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.
