Median: Difference between revisions

This set contains seven numbers. The median is the fourth of them, which is 6.

 

 

: 1, 2, 3, 4, 5, 6, 8, 9

Any [[Bias of an estimator|''mean''-unbiased estimator]] minimizes the [[risk]] ([[expected loss]]) with respect to the squared-error [[loss function]], as observed by [[Gauss]]. A [[Bias of an estimator#Median unbiased estimators.2C and bias with respect to other loss functions|''median''-unbiased estimator]] minimizes the risk with respect to the [[Absolute deviation|absolute-deviation]] loss function, as observed by [[Laplace]]. Other [[loss functions]] are used in [[statistical theory]], particularly in [[robust statistics]].

 

 

{{quote|An estimate of a one-dimensional parameter θ will be said to be median-unbiased if, for fixed θ, the median of the distribution of the estimate is at the value θ; i.e., the estimate underestimates just as often as it overestimates. This requirement seems for most purposes to accomplish as much as the mean-unbiased requirement and has the additional property that it is invariant under one-to-one transformation.|page 584}}