# 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 for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation. One such use of the term *probable error* in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation.

The probable error can also be expressed as a multiple of the standard deviation σ,[1][2], which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. For a normal distribution this is (see details)