3.98 FAQ-501 What are the confidence intervals associated with 1σ, 2σ, 3σ, and etc. for Gaussian distribution?

Last Update: 2/4/2015

A frequently used parameter when making measurements is the Confidence Interval (CI). This is the probability that a measurement will fall within a closed interval [a,b]. For the symmetric Gaussian distribution the important interval is the standard deviation or σ. The probabilities associated with intervals 1σ, 2σ, 3σ or nσ are simply calculated in Origin using the Error Function erf. Thus,

CI\left ( n\sigma \right ) = erf\left ( \frac{n}{\sqrt{2}} \right )

Repeated evaluation of the erf function produces the following helpful values and table.

1 0.6826894850
2 0.9544997241
3 0.9973002038
4 0.9999366575
5 0.9999994267
6 0.9999999980

Keywords:Gaussian, Confidence Band