A robust estimate of the population mean. For a sample of size n, with data ordered so that x(1)≤x(2)≤⋯≤x(n), the trimmed mean, x¯k, is the mean of the data if the k smallest values and the k largest values are discarded (with 1≤k < ½n). SoThe idea is to avoid the influence of extreme observations. The method was proposed by Tukey in 1962.
Tukey also proposed the Winsorized mean, named after his former colleague Charles P. Winsor, who had died in 1951. In this case the k smallest values are replaced by x(k) and the k largest are replaced by x(n−k+1) to give the estimate wk: