Probable error

In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside.[1] Thus it is equivalent to half the interquartile range, or the median absolute deviation. The probable error can also be expressed as a multiple of the standard deviation σ,[1][2] ${\displaystyle \gamma =0.6745\times \sigma }$ (where the multiplying factor 0.6745 derives from the normal distribution, see details), which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. One use of the term probable error in statistics is as the name for the scale parameter of the Cauchy distribution.