truncated mean

In this case, one can use a truncated mean.

The interquartile mean is a specific example of a truncated mean.

Thus a Winsorized mean is not the same as a truncated mean.

In some competitions subject to judges' scores, a truncated mean is used to remove extreme scores.

With more repetitions, he could use a truncated mean, discarding say the largest and smallest values and averaging the rest.

A 'truncated mean' or 'trimmed mean' is a statistical measure of central tendency, much like the mean and median.

Truncated mean - the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded.

The following table summarizes empirical data comparing three estimators of the mean for distributions of varied kurtosis; the modified mean is the truncated mean, where the maximum and minimum are eliminated.

The truncated mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models.

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 published rate is a rounded, truncated mean of the quoted rates: the highest and lowest 15% of quotes are eliminated, the remainder are averaged and the result is rounded to 3 decimal places.

One situation in which it can be advantageous to use a truncated mean is when estimating the location parameter of a Cauchy distribution, a bell shaped probability distribution with fatter tails than a normal distribution.

Other, more precise and robust methods have been developed For example, the truncated mean of the middle 24% of the sample order statistics produces an estimate for x that is more efficient than using either the sample median or the full sample mean.

The truncated mean uses more information from the distribution or sample than the median, but 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.

Note that for the Cauchy distribution, neither the truncated mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically efficient as the maximum likelihood estimator; however, the maximum likelihood estimate is difficult to compute, leaving the truncated mean as a useful alternative.