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Encyclopedia > Truncated mean

A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves discarding given parts of a probability distribution or sample at the top or the bottom end, and typically involves discarding an equal amount at each end. For Wikipedia statistics, see m:Statistics Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. ... Central tendency is a term used in some fields of empirical research to refer to what statisticians sometimes call location. A measure of central tendency is either a location parameter or a statistic used to estimate a location parameter. ... In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ... In probability theory and statistics, the median is a number that separates the higher half of a sample, a population, or a probability distribution from the lower half. ... In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ... Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ...

The scoring method used in many sports 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. 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 truncated mean is less sensitive to outliers than the mean, but uses more information from the distribution or sample than the median. Unless the underlying distribution is symmetric, the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median. Symmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... In statistics, a biased estimator is one that for some reason on average over- or underestimates what is being estimated. ... Results from FactBites:

 Truncated mean - Wikipedia, the free encyclopedia (181 words) The scoring method used in many sports 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. Unless the underlying distribution is symmetric, the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.
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