Editing Truncated mean (section)

{{short description|Statistical measure of central tendency}}
{{More citations needed|date=July 2010}}
A '''truncated mean''' or '''trimmed mean''' is a [[Statistics|statistical]] [[Average|measure of central tendency]], much like the [[mean]] and [[median]]. It involves the calculation of the mean after discarding given parts of a [[probability distribution]] or [[Sampling (statistics)|sample]] at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually given as a percentage of the total number of points, but may also be given as a fixed number of points.

For most statistical applications, 5 to 25 percent of the ends are discarded. For example, given a set of 8 points, trimming by 12.5% would discard the minimum and maximum value in the sample: the smallest and largest values, and would compute the mean of the remaining 6 points. The 25% trimmed mean (when the lowest 25% and the highest 25% are discarded) is known as the [[interquartile mean]].

The median can be regarded as a fully truncated mean and is most robust.  As with other [[trimmed estimator]]s, the main advantage of the trimmed mean is robustness and higher [[Efficiency (statistics)|efficiency]] for mixed distributions and heavy-tailed distribution (like the [[Cauchy distribution]]), at the cost of lower efficiency for some other less heavily tailed distributions (such as the normal distribution). For intermediate distributions the differences between the efficiency of the mean and the median are not very big, e.g. for the student-t distribution with 2 degrees of freedom the variances for mean and median are nearly equal.