trimmean

Last update : 20/12/2004

trimmean - trimmed mean of a vector or a matrix

### Calling Sequence

  `m=trimmean(x)`
  `m=trimmean(x,discard,'r') or m=trimmean(x,discard,1)`
  `m=trimmean(x,discard,'c') or m=trimmean(x,discard,2)`

### Parameters

- `x`real or complex vector or matrix
- `discard`number: The discarding percentage

### Description

A trimmed mean is calculated by discarding a certain percentage of the lowest and the highest scores and then computing the mean of the remaining scores. For example, a mean trimmed 50% is computed by discarding the lower and higher 25% of the scores and taking the mean of the remaining scores.

The median is the mean trimmed 100% and the arithmetic mean is the mean trimmed 0%.

A trimmed mean is obviously less susceptible to the effects of extreme scores than is the arithmetic mean. It is therefore less susceptible to sampling fluctuation than the mean for extremely skewed distributions. It is less efficient (The efficiency of a statistic is the degree to which the statistic is stable from sample to sample. That is, the less subject to sampling fluctuation a statistic is, the more efficient it is. The efficiency of statistics is measured relative to the efficiency of other statistics and is therefore often called the relative efficiency. If statistic A has a smaller standard error than statistic B, then statistic A is more efficient than statistic B. The relative efficiency of two statistics may depend on the distribution involved. For instance, the mean is more efficient than the median for normal distributions but not for some extremely skewed distributions. The efficiency of a statistic can also be thought of as the precision of the estimate: The more efficient the statistic, the more precise the statistic is as an estimator of the parameter.[from http://davidmlane.com/hyperstat/A12977.html]) than the mean for normal distributions.

Trimmed means are often used in Olympic scoring to minimize the effects of extreme ratings possibly caused by biased judges. [from http://davidmlane.com/hyperstat/A11971.html]

For a vector or matrix `x`, `t=trimmean(x,discard)` returns in scalar `t` the mean of all the entries of `x`, after discarding `discard/2` highest values and `discard/2` lowest values.

`t=trimmean(x,discard,'r')` (or, equivalently, `t=trimmean(x,discard,1)`) returns in each entry of the row vector `t` the trimmed mean of each column of `x`.

`t=trimmean(x,discard,'c')` (or, equivalently, `t=trimmean(x,discard,2)`) returns in each entry of the column vector `t` the trimmed mean of each row of `x`.

This function computes the trimmed mean of a vector or matrix `x`.

For a vector or matrix `x`, `m=trimmean(x)` returns in scalar `m` the trimmedmean of all the entries of `x`.

`m=trimmean(x,'r')` (or, equivalently, `m=trimmean(x,1)` ) returns in each entry of the row vector `m` the trimmed mean of each column of `x`.

q`m=trimmean(x,'c')` (or, equivalently, `m=trimmean(x,2)` ) returns in each entry of the column vector `m` the trimmed mean of each row of `x`.

### References

Luis Angel Garcia-Escudero and Alfonso Gordaliza, Robustness Properties of Means and Trimmed Means, JASA, Volume 94, Number 447, Sept 1999, pp956-969

### Author

Carlos Klimann