- Truncated mean
A

**truncated mean**or**trimmed mean**is astatistical measure of central tendency , much like themean andmedian . It involves the calculation of the mean after discarding given parts of aprobability distribution or sample at the high and low end, and typically discarding an equal amount of both.For most statistical applications, 5 to 25 percent of the ends are discarded.

In some regions of

Central Europe it is also known as a**Windsor mean**, but should not be confused with theWinsorized mean , which is similar but distinct.**Notation**The index of the mean is an indication of the percentage of the entries removed on both sides.

For example, if you were to truncate a sample with 8 entries by 12.5%, you would discard the first and the last entry in the sample when calculating the truncated mean.

**Interpolation**When a trimmed mean for a sample must be determined, but it cannot be accurately done, the best is to calculate the nearest two trimmed means, and interpolate (usually linearly).

For example, if you need to calculate the 15% trimmed mean of a sample containing 10 entries, you would calculate the 10% trimmed mean (removing 1 entry on either side of the sample), the 20% trimmed mean (removing 2 entries on either side), and interpolating to determine the 15% trimmed mean.

**Advantages**The trimmed mean is a useful estimator because it is less sensitive to

outlier s than the mean but will still give a reasonable estimate of central tendency or mean for almost all statistical models. In this regard it is referred to as arobust estimator .**Drawbacks**The truncated mean uses more information from the distribution or sample than the

median , so unless the underlying distribution issymmetric , the truncated mean of a sample is unlikely to produce anunbiased estimator for either the mean or the median.**Examples**The scoring method used in many

sport s that are evaluated by a panel of judges is a truncated mean: "discard the lowest and the highest scores; calculate the mean value of the remaining scores".The

interquartile mean is another example when the lowest 25% and the highest 25% are discarded, and the mean of the remaining scores are calculated.

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Mean**— This article is about the statistical concept. For other uses, see Mean (disambiguation). In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). the expected value of a… … Wikipedia**Truncated distribution**— A truncated distribution is a conditional distribution that is derived from some other probability distribution. Suppose we have a random variable, X that is distributed according to some probability density function, f(x) , with cumulative… … Wikipedia**Truncated icosahedron**— The truncated icosahedron is an Archimedean solid. It comprises 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. Construction This polyhedron can be constructed from an icosahedron with the 12 vertices truncated… … Wikipedia**Winsorized mean**— A Winsorized mean is a Winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after replacing given parts of a probability… … Wikipedia**Interquartile mean**— The interquartile mean (IQM) is a statistical measure of central tendency, much like the mean (in more popular terms called the average), the median, and the mode. The IQM is a truncated mean and so is very similar to the scoring method used in… … Wikipedia**List of statistics topics**— Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… … Wikipedia**Average**— In mathematics, an average, or central tendency[1] of a data set is a measure of the middle value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average. There are many… … Wikipedia**List of mathematics articles (T)**— NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie … Wikipedia**Cauchy distribution**— Not to be confused with Lorenz curve. Cauchy–Lorentz Probability density function The purple curve is the standard Cauchy distribution Cumulative distribution function … Wikipedia**Truncation (statistics)**— In statistics, truncation results in values that are limited above or below, similar to but distinct from the concept of statistical censoring.Usually the values that insurance adjusters receive are either left truncated, right censored or both.… … Wikipedia