A trimmed mean is the arithmetic mean computed after discarding specified proportions of the smallest and largest observations.
If 
are the order statistics, the 
-trimmed sample mean is
 |
for 
. Symmetric trimming uses
the same 
at both ends; asymmetric trimmed means are also possible.
Trimming reduces sensitivity to extreme observations at the cost of discarding data. The ordinary sample mean is obtained when 
, while increasingly heavy symmetric trimming moves the statistic
toward the sample statistical median.
