Rules for normally distributed data===
 
===Rules for normally distributed data===
  
[[Image:standard_deviation_diagram.svg|thumb|350px|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%.]]
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[[Image:standard_deviation_diagram.png|thumb|350px|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 [[normal distribution|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"'''
 
In practice, one often assumes that the data are from an approximately [[normal distribution|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"'''

Revision as of 02:50, 2 April 2007

Rules for normally distributed data

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%
95.44997361036%
99.73002039367%
99.99366575163%
99.99994266969%
99.99999980268%
99.99999999974%

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