Truncated mean

From Academic Kids

A truncated 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.

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 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.

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