Given an estimator

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....

, a trimmed estimator is obtained by excluding some of the extreme values. This is generally done to obtain a more robust statistic: the extreme values are considered outlier

Outlier

In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....

s.

Given an estimator, the n% trimmed version is obtained by discarding the n% lowest and highest observations: it is a statistic on the middle of the data. For instance, the 5% trimmed mean is obtained by taking the mean of the 2.5% to 97.5% range.

The median

Median

In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...

 equals the fully (nominally 50%) trimmed mean. Likewise, no degree of trimming has any effect on the median, because trimming always excludes an equal number of the lowest and highest values.

Quantiles can be thought of as trimmed maximums or minimums: for instance, the 5th percentile

Percentile

In statistics, a percentile is the value of a variable below which a certain percent of observations fall. For example, the 20th percentile is the value below which 20 percent of the observations may be found...

 is the 5% trimmed minimum.

Examples

• Trimmed mean
• Interquartile mean
  Interquartile mean
  The interquartile mean is a statistical measure of central tendency, much like the mean , the median, and the mode....
  
  , the 25% trimmed mean
• Interquartile range
  Interquartile range
  In descriptive statistics, the interquartile range , also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles...
  
  , the 25% trimmed range
  Range (statistics)
  In the descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion.It is measured in the same units as the data...
  
  
• Midhinge
  Midhinge
  In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.Equivalently, it is the 25% trimmed mid-range; it is an L-estimator....
  
  , the 25% trimmed mid-range

See also

• Winsorising
  Winsorising
  Winsorising or Winsorization is the transformation of statistics by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor...
  
  , a related technique
• Core inflation
  Core inflation
  Core inflation is a measure of inflation which excludes certain items that face volatile price movements, notably food and energy.The preferred measure by the Federal Reserve of core inflation in the United States is the core Personal consumption expenditures price index...
  
  , an economic statistic that omits volatile components