Probable error

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, probable error defines the <a href="/facts/Half-range/B4XTaulj">half-range</a> of an interval about a <a href="/facts/Central_tendency/9yhcQ6me">central point</a> for the distribution, such that half of the values from the distribution will lie within the interval and half outside. 
Thus for a <a href="/facts/Symmetric_distribution/l70mWYEC">symmetric distribution</a> it is equivalent to half the <a href="/facts/Interquartile_range/tRk6u8w2">interquartile range</a>, or the <a href="/facts/Median_absolute_deviation/P6SSMLdt">median absolute deviation</a>. One such use of the term probable error in this sense is as the name for the <a href="/facts/Scale_parameter/6lxcyKUf">scale parameter</a> of the <a href="/facts/Cauchy_distribution/3HS6D3Xk">Cauchy distribution</a>, which does not have a standard deviation.
The probable error can also be expressed as a multiple of the standard deviation σ, which requires that at least the second <a href="/facts/Statistical_moment/GL7vJ1nb">statistical moment</a> of the distribution should exist, whereas the other definition does not. For a <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a> this is

γ
 =
 0.6745
 ×
 σ
 
 
 {\displaystyle \gamma =0.6745\times \sigma }
 
 (see <a href="/facts/Median_absolute_deviation/P6SSMLdt">details</a>)

Probable error open-in-new

Probable error